Previous Year Paper

DSSSB TGT Maths (Male) 2 Sep 2021 Shift 3 (Previous Year Paper)

Held in 2021

200 questions120 minutes
With answers
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General Ability (20 questions)

Question 1

If a mirror is placed on the line AB, then which of the answer figures is the correct mirror image of the given figure?

  1. AOption (a)

  2. BOption (b)

  3. COption (c)

  4. DOption (d)

View answer & explanation

Correct answer

Answer: (b)B.

Question 2

In the following Venn diagram, the triangle represents 'females', the circle represents 'mammals', the square represents 'males' and the rectangle represents 'humans'. Which set of letters represents mammals that are human or female but not male?

  1. AOption (a)

    C and G

  2. BOption (b)

    G and I

  3. COption (c)

    I, D, C and B

  4. DOption (d)

    C and D

View answer & explanation

Correct answer

Answer: (a)A.

C and G

Why this answer is correct

As per the given information,

The shaded part i.e. 'C and G' represents →mammals that are human or female but not male

Hence, the correct answer is "C and G".

Question 3

Find the wrong term in the given series.

111, 100, 87, 71, 55, 36

  1. AOption (a)

    71

  2. BOption (b)

    36

  3. COption (c)

    87

  4. DOption (d)

    55

View answer & explanation

Correct answer

Answer: (a)A.

71

Why this answer is correct

Given: 111, 100, 87, 71, 55, 36

The logic follows here is:

The next term in the series is obtained by subtracting consecutive odd numbers starting from 11.

Thus, the wrong term in the series is '71'. 

Hence, the correct answer is "71".

Question 4

The following are the criteria for the selection of a management trainee.

to candidate -

a - Graduation in any subject with a minimum of 72% marks.

b - Age should not be less than 21 years and not more than 25 years.

c - Must have passed written examination and interview with minimum 70% marks.

d - Be prepared to pay a deposit of Rs 50,000 which is to be refunded on completion of the training.

However, if all the above criteria are satisfied, except –

I- As in (a) above, but have completed post-graduation with a minimum of 65% marks, the case will be referred to the Director.

 

II -In (d) above, but has experience of working in this area for more than one year, may be referred to Case Manager.

Sumit has done BBA from a government college with 74% marks and his marks in written tests and interviews are 75%. He is 25 years old and has 2 years of experience in this field. He is not willing to pay the deposit amount of Rs 50,000.

  1. AOption (a)

    The candidate has been selected.

  2. BOption (b)

    The candidate is referred to the Director.

  3. COption (c)

    The candidate has not been selected.

  4. DOption (d)

    The candidate has been referred to the manager.

View answer & explanation

Correct answer

Answer: (d)D.

The candidate has been referred to the manager.

Why this answer is correct

As per the given information,

Sumit has done BBA from a government college with 74% marks and his marks in written tests and interviews are 75%. He is 25 years old and has 2 years of experience in this field. He is not willing to pay the deposit amount of Rs 50,000.

→ Here, the candidate fulfills all the above criteria except (d) but has experience of working in this area for more than one year. Thus, the candidate has to be referred to Case Manager.

Hence, the correct answer is "option (4)".

Question 5

How many such letters are there in the word BLOKEISH, each of which is as far from the beginning of the word as it is from the beginning of the English alphabet?

  1. AOption (a)

    Four

  2. BOption (b)

    Two

  3. COption (c)

    One

  4. DOption (d)

    Three

View answer & explanation

Correct answer

Answer: (b)B.

Two

Why this answer is correct

The logic follows here is:

Given word: BLOKEISH

As per the question,

Words which are as far from the beginning of the word as it is from the beginning of the English alphabet are :

Clearly,  there are 'Two' words.

Hence, the correct answer is "Two"

Question 6

A reputed educational establishment is going to select meritorious students for scholarships for higher studies abroad who fulfill the following criteria:

  1. Age – Above 18 years but below 24 years as on 1.7.2021
  2. Minimum percentage of graduation marks – 70%
  3. Reward/Prize – Minimum first prize at the state level in essay, debate, or sports.
  4. Annual family income – not more than Rs 2,50,000.
  5. Domicile – Must have resided in India for the last 18 years or more as of 1.7.2021

However, if the candidate fulfills all the above criteria except

  1. (3), But have secured second position in Essay/Debate/Sports Competition at State level – the case may be referred to the Secretary of the Foundation.
  2. (4) But have obtained 90% marks in graduation – the case may be referred to the Chairman of the Establishment.

You have to study the information provided for the candidate in the following question and decide the course of action.

Chirag who will be 23 years old on 1.1.2021 has passed B.com. with 92% marks. Her father, a government employee, has been working in Delhi since 1989, with a current monthly income of Rs 30,000. Chirag got 1st prize in the state essay competition.

  1. AOption (a)

    The candidate is referred to the Secretary.

  2. BOption (b)

    The candidate has been selected.

  3. COption (c)

    The candidate is referred to the Chairman.

  4. DOption (d)

    The candidate has not been selected.

View answer & explanation

Correct answer

Answer: (c)C.

The candidate is referred to the Chairman.

Why this answer is correct

As per the given information,

Chirag who will be 23 years old on 1.1.2021 has passed B.com. with 92% marks. Her father, a government employee, has been working in Delhi since 1989, with a current monthly income of Rs 30,000. Chirag got 1st prize in the state essay competition.

→ Here, the candidate fulfills all the above criteria except (4) as his annual family income is Rs 360000 which is more than Rs 2,50,000 but he has obtained 92% marks in graduation, so the case may be referred to the Chairman of the Establishment.

Thus, the candidate is referred to the Chairman.

Hence, the correct answer is "option (3)".

Question 7

The following questions are based on five three-digit numbers given below.

283 395 768 534 187

If the positions of the first and second digits in each number are interchanged, which of the following will be the second highest number?

  1. AOption (a)

    534

  2. BOption (b)

    283

  3. COption (c)

    395

  4. DOption (d)

    768

View answer & explanation

Correct answer

Answer: (b)B.

283

Why this answer is correct

As per the given information: 

Given: 283 395 768 534 187

The positions of the first and second digits in each number are interchanged, then we have:

Clearly, 823 is the second highest number after the interchange.

Hence, the correct answer is "283".

Question 8

Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option which is different from the others.

  1. AOption (a)

    Silver

  2. BOption (b)

    Iodine

  3. COption (c)

    Nickel

  4. DOption (d)

    Copper

View answer & explanation

Correct answer

Answer: (b)B.

Iodine

Why this answer is correct

The logic follows here is:

Silver, Nickle, and Copper are all metals.

Whereas,

Iodine is not a metal.

Thus, Iodine is the odd one.

Hence, the correct answer is "Iodine".

Question 9

In the question a statement is given, followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at odds with commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements.

Statement:

A ≤ B ≥ C > D; A ≥ E = F < G

Conclusion:

I. B > F

II. B = F

  1. AOption (a)

    Both conclusions I and II follow

  2. BOption (b)

    Only conclusion I follows

  3. COption (c)

    Either conclusion I or II follows

  4. DOption (d)

    Only conclusion II follows

View answer & explanation

Correct answer

Answer: (c)C.

Either conclusion I or II follows

Why this answer is correct

Given statement : A ≤ B ≥ C > D; A ≥ E = F < G

On combining: G > F = E ≤ A ≤ B ≥ C > D

Conclusions :

I. B > F → FALSE (as  G > F = E ≤ A ≤ B ≥ C > D → F ≤ B, thus it is false)

II. B = F →  FALSE (as  G > F = E ≤ A ≤ B ≥ C > D → F ≤ B, thus it is false)

Conclusion I and II form a complementary pair and both of them are false. Thus, this is the case of either and or.

Hence, the correct answer is "Either conclusion I or II follows".

Additional InformationConditions of "Either and or" Case 

  • The conclusions should have complementary pair.
  • Both conclusions should be false.
  • The conclusion should be in 'Some and No' form or 'All and Some not'.

Question 10

Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option that is different from the others.

  1. AOption (a)

    X

  2. BOption (b)

    N

  3. COption (c)

    R

  4. DOption (d)

    K

View answer & explanation

Correct answer

Answer: (d)D.

K

Why this answer is correct

The logic follows here is:

The positional values of X, N, and R are even numbers while the positional value of K is an odd number.

  • X → 24
  • N → 14
  • R → 18
  • K → 11 (odd number)

Thus, 'K' is different from the others.

Hence, the correct answer is "K".

Question 11

Six friends Anil, Babita, Chaman, Dhoni, Ellen, and Farukh are going to college. Ellen is older than only Anil and Babita but shorter than only Farukh. Dhoni is younger than only Farukh and taller than only Anil and Babita. Neither Anil is the shortest nor Babita is the shortest one. How many friends are there who occupy the same position in both the orders?

  1. AOption (a)

    4

  2. BOption (b)

    2

  3. COption (c)

    1

  4. DOption (d)

    3

View answer & explanation

Correct answer

Answer: (b)B.

2

Why this answer is correct

Given: Six friends Anil, Babita, Chaman, Dhoni, Ellen, and Farukh are going to college.

  1. Ellen is older than only Anil and Babita but shorter than only Farukh.

Farukh > Ellen > Anil/Babita > Anil/Babita. ____ (1)

  1. Dhoni is younger than only Farukh and taller than only Anil and Babita.

Farukh > Dhoni  > Anil/Babita > Anil/Babita. ____ (2)

  1. Neither Anil is the shortest nor Babita is the shortest one.

After combining both the conditions, we get:

Farukh > Dhoni/Ellen  > Anil/Babita > Anil/Babita > ___

Here, Dhoni and Ellen occupy the same position in both sequences.

Hence, the correct answer is '2 friends' who occupy the same position in both sequences.

Question 12

Complete the following alphabet series:

AZOM, CXQK, EVSI, ___

  1. AOption (a)

    FTTJ

  2. BOption (b)

    GTUJ

  3. COption (c)

    GTUG

  4. DOption (d)

    GUTG

View answer & explanation

Correct answer

Answer: (c)C.

GTUG

Why this answer is correct

The logic follows here is:

Hence, the correct answer is "GTUG".

Question 13

Read all the information and answer the question.

A + B means 'A is the mother of B';

A – B means 'A is the brother of B';

A × B means 'A is the father of B';

A ÷ B means 'A is the daughter of B';

How is C related to E in the expression A - B + C × D ÷ E?

  1. AOption (a)

    Wife

  2. BOption (b)

    Father

  3. COption (c)

    Husband

  4. DOption (d)

    Brother

View answer & explanation

Correct answer

Answer: (c)C.

Husband

Why this answer is correct

Given:

A + B means 'A is the mother of B';

A – B means 'A is the brother of B';

A × B means 'A is the father of B';

A ÷ B means 'A is the daughter of B';

Let us first decode the given symbols and then draw a family tree:

A is
Symbol+–×÷
MeaningMotherBrotherFatherDaughter
of B

On checking: A - B + C × D ÷ E

1) A - B

Here, A is the brother of B.

2) B + C

Here, B is the mother of C.

  1. C × D

Here, C is the father of D.

4) D ÷ E

Here, D is the daughter of E.

  • Thus, the following family tree can be drawn:

  • Clearly, C is 'husband' of E.

Hence, the correct answer is "Husband".

Question 14

Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option which is different from the others.

  1. AOption (a)

  2. BOption (b)

  3. COption (c)

  4. DOption (d)

View answer & explanation

Correct answer

Answer: (a)A.

Why this answer is correct

The logic follows here is:

The arrows inside the circles are in the clockwise direction in all the options except option(1).

option (1)

Here. the arrow is in the anti-clockwise direction. Thus, it is different from the others.

Hence, the correct answer is "option (1)".

Question 15

The given sheet has been folded to form a cube. In the cube thus formed, which of the following pairs of symbols will be in opposite directions?

  1. AOption (a)

  2. BOption (b)

  3. COption (c)

  4. DOption (d)

View answer & explanation

Correct answer

Answer: (a)A.

Why this answer is correct

The logic follows here is:

There is a pattern in which unfolded dice occur opposite to each other.

Two opposite faces are never together or adjacent to each other.

FaceOpposite

option(1) → 

Clearly, pairs of symbols in option (1) will be in opposite directions.

Hence, the correct answer is "option (2)".

Question 16

Select the option that is related to the third term in the same way as the second term is related to the first term.

65 : 74 :: 40 : ?

  1. AOption (a)

    49

  2. BOption (b)

    50

  3. COption (c)

    51

  4. DOption (d)

    48

View answer & explanation

Correct answer

Answer: (a)A.

49

Why this answer is correct

The logic follows here is,

(First number) + 9 = (Second number)

  • 65 : 74

→ 65 + 9 = 74 = second number.

Similarly,

  • 40 : ?

→ 40 + 9 = 49 = second number.

Hence, the correct answer is "49".

Question 17

From the given answer figures, select the figure in which the question figure is hidden/embedded.

  1. AOption (a)

  2. BOption (b)

  3. COption (c)

  4. DOption (d)

View answer & explanation

Correct answer

Answer: (b)B.

Question 18

D, C, B and A are sitting around a table facing each other. They like different colors yellow, blue, black, and red.

(1) D sits opposite the one who likes black color.

(2) C sits to the immediate right of the one who likes the blue color.

(3) The person who likes yellow color is to the left of the person who likes red color.

(4) A sits opposite B who does not like the yellow colour.

Who likes red?

  1. AOption (a)

    A

  2. BOption (b)

    B

  3. COption (c)

    D

  4. DOption (d)

    C

View answer & explanation

Correct answer

Answer: (c)C.

D

Why this answer is correct

As per the given information:

 

D, C, B and A are sitting around a table facing each other. They like different colors yellow, blue, black, and red.

  • D sits opposite the one who likes black color.
  • C sits to the immediate right of the one who likes the blue color.

There are two possibilities:

  • The person who likes yellow color is to the left of the person who likes red color.

Case I will be eliminated as it contradicts the above condition.

  • A sits opposite B who does not like the yellow colour.

Clearly, 'D' likes red color.

Hence, the correct answer is "D".

Question 19

Find the missing number in the given series:

53, 55, 113, 343, ___

  1. AOption (a)

    1387

  2. BOption (b)

    1377

  3. COption (c)

    1367

  4. DOption (d)

    1357

View answer & explanation

Correct answer

Answer: (b)B.

1377

Why this answer is correct

Given: 53, 55, 113, 343, ___

The logic follows here is:

Hence, the correct answer is "1377.

Question 20

Train A crosses a man in 12 seconds and train B running in the opposite direction crosses it in 24 seconds. If the length of train B is twice the length of train A and the speed of train B is 54 km/h, then find the speed of train A.

  1. AOption (a)

    90 km/hr

  2. BOption (b)

    108 km/hr

  3. COption (c)

    100 km/hr

  4. DOption (d)

    75 km/hr

View answer & explanation

Correct answer

Answer: (b)B.

108 km/hr

Why this answer is correct

Given: 

  • Train A crosses a man in 12 seconds and train B running in the opposite direction crosses it in 24 seconds.
  • The length of train B is twice the length of train A
  • The speed of train B is 54 km/h = 54 × (5/18) = 15 m/s

Formula:

Distance = Speed × Time

Calculation:

Let the length of train A be x and the length of train B be 2x.

According to the question,

Train A crosses a man in 12 seconds.

Therefore, the speed of Train A is = x/12 m/s

Train B running in the opposite direction crosses it in 24 seconds.

The relative speed = speed of train A + speed of Train B

Relative speed = (x/12) + 15

Now, by using the formula,

where distance is equal to the sum of the lengths of both trains i.e. 3x

⇒ distance = relative speed × Time

⇒ 3x = { (x/12 + 15)} × 24

⇒ x = { (x/12 + 15)} × 8

⇒ 12x = (x + 180) × 8

⇒ 3x = (x + 180) × 2

⇒ 3x = 2x + 360

⇒ x = 360

Thus, the length of train A is 360 m.

Speed of Train A = x/12 m/s

⇒ 360 / 12

⇒ 30 m/s = 30 × (18/5) = 108 km/hr

Hence, the correct answer is "108 km/hr".

General Awareness (20 questions)

Question 21

Select the name of the peninsular country:

  1. AOption (a)

    Brazil

  2. BOption (b)

    Austria

  3. COption (c)

    India

  4. DOption (d)

    Philippines

View answer & explanation

Correct answer

Answer: (c)C.

India

Why this answer is correct

The correct answer is India.

Key Points

  • India is a peninsular country located in South Asia.
  • It is bordered by the Arabian Sea on the southwest, the Bay of Bengal on the southeast, and the Indian Ocean on the south.
  • The country is known for its diverse culture, rich history, and geographical features.
  • The Indian subcontinent extends into the Indian Ocean, forming the Indian Peninsula.
  • The peninsula is surrounded by water on three sides, giving India its distinctive peninsular shape.
  • It is home to several major rivers, including the Ganges and the Brahmaputra.
  • India has a vast coastline that stretches over 7,500 kilometers, offering numerous beaches and ports.

Additional Information

  • Examples of peninsular countries include India, Italy, Spain, Malaysia (partially), and South Korea (partially).
  • These countries have a significant portion of their landmass in the form of a peninsula and are characterized by their unique geographic features and cultural identities shaped by their peninsular nature.

Question 22

The name of the anti-covid drug developed by DRDO is:

  1. AOption (a)

    2-deoxy-D-glucose (2-DG)

  2. BOption (b)

    2-deoxy (2-D)

  3. COption (c)

    1-deoxy-D-glucose (2-DG)

  4. DOption (d)

    3-deoxy-d-glucose

View answer & explanation

Correct answer

Answer: (a)A.

2-deoxy-D-glucose (2-DG)

Why this answer is correct

The correct answer is 2-deoxy-D-glucose (2-DG).

Key PointsAnti-COVID-19 drug 2-deoxy-D-glucose (2-DG) has been developed by the Institute of Nuclear Medicine and Allied Sciences (INMAS), a lab of the Defence Research and Development Organisation (DRDO), in collaboration with Dr Reddy’s Laboratories (DRL), Hyderabad. 

  • According to the Clinical trial results, this molecule helps in faster recovery of hospitalized patients and reduces supplemental oxygen dependence.
  • A higher proportion of patients treated with 2-DG showed RT-PCR negative conversion in COVID patients.
  • The drug will be of immense benefit to people suffering from COVID-19.

Additional Information

  • The drug comes in powder form in a sachet, which is taken orally by dissolving it in water.
  • It accumulates in the virus-infected cells and prevents virus growth by stopping viral synthesis and energy production.
  • Its selective accumulation in virally infected cells makes this drug unique.

Question 23

Which of the following is not a vector borne disease?

  1. AOption (a)

    Dengue fever

  2. BOption (b)

    Ebola virus

  3. COption (c)

    Malaria

  4. DOption (d)

    lymphatic filariasis

View answer & explanation

Correct answer

Answer: (b)B.

Ebola virus

Why this answer is correct

The correct answer is the Ebola virus.

Key Points

  • The Ebola virus is a severe and often fatal illness that affects humans and nonhuman primates
  • It belongs to the family Filoviridae and is named after the Ebola River in the Democratic Republic of Congo (formerly Zaire), where it was first identified in 1976.
  • Ebola virus disease (EVD) is transmitted to humans from wild animals and can spread through human-to-human transmission.

Additional Information

  • Dengue
  • Dengue is a mosquito-borne viral disease.
  • People can contract dengue viruses by being bitten by an infected Aedes species mosquito.
  • Three to fourteen days after infection, symptoms usually appear.
  • These symptoms can include a high temperature, headache, nausea, discomfort in the muscles and joints, as well as the typical rash and itching of the skin.
  • Malaria
  • ​Malaria is a disease caused by the protozoan Plasmodium.

The severity of the disease depends on the species of Plasmodium.

  • Lymphatic filariasis.
  • Lymphatic filariasis, also known as elephantiasis, is a parasitic disease caused by infection with filarial worms.
  • It is transmitted to humans through the bites of infected mosquitoes, primarily species belonging to the genera Culex, Anopheles, and Aedes.​

Question 24

What are Mahayana and Hinayana?

  1. AOption (a)

    Two major sects of Hinduism

  2. BOption (b)

    Mahayana means 'the great vehicle'. 'Hinayana' means 'small vehicle' or 'lesser vehicle

  3. COption (c)

    Names of books written by the students of Mahatma Buddha

  4. DOption (d)

    None of the Above

View answer & explanation

Correct answer

Answer: (b)B.

Mahayana means 'the great vehicle'. 'Hinayana' means 'small vehicle' or 'lesser vehicle

Why this answer is correct

The correct answer is Mahayana means 'the great vehicle'. 'Hinayana' means 'small vehicle' or 'lesser vehicle.

<br>

Key Points

  • Mahayana and Hinayana are terms used in Buddhism to describe different branches or traditions within the religion.
  • These terms originated in ancient India and are primarily associated with the early development and classification of Buddhist schools
  • Mahayana, which means 'the great vehicle' or 'the greater vehicle,' represents one of the major branches of Buddhism.
  • It emphasizes universal compassion and the idea of the bodhisattva, an enlightened being who compassionately works for the liberation of all sentient beings.

Additional Information

  • Gautam Buddha, the founder of Buddhism, was born in Lumbini in 563 BC.
  • He belonged to the Shakya dynasty, his real name was Siddhartha.
  • Gautama attained enlightenment under a Peepal tree at Bodh Gaya in Bihar.
  • Buddha gave his first sermon in Sarnath village near Varanasi in Uttar Pradesh.
  • This event is known as Dharma Chakra Pravartan.
  • He died in 483 BCE at the age of 80 at Kushinagar in the Gorakhpur district of Uttar Pradesh.
  • This event is known as Mahaparinirvana.

Question 25

Milkha Singh was an Indian track and field sprinter who was also known as:

  1. AOption (a)

    The Flym Man

  2. BOption (b)

    The Fighter Sikh

  3. COption (c)

    The Fighter Flying Sikh

  4. DOption (d)

    The Flying Sikh 

View answer & explanation

Correct answer

Answer: (d)D.

The Flying Sikh 

Why this answer is correct

The correct answer is The Flying Sikh.

Key Points

Milkha Singh.

  • He is a former Indian track and field sprinter who had been introduced to the sport while serving in the Indian Army.
  • He was the only Indian athlete to win an individual athletics gold medal at a Commonwealth Games until Krishna Poonia at the 2010 Commonwealth Games won the gold medal for the discus.
  • In recognition of his sporting achievements, he was awarded the Padma Shri, India's fourth-highest civilian honor.
  • He represented India at the Melbourne Summer Olympics of 1956, at the Rome Summer Olympics of 1960, and at the Tokyo Summer Olympics of 1964.
<br>

Question 26

Enzymes are required to:

  1. AOption (a)

    Sharpen the eye sight

  2. BOption (b)

    Make antibodies

  3. COption (c)

    Increasing oxygen level in body

  4. DOption (d)

    Digest the food in the stomach

View answer & explanation

Correct answer

Answer: (d)D.

Digest the food in the stomach

Why this answer is correct

The correct answer is Digest the food in the stomach.

Key Points

Enzymes

  • Enzymes are biological molecules that act as catalysts in various chemical reactions within the body.
  • They facilitate and speed up biochemical reactions without being consumed or altered in the process.
  • One of the important functions of enzymes is to aid in the digestion of food.
  • When we consume food, enzymes play a crucial role in breaking down complex molecules into smaller, simpler substances that can be absorbed and utilized by the body.
  • In the case of digestion, enzymes are involved in breaking down carbohydrates, proteins, and fats into their respective components—such as simple sugars, amino acids, and fatty acids—so that they can be absorbed through the intestinal lining into the bloodstream.

Additional Information

  • The word enzyme was coined in 1878 by German Scientist Wilhelm Kuhne.
  • Enzymes act as biological catalysts (biocatalysts).
  • Catalysts accelerate chemical reactions.
  • The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products.
  • Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life.

Question 27

Select dance styles that are popular in Maharashtra:

  1. AOption (a)

    Bihu

  2. BOption (b)

    Kathak

  3. COption (c)

    Satriya

  4. DOption (d)

    Lavani 

View answer & explanation

Correct answer

Answer: (d)D.

Lavani 

Why this answer is correct

The correct answer is Lavani.

Key Points

  • Lavani is a folk dance of Maharashtra.
  • It is a combination of traditional song and dance, which is particularly performed to the beats of Dholki which is a percussion instrument.
  • Lavani is noted for its powerful rhythm and has contributed substantially to the development of Marathi folk theatre.

Additional InformationKathak:

  • ​Kathak is one of the eight major forms of Indian classical dance.
  • It is the classical dance form of Uttar Pradesh.
  • The origin of Kathak is traditionally attributed to the traveling bards in ancient northern India known as Kathakars or storytellers.

Satriya

  • The Sattriya dance form was introduced in the 15th century A.D. by the great Vaishnava saint and reformer of Assam.
  • The dance form evolved and expanded as a distinctive style of dance later on.
  • Due to its religious character and association with the Sattras, this dance style has been aptly named Sattriya.

Bihu

  • The Bihu dance is an indigenous folk dance from the Indian state of Assam related to the Bihu festival and an important part of Assamese culture.
  • The Bihu dance takes its name from the Bohag Bihu festival also called Rangali Bihu, the national festival of Assam, which celebrates the Assamese New Year.
  • The festival takes place during mid-April and the Bihu dance is meant to celebrate and emulate the seasonal spirit, celebrating fertility and passion.

Question 28

A very alkaline solution (high pH) will change the color of beetroot or beetroot juice to ______.

  1. AOption (a)

    Purple to Yellow

  2. BOption (b)

    Purple to diamond

  3. COption (c)

    Pink to black

  4. DOption (d)

    Red to purple 

View answer & explanation

Correct answer

Answer: (a)A.

Purple to Yellow

Why this answer is correct

The correct answer is ​Purple to Yellow.

Key Points

  • A very alkaline solution (high pH) will change the color of the beetroot or beetroot juice to yellowish-brown or brown color.
  • The pigments responsible for the vibrant red color of beetroot, known as betalains, are sensitive to changes in pH.
  • In acidic conditions, the betalains exhibit their characteristic red color, but as the pH increases and the solution becomes more alkaline, the color changes to a brownish hue.
  • This is due to the chemical reactions and transformations of the betalain pigments in response to the alkaline environment.

 Important Points

  • pH stands for "potential of Hydrogen."
  • It is a measure of the acidity or alkalinity of a solution.
  • The pH scale ranges from 0 to 14, with 7 considered neutral. A pH value less than 7 indicates acidity, while a pH value greater than 7 indicates alkalinity.

Question 29

Dadasaheb Phalke Award is given in which field?

  1. AOption (a)

    Cinema

  2. BOption (b)

    Sport

  3. COption (c)

    Peace

  4. DOption (d)

    literature

View answer & explanation

Correct answer

Answer: (a)A.

Cinema

Why this answer is correct

The correct answer is Cinema.

Dada Saheb Phalke Award

  • The Dadasaheb Phalke Award is India's highest honor in cinema, presented by the Directorate of Film Festivals for the recipient's contribution to the growth and development of Indian cinema.
  • The award, named after Dhundiraj Govind Phalke, who is revered as the father of Indian cinema, was instituted in 1969.
  • The recipient receives a Swarna Kamal (Golden Lotus) medallion, a shawl, and a cash prize of Rs 10 lakh.
  • Devika Rani Roerich was the first recipient of the award in 1969.
  • Prithvi Raj Kapoor is the only awardee who was conferred with the award posthumously in 1971.

Question 30

What is the theme of the Economic Survey 2020-21?

  1. AOption (a)

    Market Enablement, Promote 'Pro-Business'

  2. BOption (b)

    Saving lives and Livelihood

  3. COption (c)

    "Shifting Gear"

  4. DOption (d)

    Rural Development and Agricultural Education

View answer & explanation

Correct answer

Answer: (b)B.

Saving lives and Livelihood

Why this answer is correct

The correct answer is Saving lives and Livelihoods.

Key Points

  • Chief Economic Adviser Krishnamurthy Subramanian launched the Economic Survey 2021, which was also tabled in the Parliament by the Finance Minister on 29 Jan 2021.
  • Economic Survey 2020-21 has been conducted in the background of the COVID-19 pandemic and the economic impact of COVID-19 in India.
  • The Economic Survey 2020-21 has been dedicated to all the COVID-19 warriors, who have really helped in upholding India.
  • The fundamental theme of the Economic Survey 2020-21 is Saving Lives and Livelihoods and V-Shaped Recovery.
  • This year's Economic Survey will be presented two days before the Budget, which is scheduled for February 1, 2021.

Question 31

At present (as of 2021), who is the Speaker of the Lok Sabha?

  1. AOption (a)

    Om Birla

  2. BOption (b)

    Om Puri

  3. COption (c)

    Meera Kumar

  4. DOption (d)

    Sumitra Mahajani

View answer & explanation

Correct answer

Answer: (a)A.

Om Birla

Why this answer is correct

The correct answer is Om Birla.

Key Points

  • Om Birla is the 17th speaker of the Lok Sabha and was appointed so on June 19, 2019.
  • He belongs to Bhartiya Janata Party (BJP)and is a member of Parliament from Kota Bundi constituency in Rajasthan.
  • He was also elected as a member of the Rajasthan Legislative Assembly during the 2003, 2008, and 2013 elections.
  • He is credited with the initiation of mass movements which led to the establishment of an IIT at Kota, the Direction of the Chambal river to Kota district, and also the employment of local people in the Rawatbhat Nuclear power.

Additional Information 

 Speaker and Deputy Speaker -

  • He is the presiding officer of Lok Sabha.
  • He is elected in the first meeting of Lok Sabha following the process of general elections.
  • The current Lok Sabha speaker is Om Birla.
  • The Deputy Speaker is the second highest authority in Lok Sabha.
  • They act as presiding officers in the absence of a speaker.

Question 32

Kabaddi is the national game of which country?

  1. AOption (a)

    Bangladesh

  2. BOption (b)

    Pakistan

  3. COption (c)

    India

  4. DOption (d)

    Russia

View answer & explanation

Correct answer

Answer: (a)A.

Bangladesh

Why this answer is correct

The correct answer is Bangladesh.

Key Points

  • Kabaddi is the; national sport of Bangladesh.
  • It is popularly known as Hadudu in; Bangladesh.
  • Famous Kabaddi players of India are - Pawan Kumar Shehrawat, Anup Kumar, Manjeet Chillar, Pradeep Narwal, etc.
  • Hockey is the national game of India.

Additional Information

SportsNational ;gameFamous Players
CricketEngland and AustraliaMatthew Hayden (Aus), Virat Kohli, Sachin Tendulkar, M.S. Dhoni, etc.
FootballFrance, Italy, Italy, Poland, Mauritius, etcLionel Messi (Argentina), Christiano Ronaldo (Portugal), Neymar (Brazil), Nene (Brazil), Maradona (Argentina)
BadmintonIndonesiaSaina Nehwal, P.V. Sindhu, Lee Chong Wei (Malaysia), Chen Long (China), etc

Question 33

At present (as of 2021), who is the chairman of the Union Public Service Commission?

  1. AOption (a)

    Sujata Mehta

  2. BOption (b)

    Vinay Mittal

  3. COption (c)

    Arvind Saxena

  4. DOption (d)

    Pro. (Dr.) Pradeep Kumar Joshi 

View answer & explanation

Correct answer

Answer: (d)D.

Pro. (Dr.) Pradeep Kumar Joshi 

Why this answer is correct

The correct answer is Pro. (Dr.) Pradeep Kumar Joshi.

Key Points

  • UPSC is responsible for appointments to and examinations for All India services and Group-A and Group-B of Central services.
  • UPSC was founded on 1st October 1926 with its headquarters in New Delhi.
  • UPSC's new chairman Pradeep Kumar Joshi will have a tenure till April 4, 2022.

Additional Information

  • Vinay Mittal
  • Vinay Mittal is an Indian Civil servant who worked for the Indian Railway Traffic Service.
  • He served as Chairman of the Union Public Service Commission from January 2018 to June 2018 and Chairman of the Railway Board from July 2011 to June 2013.
  • Arvind Saxena is an Indian civil servant and the former chairman of the Union Public Service Commission.
  • Sujata Mehta is a former Indian Foreign Service officer, currently serving as a member of the Union Public Service Commission

Question 34

Article 71A deals with:

  1. AOption (a)

    It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the Supreme Court.

  2. BOption (b)

    It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the District Court

  3. COption (c)

    It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the High Court.

  4. DOption (d)

    None of the Above

View answer & explanation

Correct answer

Answer: (a)A.

It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the Supreme Court.

Why this answer is correct

The correct answer is It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the Supreme Court.

Key PointsArticles 71.

  • All doubts and disputes arising out of or in connection with the election of a President or Vice-President shall be inquired into and decided by the Supreme Court whose decision shall be final.
  • If the election of a person as President or Vice-President is declared void by the Supreme Court, acts done by him in the exercise and performance of the powers and duties of the office of President or Vice-President, as the case may be, on or before the date of the decision of the Supreme Court shall not be invalidated by reason of that declaration.
  • Subject to the provisions of this Constitution, Parliament may by law regulate any matter relating to or connected with the election of a President or Vice-President.
  • The election of a person as President or Vice-President shall not be called into question on the ground of the existence of any vacancy for whatever reason among the members of the electoral college electing him.

Important Points

ArticleInformation
Article 63There shall be a Vice-President of India.
Article 64The Vice-President shall be ex-officio Chairman of the Council of States and shall not hold any other office of profit
Article 65The Vice-President to act as President or to discharge his functions during casual vacancies in the office, or during the absence, of President.
Article 66The Vice President shall be elected by the members of an electoral college consisting of the members of both Houses of Parliament.
Article 67A Vice-President may, by writing under his hand addressed to the President, resign his office

Question 35

Which cyclone hit Gujarat recently (in May 2021)?

  1. AOption (a)

    Kyar

  2. BOption (b)

    Tauktae

  3. COption (c)

    Pawan

  4. DOption (d)

    Pabuk

View answer & explanation

Correct answer

Answer: (b)B.

Tauktae

Why this answer is correct

The correct answer is Tauktae.

Key Points

  • Extremely Severe Cyclonic Storm Tauktae was a powerful, deadly, and damaging tropical cyclone in the Arabian Sea.
  • Cyclone Tauktae, the biggest to hit the region in decades, made landfall in Gujarat, packing winds with speeds of 155-165 kilometers per hour, gusting to 190 km/hour.
  • It became the strongest tropical cyclone to make landfall in the Indian state of Gujarat since the 1998 Gujarat cyclone.
  • It means ‘Gecko’ which is a highly vocal lizard.
  • Myanmar has named this cyclone ‘ Tauktae’.

Important Points

  • A cyclone is a large-scale weather system characterized by low atmospheric pressure, strong winds, and circulating air.
  • Cyclones can occur over both land and water, but they are more commonly associated with tropical and subtropical regions.
  • In general, cyclones are classified into different types based on their location and characteristics.
  • Tropical cyclones, also known as hurricanes or typhoons depending on the region, form over warm ocean waters and are characterized by a well-defined eye at the center and spiraling rainbands.

Question 36

Which is not a dwarf planet?

  1. AOption (a)

    Venus

  2. BOption (b)

    Pluto

  3. COption (c)

    Aris

  4. DOption (d)

    Makemake

View answer & explanation

Correct answer

Answer: (a)A.

Venus

Why this answer is correct

The correct answer is Venus.

Key Points

  • Venus is the second nearest planet to the sun.
  • It is the hottest planet in our solar system.
  • The surface temperature of over 450 degrees Celsius.
  • The planet Venus rotates from east to west.
  • It is the only planet that rotates from east to west.
  • Sun appears to rise in the West and set in the East.
  • Venus is the slowest-rotating planet.

 Important Points

  • A dwarf planet is, “a celestial body orbiting a star that is massive enough to be rounded by its own gravity but has not cleared its neighboring region of planetesimals and is not a satellite.
  • More explicitly, it has to have sufficient mass to overcome its compressive strength and achieve.
  • There are currently five dwarf planets: Pluto, Eris, Makemake, Haumea, and Ceres.

Question 37

Milindapanha is a Buddhist text which may have been written initially in which language?

  1. AOption (a)

    Hindi

  2. BOption (b)

    English

  3. COption (c)

    Sanskrit

  4. DOption (d)

    Urdu

View answer & explanation

Correct answer

Answer: (c)C.

Sanskrit

Why this answer is correct

The correct answer is Sanskrit.

Key Points

  • Milindapanha is a Buddhist text that is believed to have been initially written in Sanskrit.
  • It is a dialogue between King Milinda (Menander I) and the Buddhist sage Nagasena.
  • The text addresses various philosophical and ethical questions, exploring topics such as the nature of self, morality, and the path to enlightenment.

Additional InformationSanskrit

  • Sanskrit is an ancient Indo-Aryan language that originated in the Indian subcontinent.
  • It is considered the classical language of India and holds significant cultural and religious importance.
  • Sanskrit is known for its highly structured grammar, extensive vocabulary, and rich literature.
  • Historically, Sanskrit was used as a sacred language in various religions, including Hinduism, Buddhism, and Jainism.
  • It served as the medium for the composition of many religious texts, philosophical treatises, and epic poems, such as the Vedas, Upanishads, Mahabharata, Ramayana, and various Puranas.

Question 38

Which is the hottest planet in the solar system?

  1. AOption (a)

    Mars

  2. BOption (b)

    Uranus

  3. COption (c)

    Neptune

  4. DOption (d)

    Venus

View answer & explanation

Correct answer

Answer: (d)D.

Venus

Why this answer is correct

The correct answer is Venus.

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Key Points

  • ​Venus is a small rocky planet, blanketed by a thick layer of yellowish clouds.
  • It is similar in size to Earth and there are many active volcanoes on Venus.
  • Venus spins very slowly, in the opposite direction to most other planets.
  • Venus is usually visible to the naked eye.
  • It is the brightest star in the evening sky.

 Important PointsMars

  • Mars is called Red Planet.
  • It has two satellites - Phobos and Deimos.
  • Mars is the fourth planet in the solar system.
  • It is the second smallest planet in the solar system.
  • In English Mars carries the name of the Roman God of War.

Neptune:

  • Neptune is the last planet in our solar system.
  • It is 30 times as far from the sun as the Earth is.
  • The atmosphere of this planet is made of Helium, Hydrogen, and Methane.
  • It has six rings around it. But very hard to observe due to the very long distance.

Uranus

  • Uranus orbits in a clockwise direction from east to west around the sun.
  • It was first seen as a faint bluish-green disc.
  • Uranus is also known as loop sided planet.

Question 39

At present (as of August 2021), who is the Governor of the Reserve Bank of India?

  1. AOption (a)

    Raghuram Rajan

  2. BOption (b)

    Urjit Patel

  3. COption (c)

    Mr. Shaktikanta Das

  4. DOption (d)

    T Ravi Shankar

View answer & explanation

Correct answer

Answer: (c)C.

Mr. Shaktikanta Das

Why this answer is correct

The correct answer is Mr. Shaktikanta Das.

Key Points

  • The government has extended the term of Reserve Bank of India (RBI) Governor Shaktikanta Das by another three years up to December 2024.
  • Das was appointed the RBI’s 25th governor on December 11, 2018, initially for a period of three years.
  • Before his appointment at the central bank, he served as a member of the 15th finance commission and also as India’s G20 Sherpa.

Additional Information

  • Patel served as the 24th governor of the Reserve Bank of India from September 2016 to December 2018.
  • Raghuram Govindarajan is an Indian economist.

Between 2003 and 2006, he was Chief Economist and director of research at the International Monetary Fund.

  • He assumed charge as the 23rd Governor of the Reserve Bank of India in 2013 and served till 2016.

Question 40

How many parts are there in the United Nations?

  1. AOption (a)

    Eight

  2. BOption (b)

    Six

  3. COption (c)

    Three

  4. DOption (d)

    Seven

View answer & explanation

Correct answer

Answer: (b)B.

Six

Why this answer is correct

The correct answer is Six.

Key Points

  • The United Nations (UN) consists of six main organs or parts:
  • General Assembly: It is the main deliberative body of the UN, where all member states have representation. Each member state has one vote, and decisions on important issues require a two-thirds majority.
  • Security Council: It is responsible for maintaining international peace and security. It has 15 members, including five permanent members (China, France, Russia, the United Kingdom, and the United States) with veto power and ten non-permanent members elected by the General Assembly.
  • Economic and Social Council (ECOSOC): It deals with economic, social, and environmental issues and promotes international cooperation on these matters. It has 54 member states elected by the General Assembly.

Important Points

  • Trusteeship Council: It was established to oversee the administration of trust territories until they achieved self-government or independence. As of now, all trust territories have attained independence or been placed under the administration of member states, and the Trusteeship Council is currently inactive.
  • International Court of Justice (ICJ): It is the principal judicial organ of the UN and settles legal disputes between states. It consists of 15 judges elected by the General Assembly and the Security Council.
  • Secretariat: It is the administrative arm of the UN, headed by the Secretary-General. The Secretariat carries out the day-to-day work of the organization and provides support to other UN organs.

Arithmetic Ability (20 questions)

Question 41

The police saw the thief from a distance of 200m. The speed at which the thief ran is 9 km/h and the police ran at the speed of 11 km/h. How far will the thief have to go before the police catch him?

  1. AOption (a)

    990 m

  2. BOption (b)

    800 m

  3. COption (c)

    900 m

  4. DOption (d)

    890 m

View answer & explanation

Correct answer

Answer: (c)C.

900 m

Why this answer is correct

Given:

The police saw the thief from a distance of 200m or 0.2 km,

The speed at which the thief ran is 9 km/h and the police ran at the speed of 11 km/h.

Formula used:

Case 1: When two bodies 'a' and 'b' moves in the same direction.

Relative speed between a and b = a - b km/hr

Case 2: When two bodies 'a' and 'b' moves in the apposite direction.

Relative speed between a and b = a + b km/hr

Calculation:

According to the question,

Relative speed between thief and police = 11 - 9 = 2 km/hr

Time required by thief to be captured by police = 0.2/2 = 0.1 hour

Distance travelled by thief in 0.1 hour = 9 × 0.1 = 0.9 km = 900 m

Therefore, "900 m" is the required answer.

Question 42

What is the average of the first 47 natural numbers?

  1. AOption (a)

    42

  2. BOption (b)

    2

  3. COption (c)

    24

  4. DOption (d)

    4

View answer & explanation

Correct answer

Answer: (c)C.

24

Why this answer is correct

Formula used:

Average of n natural numbers = (n+1)2\frac{(n+1)}{2}

In this formula:

"n" is the number of natural numbers you want to sum.

Calculation:

First natural number = 1

Last natural number = 47

Average = (1 + 47)/2 = 48/2 = 24

Therefore, "24" is the required answer.

Question 43

The interest rate is 14% per annum which is being compounded half yearly. The amount is Rs. 965000 and the tenure is 3 years. What is compound interest?

  1. AOption (a)

    Rs. 483420.79

  2. BOption (b)

    Rs. 483402.79

  3. COption (c)

    Rs. 483200.79

  4. DOption (d)

    Rs. 483204.79

View answer & explanation

Correct answer

Answer: (d)D.

Rs. 483204.79

Why this answer is correct

Given:

The interest rate is 14% per annum which is being compounded half yearly.

The amount is Rs 965000 and the tenure is 3 years.

Formula used:

The formula for compound interest is:

A = P(1+Rn×100)nT\left ( 1 + \frac{R}{n × 100} \right)^{nT}

Where:

A = Final Amount

P = Principal amount 

r = Annual interest rate

n = Number of times that interest is compounded per year.

t = the number of years the money is invested or borrowed

Calculation:

According to the question,

⇒ A = 965000 × (1+142×100)2×3\left ( 1 + \frac{14}{2 × 100} \right)^{2 × 3}

⇒ A = 965000 × (1.07)6\left ( 1.07\right)^{6}

⇒ A = 965000 × 1.5 = 14,48,204.78

Now, 

Compound Interest = 1448204.79 - 965000 ≈ Rs. 483204.79

Therefore, "Rs. 483204.79" is the required answer.

Question 44

The percentage of alcohol in 8L solution of alcohol and water is 13%. If 2L of water is added to the solution, what will be the new percentage of alcohol in the solution?

  1. AOption (a)

    11.0%

  2. BOption (b)

    10.4%

  3. COption (c)

    10.0%

  4. DOption (d)

    9.0%

View answer & explanation

Correct answer

Answer: (b)B.

10.4%

Why this answer is correct

Given:

The percentage of alcohol in 8L solution of alcohol and water is 13%.

Calculation:

According to the question,

Case 1: 

Quantity of alcohol in 8L solution = 13% of 8 = 1.04L

Quantity of water in 8L solution = 8 - 1.04 = 6.96L

Case 2: If 2L of water is added to the solution

New quantity of water = 6.96 + 2 = 8.96L

Quantity of alcohol (remain unchanged) = 1.04L

Total quantity = 10L

Required % = 1.04/10 × 100 = 10.4%

Therefore, "10.4%" is the required answer.

Question 45

A wall is 5.5 m high and 6.5 m wide. What is the maximum number of squares required to cover the wall with square shaped papers?

  1. AOption (a)

    143

  2. BOption (b)

    134

  3. COption (c)

    133

  4. DOption (d)

    144

View answer & explanation

Correct answer

Answer: (a)A.

143

Why this answer is correct

Given:

A wall is 5.5 m high and 6.5 m wide.

Calculation:

The maximum size of squares required to cover the wall with square-shaped papers = H.C.F of (5.5 and 6.5) = 0.5 m

The number of number of squares required to cover the wall horizontally = 5.5/0.5 = 11

The number of number of squares required to cover the wall vertically = 6.5/0.5 = 13

The maximum number of squares required = 11 × 13 = 143

Therefore, "143" is the required answer.

Question 46

P and Q can do the work of laying carpet in 6 days. Q and R can do the same carpet laying work in 8 days while R and P can do the same carpet laying work in 10 days. How much time will it take if they all work together?

  1. AOption (a)

    241/47 days

  2. BOption (b)

    240/49 days

  3. COption (c)

    240/47 days

  4. DOption (d)

    241/49 days

View answer & explanation

Correct answer

Answer: (c)C.

240/47 days

Why this answer is correct

Given:

P and Q can do the work of laying carpet in 6 days.

Q and R can do the same carpet laying work in 8 days.

R and P can do the same carpet laying work in 10 days.

Formula used:

  1. Amount of work (in units) = L.C.M of (a, b, c)

Where, 

Time taken by A to do the work = a

Time taken by B to do the work = b

Time taken by C to do the work = c

  1. Efficiency of a person = Amount of work ÷ Total time taken by the person to complete the work

Calculation:

Amount of work (in units) = L.C.M of (6, 8, 10) = 120 units

According to the question,

Efficiency of P and Q = 120/6 = 20 units per day

Efficiency of Q and R = 120/8 = 15 units per day

Efficiency of R and P = 120/10 = 12 units per day

Now, Combined Efficiency = 2(P + Q + R) = 47

 

Combined efficiency of P, Q and R = 47/2 units per day

Time taken to complete the work = 120 ÷ 47/2 = 240/47 days

Therefore, "240/47 days" is the required answer.

Question 47

A person's salary is deducted by 8% for house rent. Then 15% of the remaining is spent on household utilities and 20% of the remaining is spent on miscellaneous and children's education. After these, his savings is Rs. 988448. What is the basic salary of the person?

  1. AOption (a)

    Rs. 1850000

  2. BOption (b)

    Rs. 185000

  3. COption (c)

    Rs. 1580000

  4. DOption (d)

    Rs. 158000

View answer & explanation

Correct answer

Answer: (c)C.

Rs. 1580000

Why this answer is correct

Given:

A person's salary is deducted by 8% on house rent.

Then 15% of the remaining is spent on household utilities.

20% of the remaining is spent on miscellaneous and children's education.

After these, his savings are Rs 988448.

Calculation:

Let x be the salary of the person.

Remaining salary after house rent = (100% - 8%) of x

Remaining salary after household utilities = (100% - 15%) × (100% - 8%) of x

Remaining salary after miscellaneous and children's education = (100% - 20%) × (100% - 15%) × (100% - 8%) of x

According to the question,

⇒ (100% - 20%) × (100% - 15%) × (100% - 8%) of x = 988448

⇒ (80%) × (85%) × (92%) of x = 988448

⇒ 80100×85100×92100\frac{80}{100} × \frac{85}{100} × \frac{92}{100} × x = 988448

⇒ x = Rs. 15,80,000 

Therefore, "Rs. 15,80,000" is the required answer.

Question 48

What is the difference between the discount of 18% and two successive discounts of 12% and 6% on a bill of Rs. 48900?

  1. AOption (a)

    Rs. 351

  2. BOption (b)

    Rs. 352.08

  3. COption (c)

    Rs. 353

  4. DOption (d)

    Rs. 350

View answer & explanation

Correct answer

Answer: (b)B.

Rs. 352.08

Why this answer is correct

Given:

Bill = Rs. 48900

Case 1: Discount of 18%.

Case 2: two successive discounts of 12% and 6%.

Formula used:

  1. Discount (in Rs.) = Discount (in %) of Marked Price (in Rs.)
  2. Overall discount for two successive discounts of a% and b% = a + b - (ab)/100

Calculations:

Case 1: Discount of 18%.

Case 2: two successive discounts of 12% and 6%.

Overall discount = 12 + 6 - 12×6100\frac{12 × 6}{100} = 18 - 0.72 = 17.28%

According to the question,

The required difference between two discounts = 18% - 17.28% = 0.72%

The overall discount in Rs. = 0.72100\frac{0.72}{100} × 48900 = Rs. 352.08

Therefore, "Rs. 352.08" is the required answer.

Question 49

Ram, Shyam and Dheeraj are in a partnership. They made a profit of Rs. 531000 for the year. Their capital is in the ratio 1/2 : 1/5 : 1/7. What is Shyam's share?

  1. AOption (a)

    Rs. 126000

  2. BOption (b)

    Rs. 315000

  3. COption (c)

    Rs. 90000

  4. DOption (d)

    Rs. 125000

View answer & explanation

Correct answer

Answer: (a)A.

Rs. 126000

Why this answer is correct

Given:

Ram, Shyam and Dheeraj are in a partnership. He made a profit of Rs 531000 for the year.

Their capital is in the ratio 1/2 : 1/5 : 1/7.

Concept:

Ratio in which Profit is distributed among the partners = Ratio in which investment are made among the partners

Calculation:

Ram, Shyam and Dheeraj capital is in the ratio = 1/2 : 1/5 : 1/7

Now multiply each term by 70.

Ram, Shyam and Dheeraj capital is in the ratio = 1/2 × 70 : 1/5 × 70 : 1/7 × 70 = 35 : 14 : 10

The share of profit made by Shyam = 1459\frac{14}{59} × 531000 = Rs. 126000

Therefore, "Rs. 126000" is the required answer.

Question 50

A shopkeeper has a number of products worth Rs. 20000. 1/4 of them are sold at 14% profit. At what percentage profit should the remaining be sold so that the total profit is 16.5%?

  1. AOption (a)

    16.0%

  2. BOption (b)

    17.33%

  3. COption (c)

    15.0%

  4. DOption (d)

    170%

View answer & explanation

Correct answer

Answer: (b)B.

17.33%

Why this answer is correct

Given:

A shopkeeper has a number of products worth Rs 20000.

1/4 of them are sold at 14% profit

The total profit is 16.5%

Concept:

Profit on 1 item = Profit on n items

Calculation:

Let the total number of product = 100

The number of product sold at 14% profit = 1/4 × 100 = 25

Remaining of the product at x% profit = 100 - 25 = 75

According to the question,

⇒ (25 × 14) + (75 × x) = 100 × 16.5

⇒ 350 + (75 × x) = 1650

⇒ 75x = 1300

⇒ x = 17.33%

Therefore, "17.33%" is the required answer.

Question 51

Two numbers are in the ratio 3 : 7. When 12 is added to both the numbers the ratio becomes 9 : 17. What are the numbers?

  1. AOption (a)

    42, 65

  2. BOption (b)

    24, 56

  3. COption (c)

    24, 65

  4. DOption (d)

    56, 24

View answer & explanation

Correct answer

Answer: (b)B.

24, 56

Why this answer is correct

Given:

Case 1:

Two numbers are in the ratio 3 : 7.

Case 2:

When 12 is added to both the numbers the ratio becomes 9 : 17.

Calculation:

Let the numbers are 3x and 7x.

According to the question,

⇒ 3x+127x+12=917\frac{3x + 12}{7x + 12} = \frac{9}{17}

⇒ 51x + 204 = 63x + 108

⇒ 204 - 108 = 63x - 51x

⇒ 96 = 12x

⇒ x = 8

First number = 3x = 24

Second number = 7x = 56

Therefore, "24, 56" are the required answer.

Question 52

A person gives a discount of 16% on the list price. After the discount he makes a 12% profit at Rs. 9408. What is cost price?

  1. AOption (a)

    Rs. 4800 

  2. BOption (b)

    Rs. 8000

  3. COption (c)

    Rs. 4000

  4. DOption (d)

    Rs. 8400

View answer & explanation

Correct answer

Answer: (d)D.

Rs. 8400

Why this answer is correct

Given:

A person gives a discount of 16% on the list price.

After discount, he earns a profit of 12% on Rs 9408.

Formula used:

Selling price = (100% + Profit%) of Cost Price

Calculation:

Let cost price = x

Selling price = Rs. 9408

According to the question,

⇒ x × (100% + 12%) = 9408

⇒ x × 112% = 9408

⇒ 112100\frac{112}{100} × x = 9408 

⇒ x = Rs. 8400

The cost price of the article = Rs. 8400

Therefore, "Rs. 8400" is the required answer.

Question 53

What is the average of prime numbers between 15 to 49?

  1. AOption (a)

    31.89

  2. BOption (b)

    30.89

  3. COption (c)

    31.98

  4. DOption (d)

    31

View answer & explanation

Correct answer

Answer: (a)A.

31.89

Why this answer is correct

Formula:

Average = Sum of ’n’ numbersn\frac{\text {Sum of 'n' numbers}}{\text {n}}

Calculation:

Prime numbers between 15 and 49 are: 17, 19, 23, 29, 31, 37, 41, 43 and 47

The sum of all prime numbers between 15 and 49 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 287

Number of Prime numbers between 15 and 49 = 9

Average = 287/9 ≈ 31.89

Therefore, "31.89" is the required answer.

Question 54

The graph shows the passing percentage of different schools. Which school performs the worst?

  1. AOption (a)

    P and Q

  2. BOption (b)

    P

  3. COption (c)

    Q and R

  4. DOption (d)

    Q

View answer & explanation

Correct answer

Answer: (b)B.

P

Why this answer is correct

Given:

The graph shows the passing percentage of different schools.

Calculation:

According to the question,

The passing percentage of school P of class VI, VII, VIII, IX, and X are 39%, 34%, 31%, 37% and 32% respectively.

The passing percentage of school Q of class VI, VII, VIII, IX, and X are 45%, 41%, 44%, 43% and 41% respectively.

The passing percentage of school R of class VI, VII, VIII, IX, and X are 56%, 58%, 60%, 52% and 57% respectively.

On comparing the above data it can be inferred that school P performs the worst in compare to other schools in every class. 

Therefore, "P" is the required answer.

Question 55

Simplify:

(0.023 × 0.023 × 0.023 + 0.017 × 0.017 × 0.017) / (0.023 × 0.023 - 0.023 × 0.017 + 0.017 × 0.017)

  1. AOption (a)

    0.004

  2. BOption (b)

    0.044

  3. COption (c)

    0.4

  4. DOption (d)

    0.04

View answer & explanation

Correct answer

Answer: (d)D.

0.04

Why this answer is correct

Concept Used:-

Formula for the sum of cube of two values a and b can be given as,

a3+b3=(a+b)(a2−ab+b2)a^3+b^3=(a+b)\left(a^2-a b+b^2\right)

Explanation:-

Given expression is,

(0.023×0.023×0.023+0.017×0.017×0.017)(0.023×0.023−0.023×0.017+0.017×0.017)\frac{(0.023 × 0.023 × 0.023 + 0.017 × 0.017 × 0.017)}{(0.023 × 0.023 - 0.023 × 0.017 + 0.017 × 0.017)}

Let the result of this expression is x. Thus,

x=(0.023×0.023×0.023+0.017×0.017×0.017)(0.023×0.023−0.023×0.017+0.017×0.017)x=\frac{(0.023 × 0.023 × 0.023 + 0.017 × 0.017 × 0.017)}{(0.023 × 0.023 - 0.023 × 0.017 + 0.017 × 0.017)}

In the exponential form terms can be written as,

x=(0.023)3+(0.017)3(0.023)2−0.023×0.017+(0.017)2x=\frac{(0.023)^3 + (0.017)^3}{(0.023)^2 - 0.023 × 0.017 + (0.017)^2 }

In the numerator, there is cube of two values. Use the above mentioned formula and expand it to get,

x=(0.023+0.017)[(0.023)2−0.023×0.017+(0.017)2][(0.023)2−0.023×0.017+(0.017)2]x=\frac{(0.023+0.017)[(0.023)^2-0.023\times 0.017+(0.017)^2]}{[(0.023)^2 - 0.023 × 0.017 + (0.017)^2] }

x=0.023+0.017 x=0.04x=0.023+0.017\ x=0.04

Hence,

(0.023×0.023×0.023+0.017×0.017×0.017)(0.023×0.023−0.023×0.017+0.017×0.017)=0.04\frac{(0.023 × 0.023 × 0.023 + 0.017 × 0.017 × 0.017)}{(0.023 × 0.023 - 0.023 × 0.017 + 0.017 × 0.017)}=0.04

So, the correct option is 4.

Question 56

The table shows the students who applied and qualified from different states. What is the median of qualified students?

Year201020112012
StateApplicationQualifiedApplicationQualifiedApplicationQualified
A314719615542082875231
B161815345581804109256
C399216744101833837255
D373019032782103762238
E240317932611712550260
  1. AOption (a)

    196

  2. BOption (b)

    190

  3. COption (c)

    208

  4. DOption (d)

    183

View answer & explanation

Correct answer

Answer: (a)A.

196

Why this answer is correct

Given: 

The number of qualified students: 196, 153, 167, 190, 179, 208, 180, 183, 210, 171, 231, 256, 255, 238, 260

Formula used:

To find the median of raw discrete data, you can use the following steps:

Organize the data: Arrange the discrete data in ascending or descending order, which means listing the data values from smallest to largest.

Determine the number of data points (n): Count how many data points you have in your dataset.

Calculate the median:

Case 1: If n is odd, the median (M) is the middle value:

M = (n+12)th\left ( \frac{n+1}{2} \right )^{th} value

Case 2: If n is even, the median (M) is the average of the two middle values:

Md = Average of (n2)thvalue+(n2+1)thvalue\left ( \frac{n}{2} \right )^{th} \text {value} + \left ( \frac{n}{2} + 1 \right )^{th} \text {value}

Calculation:

Arrange the data in the ascending order:

153, 167, 171, 179, 180, 183, 190, 196, 208, 210, 231, 238, 255, 256, 260

The number of variables = 15

Median = (15 + 1)/2 = 8

Median = the value of 8th position = 196

Therefore, "196" is the required answer.

Question 57

What is the least number which should be multiplied by 1536 to make a perfect cube?

  1. AOption (a)

    7

  2. BOption (b)

    10

  3. COption (c)

    9

  4. DOption (d)

    8

View answer & explanation

Correct answer

Answer: (c)C.

9

Why this answer is correct

Given:

The given number is 1536.

Calculation:

According to the question,

Prime factorisation of 1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

Make the number in group of three to find the cube root.

⇒ 1536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3

⇒ 1536 = 23 × 23 × 23 × 3

Now, we are required to multiply the number by 32.

⇒ 1536 × 32 = 23 × 23 × 23 × 3 × 32

⇒ 1536 × 32 = 23 × 23 × 23 × 33

∴ 9 should be multiplied by 1536 to make a perfect cube.

Therefore, "9" is the required answer.

Question 58

If 7x1+11−x1+x\frac{7x}{1+\frac{1}{1-\frac{x}{1+x}}} = 2 then what is the value of x?

  1. AOption (a)

    5

  2. BOption (b)

    5/4

  3. COption (c)

    4

  4. DOption (d)

    4/5

View answer & explanation

Correct answer

Answer: (d)D.

4/5

Why this answer is correct

Given:

7x1+11−x1+x\frac{7x}{1+\frac{1}{1-\frac{x}{1+x}}} = 2

Calculation:

According to the question,

⇒ 7x1+11−x1+x\frac{7x}{1+\frac{1}{1-\frac{x}{1+x}}} = 2

⇒ 7x1+11+x−x1+x\frac{7x}{1+\frac{1}{\frac{1+x-x}{1+x}}} = 2

⇒ 7x1+1+x\frac{7x}{1+1+x} = 2

⇒ 7x = 2(2 + x)

⇒ 7x = 4 + 2x

⇒ x = 4/5 

Therefore, "4/5" is the required answer.

Question 59

What is the length of the largest ruler that can accurately measure three equilateral triangles with sides measuring 68 cm, 102 cm and 136 cm?

  1. AOption (a)

    34 cm

  2. BOption (b)

    2 cm

  3. COption (c)

    43 cm

  4. DOption (d)

    44 cm

View answer & explanation

Correct answer

Answer: (a)A.

34 cm

Why this answer is correct

Given:

What is the length of the largest ruler that can accurately measure three equilateral triangles with sides measuring 68 cm, 102 cm and 136 cm?

Three equilateral triangles with sides 68, 102 and 136.

Calculation:

According to the question,

The length of the largest ruler that can accurately measure three equilateral triangles = H.C.F of (68, 102 and 136) 

Now, 

Prime factorisation of 68 = 2 × 2 × 17

Prime factorisation of 102 = 2 × 3 × 17

Prime factorisation of 136 = 2 × 2 × 2 × 17

The highest common factor for 68, 102 and 136 = 2 × 17 = 34

Therefore, The length of the largest ruler that can accurately measure three equilateral triangles is 34 cm.

Therefore, "34 cm" is the required answer.

Question 60

A room is 17 m long, 12 m wide and 10 m tall. What will be the length of the pillar that can be kept in that room?

  1. AOption (a)

    24 m

  2. BOption (b)

    23 m

  3. COption (c)

    23.09 m

  4. DOption (d)

    23.9 m

View answer & explanation

Correct answer

Answer: (c)C.

23.09 m

Why this answer is correct

Given:

A room is 17 m long, 12 m wide and 10 m tall.

Formula used:

Diagonal = l2+b2+h2\sqrt{l^2 + b^2 + h^2} 

Where, 

l = length of the cuboid

b = breadth of the cuboid 

h = height of the cuboid 

Calculation:

According to the question,

The length of the longest pole that can be inserted = 172+122+102=533\sqrt {17^2 + 12^2 + 10^2} = \sqrt {533}  ≈ 23.09 m

Therefore, "23.09" is the required answer.

General English (20 questions)

Question 61

Select the word segment that substitutes (replaces) the bracketed word segment correctly and completes the sentence meaningfully. Select the option 'no correction required' if the sentence is correct as given.

Even though (he do not realize it, he) was responsible for his own problems.

  1. AOption (a)

    he didn’t realize it, he

  2. BOption (b)

    he don't realize it, he

  3. COption (c)

    No correction required.

  4. DOption (d)

    he don't realizes it, he

View answer & explanation

Correct answer

Answer: (a)A.

he didn’t realize it, he

Why this answer is correct

The correct solution is 'he didn't realize it'.

Key Points

  • In the sentence given above, the bracketed portion 'he do not realize it, he'  contains an error.
  • Looking at the full sentence, we know that the sentence is in a simple past tense as the second part of the sentence mentions that 'He was responsible for his own actions'.
  • So, if the sentence is in a simple past thense, the bracketed portion 'he do not realise it' also has to be in a past tense.
  • The correct form would be 'he didn't realize it' where 'didn't' is the past form of the verb 'do'.
  • The whole sentence would become 'Even though he didn't realise it, he was responsible for his own problems'.
  • Hence, the correct answer is Option 1.

Question 62

The question below consist of a set of labelled sentences. Out of four options given, select the most logical order of the sentences which form a paragraph.

Pangaea or Pangea is derived from Ancient Greek pan meaning "all, entire, whole" and Gaia "Mother Earth, land").

P. It was a supercontinent that existed during the late Palaeozoic and early Mesozoic eras.

Q. Pangaea is the most recent supercontinent to have existed and the first to be reconstructed by geologists.

R. It assembled from earlier continental units approximately 335 million years ago, and began to break apart about 175 million years ago.

S. In contrast to the present Earth and its distribution of continental mass, Pangaea was centred on the Equator and surrounded by the superocean Panthalassa.

The forming of supercontinents and their breaking up appears to have been cyclical through Earth's history.

  1. AOption (a)

    PRSQ

  2. BOption (b)

    RSPQ

  3. COption (c)

    QPSR

  4. DOption (d)

    SPRQ

View answer & explanation

Correct answer

Answer: (a)A.

PRSQ

Why this answer is correct

The correct solution is 'PRSQ'

Key Points

  • While arranging jumbled sentences, we must find a common them by analyzing all our options and arrange them accordingly.
  • In the given question above, the passage begins with the static sentence, 'Pangaea or Pangea is derived from Ancient Greek pan meaning "all, entire, whole" and Gaia "Mother Earth, land".
  • This sentence would be followed by Option P, 'It was a supercontinent that existed during the late Palaeozoic and early Mesozoic eras.' as it described the natire of Pangaea which is mentioned in the first sentence.
  • Option R*, 'It assembled from earlier continental units approximately 335 million years ago, and began to break apart about 175 million years ago.'* follows as this sentence also continues to describe what happened to Pangaea.
  • The next sentence is Option S, ' In contrast to the present Earth and its distribution of continental mass, Pangaea was centred on the Equator and surrounded by the superocean Panthalassa' as this entence introduces us to a new element Panthalassa in order to describe the position of Pangaea.
  • The next sentence would be Option Q, 'Pangaea is the most recent supercontinent to have existed and the first to be reconstructed by geologists' as this sentence concludes the description od Pangaea.
  • The passage ends with another static sentence, 'The forming of supercontinents and their breaking up appears to have been cyclical through Earth's history.'
  • Hence the correct answer is Option 1.

Question 63

Select the most appropriate meaning for the word given below.

Axiom

  1. AOption (a)

    A position requiring little or no work but giving the holder status or financial benefit.

  2. BOption (b)

    The action or offence of speaking sacrilegiously about God or sacred things

  3. COption (c)

    Denoting a sin that is not regarded as depriving the soul of divine grace

  4. DOption (d)

    A statement or proposition on which an abstractly defined structure is based

View answer & explanation

Correct answer

Answer: (d)D.

A statement or proposition on which an abstractly defined structure is based

Why this answer is correct

The correct solution is 'Axiom'.

Key Points

  • In word given in the question 'Axiom' means 'A statement or proposition on which an abstractly defined structure is based'
  • Example: A widely held axiom is that those who speak softly have gentle personality. The truth is that they can a more vibrant personality than any other.
  • Option 1, 'A position requiring little or no work but giving the holder status or financial benefit' is a definition of the word Sinecure.
  • Option 2, 'The action or offence of speaking sacrilegiously about God or sacred things' is the definition of Blasphemy.
  • Option 3, 'Denoting a sin that is not regarded as depriving the soul of divine grace' is the definition of the word Venile.
  • Hence the correct answer is Option 4.

Question 64

Select the word segment that substitutes (replaces) the bracketed word segment correctly and completes the sentence meaningfully. Select the option 'no correction required' if the sentence is correct as given.

She settles into the cockpit, (surrounding with dozen of complicating switches and sophisticated gauges,) sitting atop a massive $84 million piece of machinery.

  1. AOption (a)

    surrounding with dozens of complicating switch and sophisticating gauges

  2. BOption (b)

    No correction required

  3. COption (c)

    surrounded around dozens of complicated switches and sophisticated gauges,

  4. DOption (d)

    surrounded by dozens of complicated switches and sophisticated gauges

View answer & explanation

Correct answer

Answer: (d)D.

surrounded by dozens of complicated switches and sophisticated gauges

Why this answer is correct

The correct solution is 'surrounded by dozens of complicated switches and sophisticated gauges'

Key Points

  • In the given sentence above, the bracketed portion 'surrounding with dozen of complicating switches and sophisticated gauges' contains an error.
  • This is because, in the first part of the sentence, it is mentioned that the subject settles into the cockpit. Here she is bound to be surrounded by the machinery.
  • So the correct grammar would be 'surrounded by dozens of complicated switches and sophisticated gauges'.
  • Here we change the word 'surrounding' with 'surrounded' as the word 'surrounding' would mean an action that is going on whioch is not compatible with machinery which are stationary in nature.
  • We also change the word 'with' with 'by' as the term 'with' indicated 'accompaniment' whiole the term 'by' identifies the object surrounding the subject.
  • Hence, the correct answer is Option 4.

Question 65

The sentences below are not complete. There are four options for each question.

Choose the best word to complete the sentence.

In the _______, completing a marathon makes us happier than eating a chocolate pie.

  1. AOption (a)

    fastest run

  2. BOption (b)

    long run

  3. COption (c)

    fast running

  4. DOption (d)

    long duration

View answer & explanation

Correct answer

Answer: (b)B.

long run

Why this answer is correct

The correct solution is 'long run'.

Key Points

  • In the given sentence in the question, we have to fill in the blank with the most appropriate option.
  • Since, the second part of the sentence is comparing between two things, 'competing a marathon' and 'eating a chocolate pie', we have to fill in the blank with the time period for this comparision.
  • Option 2, 'long run' would be the most appropriate option as it means 'a long period of time after the beginning of something'. 
  • Option 1, 'fastest run' is an incorrect option as it is grammatically incorrect.
  • Option 2, 'fast running' is an incorrect option as the sentence is not tying to infer a literal 'run' but a time period.
  • Option 4, 'long duration' indicates a time period but is an incorrect option as it specifically indicate a time period which has a beginning and an end while the sentence above does not have such specified time period.
  • Hence, the correct answer is Option 2.

Question 66

Some parts of a sentence have been jumbled up, and labelled P, Q, R and S. Select the option that gives the correct sequence in which these parts can be rearranged to form a meaningful and grammatically correct sentence.

Photosynthesis is a process

P. convert light energy into chemical energy that,

Q. can later be released to fuel the

R. used by plants and other organisms to

S. through cellular respiration,

organism's metabolic activities.

  1. AOption (a)

    PQRS

  2. BOption (b)

    QSRP

  3. COption (c)

    SRQP

  4. DOption (d)

    RPSQ

View answer & explanation

Correct answer

Answer: (d)D.

RPSQ

Why this answer is correct

The correct solution is 'RPSQ'.

Key Points

  • In order to arrange jumbled sentences, we have to analyse all options first and arrange them in such a way that coherent sentences are formed.
  • In the question above, the passage starts with 'Photosynthesis is a process'.
  • This will be followed by option R which states 'used by plants and other organisms to' as this line started to describe the use of photosynthesis mentiones in the previous line.
  • Option P will come next which states 'Convert light energy into chemical energy that' as this line continues describing the process of photosynthesis.
  • Then option S will be next which states, 'through cellular respiration' as this also follows the pattern of describing the process of photosynthesis.
  • Option Q will be the last as it begins concluding the process of photosynthesis by stating that 'can later be released to fuel the'.
  • The sentence ends with the ststic line 'organism's metabolic activities'.
  • Hence the correct answer is Option 4.

Question 67

Select the word that is similar in meaning (SYNONYM) to the word given below.

RAPACIOUSNESS

  1. AOption (a)

    PROFUSION

  2. BOption (b)

    MUNIFICENCE

  3. COption (c)

    VORACIOUSNESS

  4. DOption (d)

    BENEFICENCE

View answer & explanation

Correct answer

Answer: (c)C.

VORACIOUSNESS

Why this answer is correct

The correct solution is 'VORACIOUSNESS'. 

Key Points

  • In the question above, we have to find a word that is similar to 'Rapaciousness'.
  • The word 'Rapaciousness' means 'the quality of having or showing a strong wish to take things for yourself, usually using unfair methods or force'.
  • Lets us look at the meaning of the options to find the synonym:
  • Option 1, 'profusion' means 'an abundance or large quantity of something' and is not similar to rapaciousness.
  • Option 2, 'Munificence' means 'the quality or action of being extremely generous.' and is not similar to Rapaciousness.
  • Option 3, 'Voraciousness' means 'the state of being very eager to have a lot of something' and is similar to the meaning of Rapaciousness and is the correct answer.
  • Option 4, 'beneficence' is 'the quality or state of doing or producing good ' and is not similar to the meaning of rapaciousness.
  • Hence, the correct answer is Option 3.

Question 68

Four words are given, out of which only one word is spelt correctly. Choose the correctly spelt word.

  1. AOption (a)

    LAISON

  2. BOption (b)

    LAISCION

  3. COption (c)

    LIASION

  4. DOption (d)

    LIAISON

View answer & explanation

Correct answer

Answer: (d)D.

LIAISON

Why this answer is correct

The correct solution is 'Liaison'.

Key Points

  • In the above question, we have to pick the correctly spelt word from the options .
  • The correctly spelt word is Option 4, 'Liaison'.
  • The word 'liaison' means 'communication or cooperation which facilitates a close working relationship between people or organizations'
  • Example: James works as a liaison between the student body and the teachers.
  • The other options, 'Laison', 'Laiscion' and ;'Liason' are all incorrect spelling of the word Lisison.
  • Hence, the correct answer is Option 4.

Question 69

Select the word that is similar in meaning (SYNONYM) to the word given below.

GRUDGE

  1. AOption (a)

    RAPPORT

  2. BOption (b)

    CONCORD

  3. COption (c)

    MALICE

  4. DOption (d)

    COMMUNION

View answer & explanation

Correct answer

Answer: (c)C.

MALICE

Why this answer is correct

The correct solution is 'MALICE'. 

Key Points

  • In the question above, the given word 'Grudge' means 'a persistent feeling of ill will or resentment resulting from a past insult or injury'
  • In order to find a meaning similar to the word, let us look at the meaning of the options:
  • Option 1, 'Rapport' meansp ' a friendly, harmonious relationship' and is opposite to the meaning of the word 'grudge'.
  • Option 2, 'Concord' means ' agreement and peace between countries and people' and is not similar to the meaning of the word 'grudge'.
  • Option 3, 'Malice' means ' desire to inflict injury, harm, or suffering on another, either because of a hostile impulse or out of deep-seated meanness' and is similar to the word 'grudge'
  • Option 4, 'Communion' means ' an act or instance of sharing ' and is not similar to the word 'grudge'.
  • Hence the correct answer is Option 3.

Question 70

Fill in the blank with the most appropriate choice.

Still another _________ symptom has to be considered.

  1. AOption (a)

    overwhelming

  2. BOption (b)

    critical

  3. COption (c)

    violent

  4. DOption (d)

    tuberous

View answer & explanation

Correct answer

Answer: (b)B.

critical

Why this answer is correct

The correct solution is 'critical'. 

Key Points

  • In the question given above, we have to find a word from the option which is most suited to fill in the blank.
  • Looking at the sentence, we have to find  an adjective that qualifies the word symptom.
  • The most appropriate adjective would be 'critical' which means 'having the potential to become disastrous'.
  • This would make the sentence 'Stil another critical symptom has to be considered'. 
  • Option 1, 'overwhelming'  means '. very great or very large' and is not appropriate to describe the noun 'symptom'.
  • Option 3, 'violent' means 'using or involving force to hurt or attack' and is not suitable to define the noun 'symptom'.
  • Option 4*, 'tuberous*' means 'having, looking like, or relating to a tuber ( the swollen underground stem or root of a plant such as a potato)' and is not the most appropriate the qualify the noun 'symptom'.
  • Hence, the correct answer is Option 2.

Question 71

The sentence below has been divided into three parts. Select the part of the sentence that has an error. If the sentence has no error, select the option 'No Error'.

But intellectual madness would have / resulted from a development that followed / the acceptance of it's own kind of art

  1. AOption (a)

    But intellectual madness would have

  2. BOption (b)

    the acceptance of it's own kind of art

  3. COption (c)

    resulted from a development that followed

  4. DOption (d)

    No Error

View answer & explanation

Correct answer

Answer: (b)B.

the acceptance of it's own kind of art

Why this answer is correct

The correct solution is 'the acceptance of it's own kind of art' 

Key Points

  • In the given sentence above, the third section 'the accpetance of it's own kind of art' contains an error.
  • This is because at the beginning of the sentence it mentions the subject 'intellectual madness'.
  • the same subject is again referred in the third section of the sentence and using the words 'it's own' would be wrong as it does not point to the same subject.
  • The correct way would be to use the word 'this' instead of 'it's own' as it would be referring to the same subject even in the third section.
  • The correct sentence would thus be 'But intellectual madness would have  resulted from a development that followed  the acceptance of this kind of art'.
  • Hence, the correct answer is Option 2.

Question 72

Select the most appropriate meaning of the given proverb.

The rats are leaving the sinking ship

  1. AOption (a)

    In an emergency you do things that you would not otherwise do

  2. BOption (b)

    Don’t expect a good event to happen before it has actually happened.

  3. COption (c)

    Turning away from failing or fleeing from an unpleasant situation

  4. DOption (d)

    You shouldn’t be too sure of something, even if the prospect is good.

View answer & explanation

Correct answer

Answer: (c)C.

Turning away from failing or fleeing from an unpleasant situation

Why this answer is correct

The correct solution is 'Turning away from failing or fleeing from an unpleasant situation'. 

Key Points

  • A proverb is a short, well-known pithy saying, stating a general truth or piece of advice.
  • The given proverb in the question 'The rats are leaving the sinking ship' does not literally mean rats leaving a sinking ship.
  • It instead means 'turning away from failing or fleeing an unpleasant situation'. 
  • Option 1, 'In an emergency you do things that you would not otherwise do' does not have a proverbial expression.
  • Option 2, 'Don’t expect a good event to happen before it has actually happened' is the expression for the idiom 'don't count your chickens before they hatch'.
  • Option 4, 'You shouldn’t be too sure of something, even if the prospect is good.' is also an expression for 'don't count your chocken before they hatch'
  • Hence, the correct answer is Option 3.

Question 73

Select the most appropriate meaning of the given idiom.

Burn your bridges

  1. AOption (a)

    To destroy a bridge or path behind oneself.

  2. BOption (b)

    Overcome your emotions and move on in life

  3. COption (c)

    To destroy your enemies

  4. DOption (d)

    To destroy confidential information

View answer & explanation

Correct answer

Answer: (a)A.

To destroy a bridge or path behind oneself.

Why this answer is correct

The correct solution is 'To destroy a bridge or path behind oneself'. 

Key Points

  • An idiom is a group of words established by usage as having a meaning not deducible from those of the individual words.
  • The given idiom in the question 'Burn your bridges' means 'To destroy a bridge or path behind oneself'.
  • In simpler words, it means 'make return to previous situation impossible.'
  • Example: She burned her bridges with the whole family.
  • ​Options 2, 3 and 4 do not have idiomatical expressions .
  • Hence, the correct answer is Option 1.

Question 74

The sentence below has been divided into three parts. Select the part of the sentence that has an error. If the sentence has no error, select the option 'No Error'.

This phenomena made its appearance / even during the short lived period of / the Soviet republic in Bavaria.

  1. AOption (a)

    No Error

  2. BOption (b)

    even during the short lived period of

  3. COption (c)

    the Soviet republic in Bavaria

  4. DOption (d)

    This phenomena made its appearance

View answer & explanation

Correct answer

Answer: (d)D.

This phenomena made its appearance

Why this answer is correct

The correct solution is 'This phenomena made its appearance'.

Key Points

  • In the sentence given above, the first section 'This phenomena made its appearance' contains an error.
  • This section of the sentence is erronous because the word 'this' is a singular adjective used to  indicate a person, place, thing etc.
  • While the word 'this' is singular, the first sentence used the plural noun 'phenomena' which is grammatically incorrect.
  • The singular form of the word phenomena would be phenomenon which means 'something that exists and can be seen, felt, tasted, etc., especially something unusual or interesting'.
  • So the correct sentence would be 'This phenomenon made its appearance even during the short lived period of the Soviet republic in Bavaria'.
  • Hence, the correct answer is option 4.

Question 75

Select the most appropriate antonym of the given word. 

Gratifying

  1. AOption (a)

    Dreary

  2. BOption (b)

    Eventful

  3. COption (c)

    Pleasant

  4. DOption (d)

    Delightful

View answer & explanation

Correct answer

Answer: (a)A.

Dreary

Why this answer is correct

The correct solution is 'Dreary'. 

Key Points

  • The word given in the question 'Gratifying' means 'pleasing and satisfying'.
  • In order to find a word with opposite meaning, let us look at the meaning of the options:
  • Option 1, 'Dreary' means 'sad or dull' and is the correct answer as its meaning is opposite to the meaning of gratifying'.
  • Option 2, 'Eventful' means 'full of events or incidents' and is not the meaning opposite to the word gratifying.
  • Option 3, *'*Pleasant' means 'giving a sense of happy satisfaction or enjoyment.' and is an incorrect answer as it is the synonym of the word gratifying.
  • Option 4, 'Delightful' means 'very pleasant, attractive, or enjoyable' and is also the synonym of graticying and an incorrect answer.
  • Hence, the correct answer is Option 1.

Read the passage carefully and choose the best answer to each question out of the four alternatives.

Bohemianism is the practice of an unconventional lifestyle, often in the company of like-minded people and with few permanent ties. It involves musical, artistic, literary, or spiritual pursuits. In this context, bohemians may be wanderers, adventurers, or vagabonds. This use of the word in the English language was imported from French in the mid 19th century and was used to describe the non-traditional lifestyles of artists, writers, journalists, musicians, and actors in major European cities. Bohemians were associated with unorthodox or anti-establishment political or social viewpoints, which often were expressed through free love, frugality, and—in some cases—simple living, van-dwelling or voluntary poverty. A more economically privileged, wealthy, or even aristocratic bohemian circle is sometimes referred to as haute boheme (literally "high Bohemia").

The term bohemianism emerged in France in the early 19th century, when artists and creators began to concentrate in the lower-rent, lower class, Romani neighbourhoods. Bohemian was a common term for the Romani people of France, who were mistakenly thought to have reached France in the 15th century via Bohemia (the western part of modern Czech Republic). Bohemianism and its adjective bohemian in this specific context are not connected to the native inhabitants of this region.

Question 76

Three assertions are given below (A, B & C) on the basis of your understanding of the passage, which one of the options is incorrect?

A. Bohemians were unorthodox but had strongly supported political and social viewpoints.

B. Bohemian was a common term for the Romani people of France.

C. Some of the Bohemian people choose to live a life of poverty despite being wealthy.

  1. AOption (a)

    A is correct

  2. BOption (b)

    C is correct

  3. COption (c)

    B is correct

  4. DOption (d)

    B & C are correct

View answer & explanation

Correct answer

Answer: (a)A.

A is correct

Why this answer is correct

The correct solution is '. Bohemians were unorthodox but had strongly supported political and social viewpoints.'

Key Points

  • The question above asks us to select an option which is incorrect.
  • Option A, ' Bohemians were unorthodox but had strongly supported political and social viewpoints' is an incorrect statement as the fourth sentence of the first paragraph mentions that ' Bohemians were associated with unorthodox or anti-establishment political or social viewpoints,'.
  • Comparing the two sentences, we know that Option A is an incorrect statement.
  • Option B, 'Bohemian was a common term for the Romani people of France' is a correct statement as found in the second sentence of the second paragraph, 'Bohemian was a common term for the Romani people of France'.
  • Option C, 'Some of the Bohemian people choose to live a life of poverty despite being wealthy'. is also a correct statement as found in fourth sentence of the first paragraph ' Bohemians were associated with unorthodox or anti-establishment political or social viewpoints, which often were expressed through free love, frugality, and—in some cases—simple living, van-dwelling or voluntary poverty'. Here the sentence mentions 'voluntary poverty' whichb indicates that people chose o live a live of poverty despite being wealthy.
  • Hence, the correct answer is Option 1.

Question 77

On the basis of your reading of the above passage, what is the meaning of 'vandwelling'?

  1. AOption (a)

    People who are not stationed at one location

  2. BOption (b)

    Nomadic lifestyle

  3. COption (c)

    Van converted to home, people live in the van and travel around

  4. DOption (d)

    Rich people travelling in caravan

View answer & explanation

Correct answer

Answer: (c)C.

Van converted to home, people live in the van and travel around

Why this answer is correct

The correct solution is 'Van converted to home, people live in the van and travel around'. 

Key Points

  • THe word van-dwelling can be found from the fourth sentence of the first paragraph*, 'Bohemians were associated with unorthodox or anti-establishment political or social viewpoints, which often were expressed through free love, frugality, and—in some cases—simple living, van-dwelling or voluntary poverty'.*
  • Here, van-dwelling is used to describe the life led by the bohemians amongs many other practices.
  • Van -dwelling here refers to the living in a van converted to a home, where people live and travel around.
  • Hence the correct answer is Option 3.

Question 78

Three assertions are given below (A, B & C) on the basis of your understanding of the passage, which one of the options is correct?

A. The use of the word bohemians as wanderers was imported in the English language from French in the mid 19th century.

B. Haute bohème means rich Bohemian people.

C. Bohemianism was started in the 15th century by the native inhabitants of Bohemia in France

  1. AOption (a)

     Only C is correct.

  2. BOption (b)

    Only A is correct

  3. COption (c)

    C is incorrect.

  4. DOption (d)

    Only B is correct

View answer & explanation

Correct answer

Answer: (c)C.

C is incorrect.

Why this answer is correct

The correct solution is 'C is incorrect'. 

Key Points

  • Let us analyse the given statements to see whether they are correct or incorrect:
  • Option A, 'The use of the word bohemians as wanderers was imported in the English language from French in the mid 19th century' is a correct stetement  as found in the second sentence of the first paragraph, 'This use of the word in the English language was imported from French in the mid 19th century and was used to describe the non-traditional lifestyles of artists, writers, journalists, musicians, and actors in major European cities'.,
  • Option B, ' Haute bohème means rich Bohemian people' is a correct statement as found in the last sentence of the first paragraph ' A more economically privileged, wealthy, or even aristocratic bohemian circle is sometimes referred to as haute boheme (literally "high Bohemia").'.
  • Option C, 'Bohemianism was started in the15th century by the native inhabitants of Bohemia in France' is an incorrect statement as the first sentence of the second paragraph mentions that 'The term bohemianism emerged in France in the early 19th century, when artists and creators began to concentrate in the lower-rent, lower class, Romani neighbourhoods. Bohemian was a common term for the Romani people of France'. .
  • Option A and B are correct and only Option C is an incorrect statement.
  • HEnce the correct answer is Option 3.

Question 79

According to the passage, what would mean the opposite of 'economically privileged' from the given options?

  1. AOption (a)

    Sceptical

  2. BOption (b)

    Superior

  3. COption (c)

    Destitute

  4. DOption (d)

    Affluent

View answer & explanation

Correct answer

Answer: (c)C.

Destitute

Why this answer is correct

The correct solution is 'destitute'. 

Key Points

  • In this question we have to find a word Opposite in meaning to the word 'Economically priviledged'.
  • The term Economically priviledged means 'having enough resources to be able to take on the opportunities that life has given you, '.
  • Let us look at the meaning of the options given:
  • Option 1, 'Sceptical' means 'not easily convinced' and is an incorrect option.
  • Option 2, 'Superior' means 'higher in rank, status, or quality.' and is an incorrect option.
  • Option 3, 'Destitute' means 'lacking possessions and resources' and is the correct answer.
  • Option 4, 'Affluent' means 'having a great deal of money' and is an incorrect option.
  • Hence, the correct answer is Option 3.

Question 80

According to the passage, which of the following options define bohemianism aptly?

  1. AOption (a)

    Journeying

  2. BOption (b)

    Gratification

  3. COption (c)

    Leisure

  4. DOption (d)

    Extravagant

View answer & explanation

Correct answer

Answer: (a)A.

Journeying

Why this answer is correct

The correct solution is 'Journeying' 

Key Points

  • The answer to thid question can be derived from the first two sentences of the first paragraph, 'Bohemianism is the practice of an unconventional lifestyle, often in the company of like-minded people and with few permanent ties. It involves musical, artistic, literary, or spiritual pursuits. In this context, bohemians may be wanderers, adventurers, or vagabonds'.
  • Here it is mentioned that bohemians have 'few permanent ties' and they are 'wanderers', 'adventurers' and 'vagabonds' which fits the description of 'Journeying'.
  • Hence the correct answer is Option 1.

General Hindi (20 questions)

Question 81

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए वाक्य के वृत्ति के भेद का सही विकल्प है।

क्या पता, मेरा मकान तुम्हे पसंद भी आए।

  1. AOption (a)

    संदेहार्थ

  2. BOption (b)

    निश्चयार्थ

  3. COption (c)

    संभावनार्थ

  4. DOption (d)

    संकेतार्थ

View answer & explanation

Correct answer

Answer: (c)C.

संभावनार्थ

Why this answer is correct

दिए गए वाक्य के वृत्ति के भेद का सही विकल्प "संभवनार्थ" है।

Key Points 

  • दिए गए वाक्य में संभावना का  बोध हो रहा  है, अतः यहाँ संभावनार्थ  होगा ।
  • क्रिया के जिस रुप से किसी कार्य के होने की संभावना प्रकट हो, वहाँ ‘संभावनार्थक’ होता है।

Important Points

  • सन्देहार्थ - क्रिया के जिस रुप से कार्य के होने में संदेह हो।
  • **जैसे -**वह मुझे याद करता होगा।
  • निश्चयार्थक - क्रिया के जिस रुप से कार्य के होने या न होने का अर्थ निश्चित रुप से प्रकट हो,
  • वहाँ ‘निश्चयार्थक’ होता है ।
  • जैसे - विवेक विद्यालय जाता है ।
  • संकेतार्थ - जिस क्रिया रुप में एक काम का होना दूसरे कार्य पर निर्भर हो, उसे ‘संकेतार्थ’ कहते है
  • यहाँ कार्य –कारण एक –दूसरे की ओर संकेत करते है ।
  • जैसे - वह आता तो उसे भी वरदान मिल जाता ।

Additional Information

  • वृत्ति को ‘क्रियार्थ’ भी कहते है, क्रियार्थ का अर्थ है – क्रिया का अर्थ या प्रयोजन ।
  • वृत्ति वक्ता की वह मनःस्थिति है, जो वाक्य में क्रिया रूपों द्वारा व्यक्त होती है।
  • जो कार्य या व्यापार लौकिक जगत में घटित न हुई हो, वरन जो वक्ता के मस्तिष्क में इच्छा,
  • संभावना, अनुमान आदि के रूप में निहित हो, उसका संबंध वृत्ति से होता है।

Question 82

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए मुहावरे का सही अर्थ हो।

छाती पर मूँग या कोदो दलना

  1. AOption (a)

    अनुचित शब्द कहना

  2. BOption (b)

    ईर्ष्या से हृदय जलना

  3. COption (c)

    किसी को कष्ट देना

  4. DOption (d)

    साहसिक कार्य

View answer & explanation

Correct answer

Answer: (c)C.

किसी को कष्ट देना

Why this answer is correct

दिए गए विकल्पों में से 'छाती पर मूँग या कोदो दलना' मुहावरे का सही अर्थ  "किसी को कष्ट देना"   है। 

  • वाक्य प्रयोग - आलोक के घर प्रिया, दिन-रात आलोक की विधवा माँ की छाती पर मूँग दल रही है।

Key Pointsअन्य विकल्प - 

मुहावरेअर्थवाक्य प्रयोग
जबान चलानाअनुचित शब्द कहनासीमा बहुत जबान चलाती है, उससे कौन बात करेगा?
जान पर खेलनासाहसिक कार्यभारतीय सेना आतंकवादी से नहीं डरती और सदा जान पर खेलने लिए तैयार रहती है
छाती पर साँप लोटनाईर्ष्या से हृदय जलनाजब पड़ोसी ने नई कार ली तो शेखर की छाती पर साँप लोट गया।

Additional Information

  • ‘मुहावरा’ शब्द अरबी भाषा का है जिसका अर्थ है ‘अभ्यास होना’ या आदी होना’।
  • इस प्रकार मुहावरा शब्द अपने–आप में स्वयं मुहावरा है,
  • क्योंकि यह अपने सामान्य अर्थ को छोड़कर असामान्य अर्थ प्रकट करता है।

कुछ मुहावरे - 

मुहावरेअर्थवाक्य प्रयोग
गाजर-मूली समझनातुच्छ समझनामोहन ने कहा कि उसे कोई गाजर-मूली न समझे, वह बहुत कुछ कर सकता है।
चादर से बाहर पैर पसारनाआमदनी से अधिक खर्च करनाचादर से बाहर पैर पसारोगे तो कष्ट पाओगे।
छक्के छुड़ानाहरानाभारत ने युद्ध में पाक के छक्के छुड़ा दिए।
गुड़ गोबर करनाबनाया काम बिगाड़नावीरू ने जरा-सा बोलकर सब गुड़-गोबर कर दिया।

Question 83

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो विराम चिह्न युक्त वाक्य का सही विकल्प है।

  1. AOption (a)

    'व्‍याकरण पल्लव " पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है

  2. BOption (b)

    'व्‍याकरण पल्लव  पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।

  3. COption (c)

    'व्‍याकरण पल्लव " पुस्तक आई सी .एस. ई बोर्ड में पढ़ाया जाता है।

  4. DOption (d)

    'व्‍याकरण पल्लव' पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।

View answer & explanation

Correct answer

Answer: (d)D.

'व्‍याकरण पल्लव' पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।

Why this answer is correct

दिए गए विकल्पों में से विराम चिह्न युक्त वाक्य का सही विकल्प है-

 'व्‍याकरण पल्लव " पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।

Key Points

  • इस वाक्य में , उद्धरण चिन्ह ( ' ' )  ( '' '' ), संक्षेप सूचक चिन्ह( . ) ,
  • और पूर्ण विराम ( । ) का प्रयोग उचित रुप से हुआ है।
  • जबकि अन्य विकल्पों में इनका प्रयोग उचित रूप से नही हुआ है।

Important Points

पूर्ण विराम-(।)- लिखते वक़्त वाक्य ख़त्म होने के बाद पूर्ण विराम लगाते है।
( विस्मायवाचक वाक्यों और प्रश्नवाचक वाक्यों को छोड़ कर )
सूचक चिन्ह( . ) - किसी बड़े अंश का संक्षिप्त रूप लिखने के लिए लाघव चिन्ह/ संक्षेपसूचक का प्रयोग किया जाता है।
अवतरण या उदाहरण चिन्ह-( “…” )- किसी वाक्य के खास शब्द पर जोर देने के लिए,
अवतरण चिह्न (”…”) का प्रयोग किया जाता है।

Additional Information

  • विराम का अर्थ “रुकना” है। लिखित भाषा में प्रयोग किए जाने वाले लिखित चिन्हों को विराम चिन्ह कहते है।
  • लेखक के भाव बोध को सुबोध और सरल बनाने के लिए विराम चिह्नों की आवश्यकता होती है।

हिंदी में प्रचलित प्रमुख विराम चिह्न -

विराम चिन्ह का नामविराम- चिन्ह
पूर्ण विराम(।)
अर्द्ध विराम(;)
अल्प विराम(,)
उप विराम(:)
प्रश्नवाचक चिन्ह(?)
योजक चिन्ह(–)
कोष्ठक चिन्ह()
अवतरण या उदहारणचिन्ह( “…” )
विस्मयादिबोदक चिह्न[ ! ]
लाघव चिन्ह/ संक्षेपसूचक(०)
निर्देशक चिह्न[ — ]
विवरण चिन्ह( :- )
विस्मरण चिन्ह या त्रुटिपूरक चिन्ह/हंसपद(^)

Question 84

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो विराम चिह्न युक्त वाक्य का सही विकल्प है।

  1. AOption (a)

    अपा‍हिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ "

  2. BOption (b)

    अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।

  3. COption (c)

    अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।''

  4. DOption (d)

    ​अपाहिज ने हाथ जोड़कर कहा बाबा, मैं दुखिया हूँ।''

View answer & explanation

Correct answer

Answer: (c)C.

अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।''

Why this answer is correct

दिए गए विकल्पों में से विराम चिह्न युक्त वाक्य का सही विकल्प है- 

अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।''

Key Points

  • दिए गए वाक्य में निर्देशक चिह्न (–), अल्प विराम-(,), अवतरण या उद्धरण  चिन्ह-( “…” ) और पूर्ण विराम-(।)
  • का प्रयोग उचित रूप से हो रहा है, जबकि अन्य विकल्पों में इनका प्रयोग उचित रूप से नही हो रहा है।

Important Points

पूर्ण विराम-(।)-  लिखते वक़्त वाक्य ख़त्म होने के बाद पूर्ण विराम लगाते है। (विस्मयवाचक वाक्यों और प्रश्नवाचक वाक्यों को छोड़ कर)
अल्प विराम-(,)- वाक्य के बीच में विराम उत्पन्न करने वाले विराम चिन्ह को अल्प विराम कहते हैं। किसी वाक्य में दो या दो से ज़्यादा समान पद वाले शब्दों में अल्प विराम का प्रयोग किया जाता है।
अवतरण या उद्धरण  चिन्ह-( “…” )- किसी वाक्य के खास शब्द पर जोर देने के लिए अवतरण चिह्न (”…”) का प्रयोग किया जाता है।
निर्देशक चिह्न (–) - किसी व्यक्ति के द्वारा कहे गए कथन  को अधिकृत करने से पहले निर्देशक चिह्न का प्रयोग किया जाता है।

Additional Information

  • विराम का अर्थ “रुकना” है। लिखित भाषा में प्रयोग किए जाने वाले लिखित चिन्हों को विराम चिन्ह कहते है।
  • लेखक के भाव बोध को सुबोध और सरल बनाने के लिए विराम चिह्नों की आवश्यकता होती है।

हिंदी में प्रचलित प्रमुख विराम चिह्न - 

विराम चिन्ह का नामविराम-चिन्ह
पूर्ण विराम(।)
अर्द्ध विराम(;)
अल्प विराम(,)
उप विराम(:)
प्रश्नवाचक चिन्ह(?)
योजक चिन्ह(–)
कोष्ठक चिन्ह()
अवतरण या उद्धरण चिन्ह( “…” )
विस्मयादिबोदक चिह्न[ ! ]
लाघव चिन्ह/ संक्षेपसूचक(०)
निर्देशक चिह्न[ — ]
विवरण चिन्ह( :- )
विस्मरण चिन्ह या त्रुटिपूरक चिन्ह/हंसपद(^)

Question 85

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए वाक्य के काल भेद का सही विकल्प है।

महिमा चली गई होगी।

  1. AOption (a)

    अपूर्ण वर्तमान काल

  2. BOption (b)

    हेतुहेतुमद भविष्य काल

  3. COption (c)

    संदिग्ध भूतकाल

  4. DOption (d)

    सामान्य भूतकाल

View answer & explanation

Correct answer

Answer: (c)C.

संदिग्ध भूतकाल

Why this answer is correct

दिए गए वाक्य के काल भेद का सही विकल्प "संदिग्ध भूतकाल" है।

Key Points

  • भूतकाल समय में "महिमा चली गई होगी या नही" पूर्ण रूप से पता नहीं है, इस बात में संदेह हो रहा है,
  • इसलिए वह संदिग्ध भूतकाल  है।
  • भूतकाल की जिस क्रिया से कार्य होने में अनिश्चितता अथवा संदेह प्रकट होता है वह क्रिया संदिग्ध भूतकाल कहलाती है।
  • जिस क्रिया में संदेह बना रहता है कि भूतकाल में कार्य पूरा हुआ की नहीं हुआ है।

Additional Information

  • क्रिया के जिस रूप से कार्य करने या होने के समय का ज्ञान होता है उसे 'काल' कहते है।

काल के तीन भेद होते है-

कालपरिभाषाउदाहरण
वर्तमान कालक्रिया के जिस रूप से वर्तमान में चल रहे समय का बोध होता है, उसे वर्तमान काल कहते है।पिता जी समाचार सुन रहे हैं।
भूतकालक्रिया के जिस रूप से बीते हुए समय का बोध होता है, उसे भूतकाल कहते है।वह खा चुका था।
भविष्यत कालभविष्य में होनेवाली क्रिया को भविष्यतकाल की क्रिया कहते है।वह कल घर जाएगा।

Question 86

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए शब्द -युग्‍म का सही अर्थ वाला विकल्प हो।

अजर - अजिर

  1. AOption (a)

    देवता ,आँगन

  2. BOption (b)

    हृदय, दूसरा

  3. COption (c)

    ऋण, चिंता

  4. DOption (d)

    सेना, काँटा

View answer & explanation

Correct answer

Answer: (a)A.

देवता ,आँगन

Why this answer is correct

दिए गए शब्द -युग्‍म का सही अर्थ वाला विकल्प " ​देवता ,आँगन" है ।

Key Points

  • अजर का अर्थ यहां देवता से है जबकि अजिर का अर्थ आँगन है।
  • इस प्रकार 'अजर-अजिर' शब्द युग्म का अर्थ है 'देवता-आँगन' है।

Additional Information

  • हिंदी व्याकरण में अनेक प्रकार के ऐसे शब्द होते हैं जिन का उच्चारण एक समान होता है।
  • परंतु उनके अर्थ अलग-अलग होते हैं। तो इसे युग्म शब्द कहते हैं।

जैसे - 

शब्द अर्थशब्द अर्थ
अन्न-अनाजअन्य – दूसरा
कटक - सेनाकंटक - काँटा
ओर - तरफऔर -  दूसरा
उर - हृदयऊरू - जाँघ
उद्वेक - वृद्धिउद्वेग - चिन्ता

Question 87

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए शब्द का सही तत्सम शब्द है।

खोपड़ी

  1. AOption (a)

    लोक

  2. BOption (b)

    व्‍याघ्र

  3. COption (c)

    लवंग

  4. DOption (d)

    खर्पर

View answer & explanation

Correct answer

Answer: (d)D.

खर्पर

Why this answer is correct

दिए गए विकल्पों में से "खोपड़ी" शब्द का सही तत्सम शब्द "खर्पर" है। 

 Key Points"खोपड़ी" तद्भव शब्द है इसका तत्सम रूप "खर्पर" है। 

अन्य विकल्प - 

तत्सम शब्दतद्भव शब्द
लोकलोग
व्याघ्रबाघ
लवंगलौंग

Additional Information

  • तत्सम शब्द-  ऐसे शब्द जिनकी उत्पत्ति संस्कृत भाषा में हुई ओर वे हिन्दी भाषा में बिना,
  • किसी परिवर्तन के प्रयोग में आने लगे, ऐसे शब्द तत्सम शब्द कहलाते हैं।
  • जैसे- कवि, माता, विद्या, नदी, फल, पुष्प, पुस्तक, पृथ्वी, क्षेत्र, कार्य, मृत्यु आदि।
  • तद्भव शब्द - ऐसे शब्द जो संस्कृत भाषा से उत्पन्न होते हैं,
  • लेकिन वो रूप बदलकर हिन्दी में आ गए हों, ऐसे शब्द तद्भव शब्द कहलाते हैं।
  • जैसे-  दुग्ध —-> दूध
  • अग्नि —-> आग
  • कार्य —> काम
  • कर्पूर —> कपूर

Question 88

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए शब्द का सही समानार्थी नहीं है।

कुसुमाकर

  1. AOption (a)

    ऋतुराज

  2. BOption (b)

    मधु

  3. COption (c)

    माधव

  4. DOption (d)

    इन्द्रलोक

View answer & explanation

Correct answer

Answer: (d)D.

इन्द्रलोक

Why this answer is correct

दिए गए विकल्पों में से "इन्द्रलोक" शब्द कुसुमाकर का समानार्थी शब्द नहीं है।

Key Points

  • कुसुमाकर के समानार्थी शब्द हैं - वसंत, बगीचा, मधु,  ऋतुराज, माधव, फुलवारी, बाग, पुष्पवाटिका आदि।
  • इंद्रलोक के समानार्थी शब्द हैं - इंद्रपुरी , अमरावती , देवपुरी , देवलोक  आदि।
  • समान अर्थ प्रदान करने वाले शब्द पर्यायवाची शब्द अथवा समानार्थक शब्द कहलाते हैं।

Additional Informationकुछ समानार्थी शब्द - 

  • अतिथि- मेहमान ,पाहुन ,आगंतुक, अभ्यागत।
  • घड़ा- घट, कलश, कुंभ, घटक, कुट।
  • छाछ- गोरस, मठा, दधि स्वेद, मट्ठा।
  • जहर- हलाहल, विष, गरल, कालकूट, गर।
  • पथ- मग, मार्ग, राह, पंथ, रास्ता।
  • बंजर- अनुपजाऊ, अनुर्वर, ऊसर।
  • रात्रि -  राका, निशा, रजनी, यामिनी, विभावरी।
  • आँख- नेत्र, दृग, नयन, लोचन, चक्षु, अक्षि, अंबक, दृष्टि, विलोचन।
  • शिक्षक- गुरु, अध्यापक, आचार्य, उपाध्याय।

Question 89

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो शुद्ध वाक्य का सही विकल्प हो।

  1. AOption (a)

    लक्ष्‍मीबाई वीर थी।

  2. BOption (b)

    मीरा विलाप करके रो रही थी।

  3. COption (c)

    मैं आगामी रविवार मुंबई जाऊंगा।

  4. DOption (d)

    उसने ऐसा कार्य किया कि सब विस्मय हो गए।

View answer & explanation

Correct answer

Answer: (c)C.

मैं आगामी रविवार मुंबई जाऊंगा।

Why this answer is correct

दिए गए विकल्पों में से शुद्ध वाक्य का सही विकल्प है - मैं आगामी रविवार मुंबई जाऊंगा।

Key Pointsअन्य विकल्प -

अशुद्ध वाक्यशुद्ध वाक्य
- लक्ष्‍मीबाई वीर थी।वाक्य में लिंग संबंधी अशुद्धि है। अतः वीर के स्थान पर  वीरांगना होगा। - लक्ष्‍मीबाई वीरांगना थी।
- मीरा विलाप करके रो रही थी।वाक्य में पुनरावृत्ति की अशुद्धि है। - मीरा विलाप कर रही थी। - मीरा रो रही थी।
- उसने ऐसा कार्य किया कि सब विस्मय हो गए।वाक्य में विस्मय के स्थान पर विस्मित  होगा।( क्रिया संबंधी अशुद्धि) - उसने ऐसा कार्य किया कि सब विस्मित हो गए।

Additional Information

  • शब्द शुद्धि के साथ वाक्य शुद्धि का भी भाषा में महत्त्वपूर्ण स्थान होता है।
  • वाक्य में अनावश्यक शब्द प्रयोग से, अनुपयुक्त शब्द के प्रयुक्त होने से, सही क्रम या अन्विति न होने से,
  • लिंग, वचन, कारक का सही प्रयोग नहीं होने से, सही सर्वनाम एवं क्रिया का प्रयोग न होने से वाक्य अशुद्ध हो जाता है।
  • जो अर्थ के साथ भाषा सौन्दर्य को हानि पहुँचाता है।

Question 90

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए लोकोक्ति का सही अर्थ हो।

कबहुँ निरामिष होय न कागा

  1. AOption (a)

    बहुत कठिन परिश्रम का थोड़ा लाभ

  2. BOption (b)

    दुष्ट अपनी दुष्टता नहीं छोड़ता

  3. COption (c)

    कोई अपने माल को खराब नहीं कहता

  4. DOption (d)

    ऊपरी वेशभूषा से किसी के अवगुण नहीं छिप जाते

View answer & explanation

Correct answer

Answer: (b)B.

दुष्ट अपनी दुष्टता नहीं छोड़ता

Why this answer is correct

दिए गए विकल्पों में से "कबहुँ निरामिष होय न कागा" लोकोक्ति का सही अर्थ है - "दुष्ट अपनी दुष्टता नहीं छोड़ता" 

  • वाक्य प्रयोग- रमन ने कहा था कि यह इंजीनियर उसका जानने वाला है,
  • अतः बिना कुछ लिए दिए नक्शा पास कर देगा पर वह तो पचास हजार माँग रहा है। मुझे तो अब इस कहावत पर विश्वास हो गया है कि 'कबहुँ निरामिष होय न कागा'।

Key Pointsअन्य विकल्प - 

लोकोक्तिअर्थवाक्य प्रयोग
खोदा पहाड़ निकली चुहियाबहुत कठिन परिश्रम का थोड़ा लाभ।बच्चा बेचारा दिन भर लाल बत्ती पर अख़बार बेचता रहा, परंतु उसे कमाई मात्र बीस रुपये की हुई। यह वही बात है- खोदा पहाड़ निकली चुहिया।
कुंजड़ा अपने बेरों को खट्टा नहीं बताताकोई अपने माल को खराब नहीं कहता।सब्जी वाले बासी सब्जी को भी ताजी बताकर बेचते हैं। कहावत सच है कुंजड़ा अपने बेरों को खट्टा नहीं बताता।
कमली ओढ़ने से फकीर नहीं होताऊपरी वेशभूषा से किसी के अवगुण नहीं छिप जाते।विवेक साइकिल चोर है लेकिन सूट-बूट में रहता है। लोग उसे जानते है इसलिए उससे कतराते हैं। सच है कमली ओढ़ने से फकीर नहीं होता।

Additional Information

  • किसी विशेष स्थान पर प्रसिद्ध हो जाने वाले कथन को 'लोकोक्ति' कहते हैं।
  • इसी को कहावत कहते है।

कुछ लोकोक्तियाँ- 

लोकोक्तियाँअर्थवाक्य प्रयोग
अंधों के आगे रोना, अपना दीदा खोनामूर्खों को सदुपदेश दे���ा या अच्छी बात बताना व्यर्थ है।मुन्ना को समझाना तो अंधे के आगे रोना, अपना दीदा खोना वाली बात है।
खरी मजूरी चोखा काममजदूरी के तुरन्त बाद नकद पैसे मिलना।रवि ने मालिक से कहा कि उसे अपनी मजदूरी के पैसे तुरन्त चाहिए- 'खरी मजूरी चोखा काम'।
कोठी वाला रोवे छप्पर वाला सोवैअधिक धन चिन्ता का कारण होता है।सेठ रामलाल सारी रात जागते रहते हैं, चोरों के भय से उन्हें नींद नहीं आती। सच है कोठी वाला रोवे छप्पर वाला सोवे।
चिराग में बत्ती और आँख में पट्टीशाम होते ही सोने लगना।अब राज के घर जाना बेकार है वह तो चिराग में बत्ती और आँख में पट्टी वालों में है।

Question 91

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए संधि शब्द का सही संधि - विच्‍छेद का विकल्‍प हो।

उद्धाटन =

  1. AOption (a)

    ऊत + घाटन

  2. BOption (b)

    उद + घटन

  3. COption (c)

    उत् + घाटन

  4. DOption (d)

    उद + घाटन

View answer & explanation

Correct answer

Answer: (c)C.

उत् + घाटन

Why this answer is correct

दिए गए विकल्पों में से 'उद्धाटन' शब्द का सही संधि - विच्‍छेद "उत् + घाटन" होगा।

Key Points

  • उत् + घाटन = उद्धाटन
  • उद्धाटन शब्द में व्यंजन संधि है।
  • किसी वर्ग के पहले वर्ण ('क्', 'च्', 'ट्', 'त्', 'प') का मेल किसी स्वर या वर्ग के तीसरे, चौथे वर्ण, य र ल व में से किसी वर्ण से हो तो वर्ण का पहला वर्ण स्वयं ही तीसरे वर्ण में परिवर्तित हो जाता है।

Additional Information

  • दो वर्णों के मेल से होने वाले विकार को संधि कहते हैं।
  • दो शब्दों के मेल से बने शब्द को पुनः अलग अलग करने को संधि विच्छेद कहते हैं।

संधि के तीन प्रकार होते हैं- 

संधिपरिभाषाउदाहरण
स्वर संधिजब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है।- विद्या+आलय -विद्यालय
व्यंजन संधिव्यंजन वर्ण के साथ स्वर वर्ण या व्यंजन वर्ण अथवा स्वर वर्ण के साथ व्यंजन वर्ण के मेल से जो विकार उत्पन हो, उसे ‘व्यंजन संधि’ कहते हैं।- दिक+अंबर-दिगंबर - अभी+सेक- अभिषेक
विसर्ग संधिजब  विसर्ग के साथ स्वर या व्यंजन आ जाए तब जो परिवर्तन होता है ,वह विसर्ग संधि कहलाता है।- मन: + अनुकूल = मनोनुकूल - नि: + पाप =निष्पाप

Question 92

निम्नलिखित प्रश्न में 'चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए वाक्य के भेद का सही विकल्प है।

उसे जूते खरीदने थे, इसलिए वह बाज़ार गया।

  1. AOption (a)

    सरल वाक्‍य

  2. BOption (b)

    संयुक्‍त वाक्‍य

  3. COption (c)

    मिश्रित वाक्‍य

  4. DOption (d)

    विधान वाचक वाक्‍य

View answer & explanation

Correct answer

Answer: (b)B.

संयुक्‍त वाक्‍य

Why this answer is correct

दिए गए वाक्य के भेद का सही विकल्प "संयुक्‍त वाक्‍य" है।

Key Points

  • वाक्य - उसे जूते खरीदने थे, इसलिए वह बाज़ार गया।
  • इस वाक्य में दो सरल वाक्यों को जोड़ने वाला संयोजक 'इसलिए' है।
  • जिन वाक्यों में दो या दो से अधिक सरल वाक्य योजकों से जुड़े हों, उन्हें संयुक्त वाक्य कहते है।
  • योजक: और, एवं, तथा, या, अथवा, इसलिए, अतः, फिर भी, तो, नहीं तो, किन्तु, परन्तु, लेकिन, पर आदि।

Additional Information

  • दो या दो से अधिक पदों के सार्थक समूह को, जिसका पूरा पूरा अर्थ निकलता है, वाक्य कहते हैं।

रचना की दृष्टि से वाक्य तीन प्रकार के होते हैं- 

वाक्यपरिभाषाउदाहरण
सरल वाक्यसरल वाक्य वह जिसमें एक ही क्रिया होती है और एक उद्देश्य होता है और एक विधेय। इनमें एक-एक उद्देश्य अर्थात् कर्ता और विधेय अर्थात् क्रिया होती है। इसीलिए इन्हें सरल वाक्य कहा जाता है।बादल बरसता है।
मिश्र वाक्यजिस वाक्य में एक से अधिक वाक्य मिले हों किन्तु एक प्रधान उपवाक्य तथा शेष आश्रित उपवाक्य हों, मिश्रित वाक्य कहलाता है।मेरा दृढ़ विश्वास है कि भारत जीतेगा।
संयुक्त वाक्यजिस वाक्य में साधारण अथवा मिश्र वाक्यों का मेल संयोजक अवयवों द्वारा होता है, उसे संयुक्त वाक्य कहते हैं।वह सुबह गया और शाम को लौट आया।

Question 93

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो वाक्यांश के लिए प्रयुक्त एक शब्द का सही विकल्प हो।

जिसका उल्लेख किया जा सके -

  1. AOption (a)

    अनन्य

  2. BOption (b)

    अकथनीय

  3. COption (c)

    अतुलनीय

  4. DOption (d)

    उल्लेखनीय

View answer & explanation

Correct answer

Answer: (d)D.

उल्लेखनीय

Why this answer is correct

दिए गए विकल्पों में से "जिसका उल्लेख किया जा सके"  वाक्यांश के लिए प्रयुक्त एक शब्द होगा - "उल्लेखनीय"

Key Pointsअन्य  विकल्प - 

  • अनन्य- अन्य से सम्बन्ध न रखने वा��ा।
  • अकथनीय - जिसका कथन न किया जा सके।
  • अतुलनीय - जिसकी तुलना न हो सके।

Additional Information

  • जब किसी वाक्य में प्रयुक्त या स्वतन्त्र किसी वाक्यांश के लिए किसी एक शब्द का प्रयोग किया जाता है,
  • जो उस वाक्यांश के अर्थ को पूरी तरह सिद्ध करता हो तो उसे वाक्यांश के लिए एक शब्द कहते हैं।

वाक्यांश के लिए एक शब्द के उदाहरण- 

  • जिस पुस्तक में आठ अध्याय हो  - अष्टाध्यायी
  • देखने योग्य- दर्शनीय
  • जहां सैनिक निवास करते हो - छावनी
  • जहां सिक्कों की ढलाई होती है - टकसाल
  • जो किनारे से सटे हुए हो - तटवर्ती
  • दूसरे के मन की बात जानने वाला- अन्तर्यामी
  • दस वर्षो का समय- दशक
  • देश के लिए अपने प्राण देने वाला- शहीद

Question 94

निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए संधि - विच्छेद शब्द का सही संधि का विकल्प हो।

अच् + अन्‍त =

  1. AOption (a)

    अचंत

  2. BOption (b)

    अचिन्‍त्‍य

  3. COption (c)

    अंत

  4. DOption (d)

    अजन्‍त

View answer & explanation

Correct answer

Answer: (d)D.

अजन्‍त

Why this answer is correct

दिये गए संधि - विच्छेद शब्द का सही संधि का विकल्प "अजन्‍त" होगा। 

  • अच् + अन्‍त = अजन्‍त

Key Points

  • अच् + अन्‍त = अजन्‍त ( च्  + अ = ज तीसरे वर्ण )
  • इसमें  "व्यंजन संधि" लागू होती है।
  • किसी वर्ग के पहले वर्ण ('क्', 'च्', 'ट्', 'त्', 'प') का मेल किसी स्वर या वर्ग के तीसरे, चौथे वर्ण य र ल व में से किसी वर्ण से हो तो वर्ण का पहला वर्ण स्वयं ही तीसरे वर्ण में परिवर्तित हो जाता है।

Additional Information

  • दो वर्णों के मेल से होने वाले विकार को संधि कहते हैं।
  • दो शब्दों के मेल से बने शब्द को पुनः अलग अलग करने को संधि विच्छेद कहते हैं।

संधि के तीन प्रकार होते हैं-

संधिपरिभाषाउदाहरण
स्वर संधिजब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है।- विद्या+आलय -विद्यालय
व्यंजन संधिव्यंजन वर्ण के साथ स्वर वर्ण या व्यंजन वर्ण अथवा स्वर वर्ण के साथ व्यंजन वर्ण के मेल से जो विकार उत्पन हो, उसे ‘व्यंजन संधि’ कहते हैं।- दिक+अंबर-दिगंबर - अभी+सेक- अभिषेक
विसर्ग संधिजब  विसर्ग के साथ स्वर या व्यंजन आ जाए तब जो परिवर्तन होता है ,वह विसर्ग संधि कहलाता है।- मन: + अनुकूल = मनोनुकूल - नि: + पाप =निष्पाप

Question 95

निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए शब्द का सही तद्भव शब्द है।

कोटर

  1. AOption (a)

    खोखल

  2. BOption (b)

    शत

  3. COption (c)

    कोटक

  4. DOption (d)

    नित्‍य

View answer & explanation

Correct answer

Answer: (a)A.

खोखल

Why this answer is correct

दिए गए विकल्पों में से 'कोटर' शब्द का  सही तद्भव शब्द "खोखल" है।

Key Points

  • "कोटर" तत्सम शब्द है इसका तद्भव रूप "खोखल" है।
  • "शत" तत्सम शब्द है इसका तद्भव रुप "सौ" है।
  • "नित्‍य" तत्सम शब्द है इसका तद्भव रूप "नित" है।

Important Points

  • कोटक का हिंदी अर्थ - कोट, भवन या झोपड़े बनाने वाला।
  • कोटर का हिन्दी अर्थ - पेड़ का खोखला भाग।
  • नित्य का हिंदी अर्थ - प्रतिदिन किया जाने वाला।

Additional Information

  • तत्सम शब्द- ऐसे शब्द जिनकी उत्पत्ति संस्कृत भाषा में हुई ओर वे हिन्दी भाषा में बिना किसी,
  • परिवर्तन के प्रयोग में आने लगे, ऐसे शब्द तत्सम शब्द कहलाते हैं।
  • जैसे- कवि, माता, विद्या, नदी, फल, पुष्प, पुस्तक, पृथ्वी, क्षेत्र, कार्य, मृत्यु आदि।
  • तद्भव शब्द- ऐसे शब्द जो संस्कृत भाषा से उत्पन्न होते हैं, लेकिन वो रूप बदलकर हिन्दी में आ गए हों,
  • ऐसे शब्द तद्भव शब्द कहलाते हैं।
  • जैसे- दुग्ध --  दूध
  • अग्नि -- आग
  • कार्य -- काम
  • कर्पूर -- कपूर

नीचे दिए गए गद्यांश को ध्यानपूर्वक पढ़ें और पूछे गए प्रश्नों का सर्वोत्तम उत्तर चुनें।

अपने कार्य को आप ही करना स्वावलंबन कहलाता है। बालक जब से होश संभालता है, अपने निजी कार्य स्वयं करने लगता है। इसी प्रकार यदि मनुष्य जीवन की किसी भी स्थिति में अपना कार्य स्वयं करे, तो वह स्वावलंबी कहलाता है। स्वावलंबी होना नागरिकता का महान गुण है। स्वावलंबन बड़प्पन का गुण है। कहते हैं कि एक दिन प्रसिद्ध विद्वान्‌ ईश्वरचंद्र विद्यासागर रेलवे स्टेशन के बाहर खड़े थे। तभी भीतर से एक व्यक्ति हाथ में एक छोटा सा बक्सा लिए उनके पास आया। उन्हें साधारण वेश में देखकर भूल से कुली समझ बैठा और बोला, “मेरा सामान ले चलोगे? ” ईश्वरचंद्र बिना कुछ बोले उसका सामान उठाकर चल दिए। लक्ष्य पर पहुंचकर जब वह उन्हें मजदूरी देने लगा तो वे बोले, “ मजदूरी नहीं चाहिए। तुम अपना काम स्वयं नहीं कर सकते, इसलिए मैंने तुम्हारी सहायता कर दी है।” व्यक्ति लज्जित हुआ। जब उसे यह पता चला कि उनका कुली बंगाल का प्रसिद्ध विद्वान्‌ है तो वह उनके पाँव में गिर पड़ा। उसने अपना कार्य आप करने की सौगंध ली

Question 96

रेलवे स्टेशन के बाहर ईश्वरचंद्र विद्यासागर किस वेशभूषा में खड़े थे?

  1. AOption (a)

    देखरेख करने वाले के रूप में

  2. BOption (b)

    सभ्य एवं शिक्षित व्यक्ति की वेशभूषा में

  3. COption (c)

    कुली की वेशभूषा में 

  4. DOption (d)

    अत्यंत साधारण से दिखने वाले व्यक्ति की वेशभूषा में

View answer & explanation

Correct answer

Answer: (d)D.

अत्यंत साधारण से दिखने वाले व्यक्ति की वेशभूषा में

Why this answer is correct

रेलवे स्टेशन के बाहर ईश्वरचंद्र विद्यासागर अत्यंत साधारण से दिखने वाले व्यक्ति की वेशभूषा में खड़े थे। 

  • अनुछेद के अनुसार-
  • कहते हैं कि एक दिन प्रसिद्ध विद्वान्‌ ईश्वरचंद्र विद्यासागर रेलवे स्टेशन के बाहर खड़े थे।
  • तभी भीतर से एक व्यक्ति हाथ में एक छोटा सा बक्सा लिए उनके पास आया।
  • उन्हें साधारण वेश में देखकर भूल से कुली समझ बैठा और बोला, “मेरा सामान ले चलोगे? ”
  • ईश्वरचंद्र बिना कुछ बोले उसका सामान उठाकर चल दिए। ​

Key Points

  • साधारण- सब जगह पाया जानेवाला, आम
  • वेशभूषा- कपड़े आदि पहनने का तरीका या ढंग।

Additional Informationसभ्य:-

  • अर्थ: सज्जन, साधु, भद्र, शिष्ट, कुलीन।

कुली:-

  • अर्थ: स्टेशन पर बोझ ढोनेवाला मज़दूर।

शिक्षित:-

  • अर्थ: शिक्षा प्राप्त, पढ़ा लिखा।

नीचे दिए गए गद्यांश को ध्यानपूर्वक पढ़ें और पूछे गए प्रश्नों का सर्वोत्तम उत्त��� चुनें।

अपने कार्य को आप ही करना स्वावलंबन कहलाता है। बालक जब से होश संभालता है, अपने निजी कार्य स्वयं करने लगता है। इसी प्रकार यदि मनुष्य जीवन की किसी भी स्थिति में अपना कार्य स्वयं करे, तो वह स्वावलंबी कहलाता है। स्वावलंबी होना नागरिकता का महान गुण है। स्वावलंबन बड़प्पन का गुण है। कहते हैं कि एक दिन प्रसिद्ध विद्वान्‌ ईश्वरचंद्र विद्यासागर रेलवे स्टेशन के बाहर खड़े थे। तभी भीतर से एक व्यक्ति हाथ में एक छोटा सा बक्सा लिए उनके पास आया। उन्हें साधारण वेश में देखकर भूल से कुली समझ बैठा और बोला, “मेरा सामान ले चलोगे? ” ईश्वरचंद्र बिना कुछ बोले उसका सामान उठाकर चल दिए। लक्ष्य पर पहुंचकर जब वह उन्हें मजदूरी देने लगा तो वे बोले, “ मजदूरी नहीं चाहिए। तुम अपना काम स्वयं नहीं कर सकते, इसलिए मैंने तुम्हारी सहायता कर दी है।” व्यक्ति लज्जित हुआ। जब उसे यह पता चला कि उनका कुली बंगाल का प्रसिद्ध विद्वान्‌ है तो वह उनके पाँव में गिर पड़ा। उसने अपना कार्य आप करने की सौगंध ली

Question 97

अनुछेद के अनुसार 'स्वावलंबन' का क्या अर्थ है?

  1. AOption (a)

    दूसरों पर अवलंबित रहना

  2. BOption (b)

    दूसरों की सहायता से अपना काम करना

  3. COption (c)

    दूसरों को अपने पर अवलंबित रखना

  4. DOption (d)

    अपने कार्य को अपने आप करना

View answer & explanation

Correct answer

Answer: (d)D.

अपने कार्य को अपने आप करना

Why this answer is correct

अनुछेद के अनुसार 'स्वावलंबन' का अर्थ है- अपने कार्य को अपने आप करना

  • अनुछेद के अनुसार-
  • ​अपने कार्य को आप ही करना स्वावलंबन कहलाता है।
  • बालक जब से होश संभालता है, अपने निजी कार्य स्वयं करने लगता है। ​

Key Pointsअवलंबित:-

  • अर्थ: आश्रित, सहारे पर स्थित, टिका हुआ।

परावलम्बी:- 

  • अर्थ: दूसरों पर अवलंबित या आश्रित।

Question 98

इनमे से कौन-सा 'स्वावलंबी' का विलोम शब्द है ?

  1. AOption (a)

    आत्मनिर्भरता

  2. BOption (b)

    स्वयं

  3. COption (c)

    स्वाश्रय

  4. DOption (d)

    परावलम्बी

View answer & explanation

Correct answer

Answer: (d)D.

परावलम्बी

Why this answer is correct

'स्वावलंबी' का विलोम शब्द है- परावलम्बी

  • स्वावलंबी- अपना ही सहारा लेनेवाला, स्वाश्रय, आत्मनिर्भर।
  • परावलम्बी- दूसरों पर अवलंबित या आश्रित।

Key Pointsस्वयं**-**

  • अर्थ: अपने आप, खुद।
  • विलोम शब्द - 'दूसरा'
  • अर्थ: पहले के बाद का।

Additional Informationकुछ अन्य महत्वपूर्ण विलोम शब्द:-

  • शब्द - विलोम
  • उत्थान - पतन
  • अधोगामी - उर्ध्वगामी
  • ओजस्वी - निस्तेज
  • कृत्रिम - प्राकृत
  • औपचारिक - अनौपचारिक
  • निर्विरोध - गतिरोध
  • शाश्वत - क्षणिक
  • प्राचीन - अर्वाचीन
  • निरालम्ब - अवलम्ब

Question 99

ईश्वरचंद्र विद्यासागर के सम्मुख वह व्यक्ति बहुत लज्जित क्यों हुआ ?

  1. AOption (a)

    क्योंकि उसका काम किसी और ने किया

  2. BOption (b)

    क्योंकि उसने अपना काम स्वयं किया था

  3. COption (c)

    ईश्वरचंद्र विद्यासागर को कुली समझ लिया था

  4. DOption (d)

    उसकी मदद करने वाले ने पैसा लेने से मना कर दिया

View answer & explanation

Correct answer

Answer: (c)C.

ईश्वरचंद्र विद्यासागर को कुली समझ लिया था

Why this answer is correct

ईश्वरचंद्र विद्यासागर के सम्मुख वह व्यक्ति बहुत लज्जित हुआ क्योंकि वह ईश्वरचंद्र विद्यासागर को कुली समझ लिया था

  • अनुछेद के अनुसार-
  • कहते हैं कि एक दिन प्रसिद्ध विद्वान्‌ ईश्वरचंद्र विद्यासागर रेलवे स्टेशन के बाहर खड़े थे।
  • तभी भीतर से एक व्यक्ति हाथ में एक छोटा सा बक्सा लिए उनके पास आया।
  • उन्हें साधारण वेश में देखकर भूल से कुली समझ बैठा और बोला, “मेरा सामान ले चलोगे? ”
  • ईश्वरचंद्र बिना कुछ बोले उसका सामान उठाकर चल दिए।
  • लक्ष्य पर पहुंचकर जब वह उन्हें मजदूरी देने लगा तो वे बोले, “ मजदूरी नहीं चाहिए।
  • तुम अपना काम स्वयं नहीं कर सकते, इसलिए मैंने तुम्हारी सहायता कर दी है।” व्यक्ति लज्जित हुआ।​

Key Pointsईश्वर चन्द्र विद्यासागर:-

  • ईश्वर चन्द्र विद्यासागर उन्नीसवीं शताब्दी के बंगाल के प्रसिद्ध दार्शनिक, शिक्षाविद,
  • समाज सुधारक, लेखक, अनुवादक, मुद्रक, प्रकाशक, उद्यमी और परोपकारी व्यक्ति थे।
  • वे बंगाल के पुनर्जागरण के स्तम्भों में से एक थे। उनके बचपन का नाम ईश्वर चन्द्र बन्द्योपाध्याय था।
  • संस्कृत भाषा और दर्शन में अगाध पाण्डित्य के कारण विद्यार्थी जीवन में ही संस्कृत कॉलेज ने उन्हें 'विद्यासागर' की उपाधि प्रदान की थी।

Additional Informationकुली:-

  • अर्थ: स्टेशन पर बोझ ढोनेवाला मज़दूर।

Question 100

अनुच्छेद के लिए उचित शीर्षक दीजिये।

  1. AOption (a)

    अवलंबन की आवश्यकता

  2. BOption (b)

    परावलंबन एक श्रेष्ठ गुण

  3. COption (c)

    स्वावलंबन एक श्रेष्ठ गुण

  4. DOption (d)

    अवलंबन एक श्रेष्ठ गुण

View answer & explanation

Correct answer

Answer: (c)C.

स्वावलंबन एक श्रेष्ठ गुण

Why this answer is correct

अनुच्छेद के लिए उचित शीर्षक है- स्वावलंबन एक श्रेष्ठ गुण

  • अनुछेद के अनुसार-
  • मनुष्य जीवन की किसी भी स्थिति में अपना कार्य स्वयं करे, तो वह स्वावलंबी कहलाता है।
  • स्वावलंबी होना नागरिकता का महान गुण है। स्वावलंबन बड़प्पन का गुण है। ​

Key Pointsस्वावलंबन:- 

  • अर्थ: आत्मनिर्भर होने की अवस्था, गुण या भाव
  • विलोम शब्द - 'परावलंबन'
  • अर्थ: दूसरे पर अवलंबित होने की क्रिया, पराधीनता।

Additional Informationअवलंब:-

  • अर्थ: सहारा लेना, आश्रय, ओट।
  • विलोम शब्द - 'निरालंब'
  • अर्थ: बिना आलंब या सहारे का।

श्रेष्ठ:-

  • अर्थ: उत्तम, उत्कृष्ट, उन्नत, अच्छा, बढ़िया, उम्दा। 
  • विलोम शब्द - 'निम्न'
  • अर्थ: नीचा, निचला

Discipline 1 (20 questions)

Question 101

What is the curved surface area of the cone in general form?

  1. AOption (a)

    πr (r + l)

  2. BOption (b)

    πrh

  3. COption (c)

    πrhl

  4. DOption (d)

    πrl

View answer & explanation

Correct answer

Answer: (d)D.

πrl

Why this answer is correct

Explanation:

The Curved Surface Area of Cone is πrl

Where r is the radius and l is the slant height of the cone 

Hence, The Correct Answer is option 4.

Question 102

What will be the rank of every non singular matrix of order n?

  1. AOption (a)

    2n + 1

  2. BOption (b)

    n + 1

  3. COption (c)

    n

  4. DOption (d)

    2n

View answer & explanation

Correct answer

Answer: (c)C.

n

Why this answer is correct

Concept use:

Rank of the Matrix : The Smallest Sub Matrix from the Given Marix having Determinant non zero then order of that matrix is rank.

Non Singular Matrix: The Matrix having determinant non zero.

 

Explanation:

Given that Matrix is Non Singular means Determinant non zero 

means Rank of Matrix is n.

Since, The Non Singular Matrix is of order n.

Hence, The Correct Option is 3.

Question 103

2587322568103 is a number, which will be divisible by which number?

  1. AOption (a)

    2

  2. BOption (b)

    7

  3. COption (c)

    6

  4. DOption (d)

    11

View answer & explanation

Correct answer

Answer: (b)B.

7

Why this answer is correct

Concept -

(i) A number is divisible by 2 if its last digit is even.

(ii) A number is divisible by 6 if the number is divisible by 2 and 3 both.

(iii) A number is divisible by 3 if the sum of all the digits of the number is divisible by 3. 

(iv) A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11 .

Explanation -

For Option (1) -

A number is divisible by 2 if its last digit is even.

The last digit of 2587322568103 is 3, which is odd.

Therefore, 2587322568103 is not divisible by 2.

For Option (2) -

There isn't a simple divisibility rule for 7, but you could use long division. In this case, 2587322568103 is divisible by 7.

For Option (3)  -

A number is divisible by 6 if the number is divisible by 2 and 3 both.

The sum of the digits of  2587322568103 is 63, which is divisible by 3.

But this number is not divisible by 2.

Therefore, 2587322568103 is not divisible by 6.

For Option (4)  -

A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11 .

However, in this case, the difference is not divisible by 11. 

So, the option(2) is correct.

Question 104

The curve given by xy = 15 is symmetrical about what?

  1. AOption (a)

    x axis

  2. BOption (b)

    about the line x = y

  3. COption (c)

    about the origin

  4. DOption (d)

    y axis

View answer & explanation

Correct answer

Answer: (b)B.

about the line x = y

Why this answer is correct

Concept use:

Symmetry defines that the shape is identical on both sides when it is divided by a line. The symmetry of different shapes, regular or irregular.

Explanation:

The curve given by xy = 15 is symmetrical about about the line x = y.

Option (2) is true.

Question 105

A polynomial with real coefficients of n degree has ______ roots?

  1. AOption (a)

    n imaginary roots

  2. BOption (b)

    n real roots

  3. COption (c)

    n (may be real or imaginary)

  4. DOption (d)

    n - 1 roots

View answer & explanation

Correct answer

Answer: (c)C.

n (may be real or imaginary)

Why this answer is correct

Concept use:

Fundamental Theorem of Algebra States that A polynomial with real coefficients of n degree has n roots

Explanation:

A polynomial with real coefficients of n degree has n roots may be real or imaginary 

For example x2 - 1 having two roots (equal to its degree) and real 

x2 + 1 having two roots (equal to its degree) and real and imaginary.

Hence, The Correct Option is 3.

Question 106

Find total number of asymmetric relations on a set A = {e, f, g} ?

  1. AOption (a)

    34

  2. BOption (b)

    64

  3. COption (c)

    27

  4. DOption (d)

    128

View answer & explanation

Correct answer

Answer: (c)C.

27

Why this answer is correct

Concept use:

The Total Number of asymetric relation is 3(n^2 - n)/2

Explanation:

total number of asymmetric relations on a set A = {e, f, g}

The Total Number of asymetric relation is 3(3^2 - 3)/2 = 3(9-3)/2 = 33 = 27

Hence, The Correct Answer is option 3.

Question 107

Euler function tends to infinity if which condition follows?

  1. AOption (a)

    n tends to zero

  2. BOption (b)

    n tends to infinity

  3. COption (c)

    n tends to a positive limit

  4. DOption (d)

    n tends to a negative limit

View answer & explanation

Correct answer

Answer: (b)B.

n tends to infinity

Why this answer is correct

Explanation:

Euler's totient function ϕ(n) counts the number of positive integers less than n that are coprime to n.

Euler function tends to infinity if n tends to infinity.

(2) is correct

Question 108

Which of the following properties does not possess?

  1. AOption (a)

    [x] = x if x is integer

  2. BOption (b)

    [-x] = -[x] - 1 if x is integer

  3. COption (c)

    [x + y] > [x] + [y]

  4. DOption (d)

    [- x] = [x] if x is integer

View answer & explanation

Correct answer

Answer: (d)D.

[- x] = [x] if x is integer

Why this answer is correct

Concept use:

The greatest integer function is a function that results in the integer nearer to the given real number. It is also called the step function. The greatest integer function rounds off the given number to the nearest integer.

Explanation:

The greatest integer function of x is given by

[x] = x if x is integer

[-x] = -[x] - 1 if x is integer

Also, [x + y] > [x] + [y].

So, options (1), (2), (3) are satisfied.

But option (4) is not true as

For x = 2

[-x] = [-2] = -2

and [2] = 2

Hence [- x] ≠ [x] if x is integer.

Question 109

Find the middle term of an AP if it is given that the sum of three numbers in the AP is 15?

  1. AOption (a)

    10

  2. BOption (b)

    5

  3. COption (c)

    15

  4. DOption (d)

    20

View answer & explanation

Correct answer

Answer: (b)B.

5

Why this answer is correct

Explanation:

Let's represent the three consecutive terms as a, a + d, and a + 2d, where a is the first term, and d is the common difference between the terms.

The sum of the three consecutive terms is 15.

We can write the equation:

a + (a + d) + (a + 2d) = 15

3a + 3d = 15

a = (15 - 3d) / 3

Let  a = 5 because if we substitute d = 0, then a = 5, and the three terms become 5, 5, and 5, whose sum is 15.

While taking a + d = 15, 20, 10 then This will not form Arithmetic Progression.

Hence, the middle term (a + d) = 5 + 0 = 5

Hence, the correct option is: 2) 5

Question 110

Find the gradient of the scalar field if f(x, y) = x + y at (1, 2)?

  1. AOption (a)

    j + 2i

  2. BOption (b)

    i + 2j

  3. COption (c)

    j - i

  4. DOption (d)

    i + j

View answer & explanation

Correct answer

Answer: (d)D.

i + j

Why this answer is correct

Explanations:

The gradient of a scalar field f(x, y) is defined as the vector (df/dx, df/dy), and it gives the direction of the maximum rate of increase of the function.

Let's proceed by taking the required partial derivatives for f(x,y) = x + y:

df/dx = 1 df/dy = 1

So the gradient of the function at a give point, (∇f) is given by (∇f) = i*(df/dx) + j*(df/dy).

So, (∇f) = i1 + j1 = i + j.

The gradient of the function at any point is a constant vector i + j, and this also holds at the point (1,2).

Question 111

How many subsets of the set A will there be if A = {1, 2, 3, 4)?

  1. AOption (a)

    8

  2. BOption (b)

    2

  3. COption (c)

    4

  4. DOption (d)

    16

View answer & explanation

Correct answer

Answer: (d)D.

16

Why this answer is correct

Concept use:

The Number of Subset of Set A is 2n  where, n is the Cardinality of the set.

Explanation:

Given Set A = {1, 2, 3, 4}

The Number of Subset of A is 24 = 16 

Hence, The Correct Answer is Option 4.

Question 112

If the inner product between the vectors vanishes then what will be the angle between them?

  1. AOption (a)

    45

  2. BOption (b)

    90

  3. COption (c)

    35

  4. DOption (d)

    0

View answer & explanation

Correct answer

Answer: (b)B.

90

Why this answer is correct

Explanation:

Real and complex inner products are generalizations of the real and complex dot products, respectively.

■

An inner product space is a vector space that possesses three operations: vector addition, scalar multiplication, and inner product.

■

For vectors x, y and scalar k in a real inner product space, 〈x, y〉 = 〈y, x〉, and 〈x, ky〉 = k 〈x, y〉.

■

For vectors x, y and scalar k in a real or complex inner product space, 〈kx, y〉 = k 〈x, y〉.

■

For vectors x, y and scalar k in a complex inner product space,

〈 x, y 〉 = 〈 y, x 〉

〈 x, ky 〉 = k 〈 x, y 〉 and ||kx|| = | k|| x is = ∥kx∥=|k|∥x∥∥kx∥=|k|∥x∥∥kx∥=|k|∥x∥‖kx‖=|k|‖x‖ .

■

The length of a vector x in an inner product space is ||x|| =  〈 x, x 〉, and the distance between vectors x and y in an inner product space is ||x−y||||x−y||||x−y||||x−y|| .

■

The angle θ between two vectors in a real inner product space is defined as the angle between 0 and π such that θ = 〈 x, y 〉 / ||x|| ||y||).

■

Orthogonal and orthonormal sets of vectors, and orthogonal complements of subspaces, are defined for inner product spaces analogously as for real vector spaces.

Thus, If the inner product between the vectors vanishes then what will be the angle between them is zero.

because cosθ = 0 is possible only when θ = 90°.

Question 113

The rank of a matrix in echleon form is equal to:

  1. AOption (a)

    number of zero rows of the matrix

  2. BOption (b)

    order of matrix

  3. COption (c)

    number of variables

  4. DOption (d)

    Number of non zero rows of the matrix

View answer & explanation

Correct answer

Answer: (d)D.

Number of non zero rows of the matrix

Why this answer is correct

Explanation:

A matrix is in reduced row echelon form if it is in row echelon form, the first nonzero entry of each row is equal to 1

and the ones above it within the same column equal 0. The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it.

Rank of that matrix is equal to the Number of Non Zero rows of the matrix.

Hence, The Correct Option is 4.

Question 114

In what range does sec(x) become invertible?

  1. AOption (a)

    R

  2. BOption (b)

    R - (-1,1)

  3. COption (c)

    R - {0}

  4. DOption (d)

    Z

View answer & explanation

Correct answer

Answer: (b)B.

R - (-1,1)

Why this answer is correct

Explanation:

sec x will not be defined at the points where cos x is 0. Hence, the domain of sec x will be R-(2n+1)π/2, where n∈I. The range of sec x will be R- (-1,1). 

The domain of sec inverse x is given by (-∞, -1] U [1, ∞) and its range is [0, π/2) U (π/2, π].

Hence, Sec(x) become invertible R - (-1, 1)

Hence, The Correct option is 2.

Question 115

What is the volume of curve between the ordinate 0 to 4 around the curve x = y?

  1. AOption (a)

    31.33

  2. BOption (b)

    21 π 

  3. COption (c)

    21.33 π

  4. DOption (d)

    31 π 

View answer & explanation

Correct answer

Answer: (c)C.

21.33 π

Why this answer is correct

Concept:

Suppose y = f(x) is non-negative and continuous on [a,b]. If the region bounded above by the graph of f, below by the x-axis, and on the sides by x = a and x = b is revolved around the x-axis, the volume V of the generated solid is

V = π∫ab[f(x)]2dxπ\int_a^b [f(x)]^2dx

Explanation:

Volume of the curve between the ordinate 0 to 4 around the curve x = y is

V = π∫04x2dxπ\int_0^4 x^2 dx = π[x33]04\left[{x^3\over 3}\right]_0^4 = 21.33π

Option (3) is true.

Question 116

At what point are the tangents to the asymptotes curve?

  1. AOption (a)

    Infinity

  2. BOption (b)

    Three point

  3. COption (c)

    Two points

  4. DOption (d)

    One point

View answer & explanation

Correct answer

Answer: (a)A.

Infinity

Why this answer is correct

Concept use:

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

Explanation:

An asymptote of a curve is a line that is tangent to the curve at a point at infinity.

Option (1) is true.

Question 117

For any matrix to be in row reduced form which of the following conditions is not satisfied?

  1. AOption (a)

    Each leading one is to the right of one preceding row

  2. BOption (b)

    Any row if has zero is at the bottom

  3. COption (c)

    zero row is at the top of the matrix

  4. DOption (d)

    any leading entry is one

View answer & explanation

Correct answer

Answer: (c)C.

zero row is at the top of the matrix

Why this answer is correct

Explanation:

The conditions for a matrix to be in row echelon form are

(i) All non-zero rows should be above all zero rows.

(ii) 1st non-zero element of each row should be 1

(iii) Number of zeros before the 1st non-zero element in 1st, 2nd, 3rd …. rows should be increasing.

Therefore the incorrect option is option (3)

Question 118

If the discriminant D > 0 then what can you say about the nature of the root?

  1. AOption (a)

    No real root

  2. BOption (b)

    Same root

  3. COption (c)

    Exclusive genuine root

  4. DOption (d)

    Fictional root

View answer & explanation

Correct answer

Answer: (c)C.

Exclusive genuine root

Why this answer is correct

Explanation:

The general form of a quadratic equation is ax2 + bx +c = 0, a ≠ 0

whose discriminant (D) = b2 - 4ac.

If D > 0 then the roots are real and unequal i.e., roots are exclusive genuine roots.

If D < 0 then roots are complex conjugate.

If D = 0 then roots are equal.

Option (3) is true.

Question 119

If A = 3i + j + k; B = 5i + j – k; C = i + j - k then find the volume of parallelogram if A, B, and C are the sides of the parallelepiped respectively.

  1. AOption (a)

    16

  2. BOption (b)

    32

  3. COption (c)

    0

  4. DOption (d)

    8

View answer & explanation

Correct answer

Answer: (d)D.

8

Why this answer is correct

Explanation:

A = 3i + j + k; B = 5i + j – k; C = i + j - k

The volume of parallelogram if A, B, and C are the sides of the parallelepiped

= \(\begin{vmatrix}3&1&1\5&1&-1\1&1&-1\end{vmatrix}\)

= 3(-1 + 1) +1(-1 + 5) +1(5 - 1)

= 0 + 4 + 4 = 8

Option (4) is true.

Question 120

What is the scope of the definition of exponential function?

  1. AOption (a)

    Whole numbers

  2. BOption (b)

    Integers

  3. COption (c)

    Rational Numbers

  4. DOption (d)

    Real numbers

View answer & explanation

Correct answer

Answer: (d)D.

Real numbers

Why this answer is correct

Explanation -

The scope of the definition of an exponential function (f(x) = ex) encompasses real numbers.

Exponential functions can be defined for any real number base raised to any real number exponent.

Therefore, the correct answer is (4).

Discipline 2 (20 questions)

Question 121

Which model is the one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables?

  1. AOption (a)

    continuous model

  2. BOption (b)

    discrete model

  3. COption (c)

    deterministic model

  4. DOption (d)

    probability model

View answer & explanation

Correct answer

Answer: (c)C.

deterministic model

Why this answer is correct

Concept -

A deterministic model is a mathematical representation where the outcome is completely determined by the initial conditions and the parameters of the model.

In other words, there is no randomness involved, and given the same inputs, the model will always produce the same outputs.

This makes deterministic models predictable and suitable for situations where outcomes can be precisely calculated based on known factors.

Explanation -

The model described in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables is a "deterministic model."

Therefore, the correct option is (3)

Question 122

Let f be a sequence of bounded functions and the series given by f is uniformly continuous to some function say g then ______.

  1. AOption (a)

    g is bounded

  2. BOption (b)

    g occurs virtually to follow 1

  3. COption (c)

    g is infinite

  4. DOption (d)

    g is unbounded

View answer & explanation

Correct answer

Answer: (a)A.

g is bounded

Why this answer is correct

Concept -

If a sequence of bounded functions f converges uniformly to some function g, then the limit function g  is also bounded. This property follows from the fact that uniform convergence preserves boundedness of functions. 

Explanation:

Let f be a sequence of bounded functions and the series given by f is uniformly continuous to some function say g then bounded.

(1) is correct

Question 123

The general solution of the equation y" (x) = 0 with the initial value problem s.t. at x = 0; y = 0 and y' = 0 is?

  1. AOption (a)

    y(x) = x2/2

  2. BOption (b)

    y(x) = 0

  3. COption (c)

    y(x) = x

  4. DOption (d)

    y(x) = x/2

View answer & explanation

Correct answer

Answer: (b)B.

y(x) = 0

Why this answer is correct

The given differential equation is y''(x) = 0.

Integrate both sides  y'(x) = c1'

again Integrate both sides y(x) = c1''x + c1

y(0) = 0 = c1'' × 0 + c1 ⇒ c1 = 0

y(x) = c1' x  by y' = 0 we get c1' = 0

Hence, y(x) = 0

Question 124

If a function f is from R\mathbb R to R\mathbb R and a be a point which is given convergent to us, then what can we say about the sequence which is generated by its image i.e. f(a)

  1. AOption (a)

    it is divergent

  2. BOption (b)

    it is convergent

  3. COption (c)

    it occurs finitely

  4. DOption (d)

    it is bounded

View answer & explanation

Correct answer

Answer: (b)B.

it is convergent

Why this answer is correct

Concept -

If a function f is continuous at a point a and the sequence an converges to a, then the sequence of function values f(an) converges to f(a). This is a fundamental property of continuous functions, known as the continuity of limits. 

Explanation:

If a function f is from R\mathbb R to R\mathbb R and a be a point which is given convergent to us, then the sequence is convergent which is generated by its image i.e. f(a)

(4) is correct

Question 125

Which of the following is used in mathematical modelling in Boolean algebra?

  1. AOption (a)

    mines geometry

  2. BOption (b)

    constructive solid geometry

  3. COption (c)

    lines figure

  4. DOption (d)

    complex analysis

View answer & explanation

Correct answer

Answer: (b)B.

constructive solid geometry

Why this answer is correct

Explanation -

Constructive solid geometry (CSG) is a technique used in computer graphics and mathematical modeling to represent complex shapes and objects by combining simple geometric primitives like cubes, spheres, and cylinders using Boolean operations such as union, intersection, and difference.

In the context of Boolean algebra, CSG is often employed to create models and representations of logical operations and relationships.

Hence Option (2) is correct.

Question 126

The graph of the solution of the curve given y = f (x), where y is the function of x, also x and y are real numbers and is termed as

  1. AOption (a)

    functional curve

  2. BOption (b)

    bitsman curve

  3. COption (c)

    solution curve

  4. DOption (d)

    polynomial curve

View answer & explanation

Correct answer

Answer: (c)C.

solution curve

Why this answer is correct

Explanation:

The graph of the solution of the curve given y = f (x), where y is the function of x, also x and y are real numbers and is termed as solution curve.

Option (3) is true.

Question 127

How many singular solutions occur for nth order ordinary linear diffrential equation?

  1. AOption (a)

    no singular solutions

  2. BOption (b)

    three

  3. COption (c)

    two

  4. DOption (d)

    one

View answer & explanation

Correct answer

Answer: (a)A.

no singular solutions

Why this answer is correct

Explanation -

The number of singular solutions for an ordinary differential equation depends on the nature of the equations. But usually, for an ordinary linear differential equation of order 'n', the total number of independent solutions (including both regular and singular) is 'n'.

Not all differential equations have singular solutions. Like ordinary linear differential equations with constant coefficients do not have singular solutions.

Hence option (i) is correct.

Question 128

What type of curve is obtained in exponential growth?

  1. AOption (a)

    S shaped curve

  2. BOption (b)

    J shaped curve

  3. COption (c)

    T shaped curve

  4. DOption (d)

    W shaped curve

View answer & explanation

Correct answer

Answer: (b)B.

J shaped curve

Why this answer is correct

Explanation:

Graph for exponential growth is

i.e., the curve obtained in exponential growth is J shaped curve.

Option (2) is true.

Question 129

Which model accounts for time dependent change of a model?

  1. AOption (a)

    dynamic model

  2. BOption (b)

    bi-model

  3. COption (c)

    generalized model

  4. DOption (d)

    static model

View answer & explanation

Correct answer

Answer: (a)A.

dynamic model

Why this answer is correct

The correct answer is the dynamic model.

Key Points

  • A dynamic model is a mathematical model that accounts for changes in a system over time. It can be used to represent a wide variety of systems, including physical systems (e.g., the motion of a planet), biological systems (e.g., the growth of a population), and economic systems (e.g., the stock market).
  • Bi-models, generalized models, and static models are all types of models that do not account for time-dependent change. A bi-model is a model that has two distinct parts. A generalized model is a model that can be applied to a wide range of problems. A static model is a model that does not change over time.

Here are some examples of dynamic models:

  • A model of the spread of a disease
  • A model of the climate
  • A model of the economy
  • A model of the financial markets
  • A model of the solar system

Dynamic models can be used to predict future outcomes, make informed decisions, and design systems that are more efficient and effective.

Question 130

Every bounded sequence with a unique limit point is ______?

  1. AOption (a)

    convergent

  2. BOption (b)

    doesn't exist

  3. COption (c)

    divergent

  4. DOption (d)

    oscillatory

View answer & explanation

Correct answer

Answer: (a)A.

convergent

Why this answer is correct

Concept -

Every bounded sequence with a unique limit point is  Convergent.

Explanation:

Every bounded sequence with a unique limit point is convergent

(1) is correct

Question 131

The sum of the series n(Sin(n)) is ______.

  1. AOption (a)

    convergent

  2. BOption (b)

    oscillates infinitely

  3. COption (c)

    divergent

  4. DOption (d)

    oscillates finitely

View answer & explanation

Correct answer

Answer: (c)C.

divergent

Why this answer is correct

Concept:

A series ∑ an is convergent then lim⁡n→∞an\lim_{n\to\infty}a_n = 0 i.e, if lim⁡n→∞an\lim_{n\to\infty}a_n ≠ o then the series ∑ an divergent.

Explanation:

The sum of the series n(sin(n)) = ∑n=1∞nsin⁡n∑_{n=1}^{\infty} n\sin n is divergent.

lim⁡n→∞nsin⁡n\lim_{n\to\infty}n\sin n ≠ 0

Hence ∑n=1∞nsin⁡n∑_{n=1}^{\infty} n\sin n is diveregent.

Option (3) is true.

Question 132

What condition is satisfied if sequence of functions f is said to be uniformly bounded?

  1. AOption (a)

    f(x) converge to a finite point

  2. BOption (b)

    f(x) converge to an infinite point

  3. COption (c)

    |f(x)| = M for some constant M

  4. DOption (d)

    |f(x)| ≤ M for some constant M and for all values of x

View answer & explanation

Correct answer

Answer: (d)D.

|f(x)| ≤ M for some constant M and for all values of x

Why this answer is correct

Concept -

A sequence of functions fn(x)  is said to be uniformly bounded if there exists a constant M  such that the absolute value of each function fn(x) in the sequence is less than or equal to M  for all n and for all x  in the domain of the functions.

Explanation:

A sequence of functions f(x) is said to be uniformly bounded if there exist a constat M such that |f(x)| ≤ M for all values of x.

(4) is correct

Question 133

The greatest limit point of a bounded sequence is called

  1. AOption (a)

    minimum point of f

  2. BOption (b)

    limit superior of f

  3. COption (c)

    limit inferior of f

  4. DOption (d)

    maximum point of f

View answer & explanation

Correct answer

Answer: (b)B.

limit superior of f

Why this answer is correct

Concept -

If a be the term of  the sequence and it repeats infinite times in the sequence then a is the limit point for the sequence. and limit superior ( lim sup ) is greatest limit point of the sequence.

Explanation:

The greatest limit point of a bounded sequence is called limit superior of f

(2) is correct

Question 134

The limit of the function f (x, y) = x + y - 6 at x = 1; y = 2 is ?

  1. AOption (a)

    -3

  2. BOption (b)

    -4

  3. COption (c)

    4

  4. DOption (d)

    3

View answer & explanation

Correct answer

Answer: (a)A.

-3

Why this answer is correct

Explanation -

We have the function f (x, y) = x + y - 6

The limit of the function f(x, y) = x + y - 6 as  x →  1 and y → 2,

we simply substitute these values into the function:

f(1, 2) = 1 + 2 - 6 = -3 

So, the limit of the function f(x, y) = x + y - 6 as x → 1 and y → 2 is -3.

Hence Option(1) is correct.

Question 135

Change in number of individuals in population over time is called?

  1. AOption (a)

    remainder rate

  2. BOption (b)

    immigration rate

  3. COption (c)

    mortality rate

  4. DOption (d)

    Population growth rate

View answer & explanation

Correct answer

Answer: (d)D.

Population growth rate

Why this answer is correct

Explanation:

Let N be the number of population then the changes in number of individuals in population over time i.e., dNdtdN\over dt is called population growth rate.

where as the mortality or death rate is the proportion of a population who die of a defined cause. 

Option (4) is true.

Question 136

Any non-empty set of R which is bounded from above has ______?

  1. AOption (a)

    An infinite exists

  2. BOption (b)

    Both exist finitely

  3. COption (c)

    l.u.b

  4. DOption (d)

    g.l.b

View answer & explanation

Correct answer

Answer: (c)C.

l.u.b

Why this answer is correct

Explanation:

Any non-empty set of R which is bounded from above has least upper bound (l.u.b) and the non-empty set of R which is bounded from below has the greatest lower bound (g.l.b)

Let's consider the set �={�∈�:�<3} A = {x ∈ R : x < 3}. This set contains all real numbers that are strictly less than 3.

  • The set �����

    Code
     A is bounded from above because 3 is an upper bound for �����[Math Processing Error]
    
     A. Any number less than 3 is also an upper bound.
    
  • However, the least upper bound (supremum) of � A is 3, because it is the smallest real number greater than or equal to all elements of ����

    Code
     A. No number less than 3 is an upper bound for �����[Math Processing Error]
    
     A.
    

Option (3) is true.

Question 137

When the per capita rate of increase (r) takes the same positive value regardless of the population size, then we get which growth?

  1. AOption (a)

    transversal growth

  2. BOption (b)

    exponential growth

  3. COption (c)

    both logistic and exponential

  4. DOption (d)

    logistics growth

View answer & explanation

Correct answer

Answer: (b)B.

exponential growth

Why this answer is correct

Concept -

Exponential growth occurs when the per capita rate of increase (r) remains constant, leading to a growth rate that accelerates over time and results in a continuously increasing population size.

This growth pattern is characteristic of scenarios where resources are abundant and population growth is not limited by factors such as competition or resource depletion.

Explanation:

When the per capita rate of increase (r) takes the same positive value regardless of the population size, then we get exponential growth.

Option (2) is true.

Question 138

Pick the wrong statement?

  1. AOption (a)

    Any Cauchy sequence is bounded.

  2. BOption (b)

    In real every bounded monotonic sequence is divergent

  3. COption (c)

    Any real Cauchy sequence is convergent

  4. DOption (d)

    Any convergent sequence is Cauchy

View answer & explanation

Correct answer

Answer: (b)B.

In real every bounded monotonic sequence is divergent

Why this answer is correct

Explanation:

We know that

Any cauchy sequence is bounded.

In real every bounded monotonic sequence is convergent.

Any real Cauchy sequence is convergent

Any convergent sequence is cauchy

Hence (2) is the wrong statement.

Question 139

If cardinality of a set A is 6 and that of set B is 7 then find the Cardinality of A Δ B?

  1. AOption (a)

    7

  2. BOption (b)

    35

  3. COption (c)

    5

  4. DOption (d)

    can not be determined

View answer & explanation

Correct answer

Answer: (d)D.

can not be determined

Why this answer is correct

Concept use:

 

n(A Δ B) = n(A ∪ B) - n(A ∩ B)

Explanation:

Given cardinality of A, n(A) = 6, cardinality of B, n(B) = 7.

n(A Δ B) = n(A ∪ B) - n(A ∩ B) = n(A) + n(B) - n(A ∩ B) -  n(A ∩ B)

Here cardinality of A ∩ B i.e., n(A ∩ B) is not given.

So, the cardinality of A Δ B can not be determined.

Option (4) is true

Question 140

What is the limit point of the sequence < f > = 1?

  1. AOption (a)

    2

  2. BOption (b)

    infinity

  3. COption (c)

    0

  4. DOption (d)

    1

View answer & explanation

Correct answer

Answer: (d)D.

1

Why this answer is correct

Concept -

If a be the term of the sequence and it repeats infinite times in the sequence then a is the limit point for the sequence.

Explanation:

<f> = 1

This implies that it is constant sequence.

Hence limit point is 1

(4) is correct

Discipline 3 (20 questions)

Question 141

Let f and g be two uniformly continuous functions on interval I and also each function is bounded on I, then what can you not say about product f.g?

  1. AOption (a)

    f.g is continous

  2. BOption (b)

    f.g is bounded

  3. COption (c)

    f.g is integrable

  4. DOption (d)

    f.g is uniformly continous on R

View answer & explanation

Correct answer

Answer: (d)D.

f.g is uniformly continous on R

Why this answer is correct

Concept -

Let f and g be two uniformly continuous functions on interval I and also each function is bounded on I then 

(i) f.g is continous

(ii) f.g is bounded

(iii) f.g is integrable

Explanation:

Let f and g be two uniformly continuous functions on interval I and each function is bounded on I, then f.g may not be uniformly continous on R\mathbb R.

Counter example -

If f(x) = x and g(x) = x and the interval I = [0,1]

Now f and g is uniformly continuous on R as well but f.g = x2 is not uniformly on R\mathbb R.

(4) is correct

Question 142

If f(x, y) = 0 then find the directional derivative at c = (0, 0) along the direction u = (a, b)?

  1. AOption (a)

    1

  2. BOption (b)

    2

  3. COption (c)

    0

  4. DOption (d)

    3

View answer & explanation

Correct answer

Answer: (c)C.

0

Why this answer is correct

Concept:

Directional derivative at c = (x0, y0) along the direction of u = (a, b) is

Duf = lim⁡h→0f(x0+ha,y0+hb)−f(x0,y0)h\lim_{h\to0}\frac{f(x_0+ha, y_0+hb)-f(x_0, y_0)}{h}

Explanation:

f(x, y) = 0

Hence directional derivative at c = (0, 0) along the direction u = (a, b)

Duf = lim⁡h→0f(0+ha,0+hb)−f(0,0)h\lim_{h\to0}\frac{f(0+ha, 0+hb)-f(0, 0)}{h} = lim⁡h→00−0h\lim_{h\to0}\frac{0- 0}{h} = 0

(3) is correct

Question 143

Find the value of ∫∫CurlF⃗.dr⃗\int \int Curl \vec F. d\vec r  where F(x, y, z) = (y + z, z + x, x + y)

  1. AOption (a)

    -1

  2. BOption (b)

    2

  3. COption (c)

    0

  4. DOption (d)

    1

View answer & explanation

Correct answer

Answer: (c)C.

0

Why this answer is correct

Concept -

The curl of a vector field F=(P,Q,R) \mathbf{F} = (P, Q, R) is given by the vector cross product of the del operator with F \mathbf{F} , i.e., ∇×F\nabla \times \mathbf{F} . It is computed as:

∇×F\nabla \times \mathbf{F}  = (∂R∂y−∂Q∂z,∂P∂z−∂R∂x,∂Q∂x−∂P∂y)\left( \frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z}, \frac{\partial P}{\partial z} - \frac{\partial R}{\partial x}, \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right)

Explanation -

The form f corresponds to a vector field F=(y+z,z+x,x+y) \mathbf{F} = (y+z, z+x, x+y).

Now P = y+z , Q = z+x , and  R = x+y  into the formula for the curl:

  1. Compute ∂R∂y−∂Q∂z \frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z} :

∂R∂y=∂(x+y)∂y=1,∂Q∂z=∂(z+x)∂z=1 \frac{\partial R}{\partial y} = \frac{\partial (x + y)}{\partial y} = 1, \quad \frac{\partial Q}{\partial z} = \frac{\partial (z + x)}{\partial z} = 1   

⇒ ∂R∂y−∂Q∂z \frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z} = 1 - 1 = 0 

  1. Compute ∂P∂z−∂R∂x \frac{\partial P}{\partial z} - \frac{\partial R}{\partial x} :

∂P∂z=∂(y+z)∂z=1,∂R∂x=∂(x+y)∂x=1\frac{\partial P}{\partial z} = \frac{\partial (y + z)}{\partial z} = 1, \quad \frac{\partial R}{\partial x} = \frac{\partial (x + y)}{\partial x} = 1

⇒ ∂P∂z−∂R∂x \frac{\partial P}{\partial z} - \frac{\partial R}{\partial x}  = 1 - 1 = 0 

  1. Compute ∂Q∂x−∂P∂y\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} :

∂Q∂x=∂(z+x)∂x=1,∂P∂y=∂(y+z)∂y=1\frac{\partial Q}{\partial x} = \frac{\partial (z + x)}{\partial x} = 1, \quad \frac{\partial P}{\partial y} = \frac{\partial (y + z)}{\partial y} = 1

⇒ ∂P∂z−∂R∂x \frac{\partial P}{\partial z} - \frac{\partial R}{\partial x}  = 1 - 1 = 0 

Put these values in the given formula we get -

Hence, the curl of  F\mathbf{F}  is:

CurlF⃗=∇×F=(0,0,0)Curl \vec F =\nabla \times \mathbf{F} = (0, 0, 0)

Now ∫∫CurlF⃗.dr⃗=∫∫0.dr⃗=0\int \int Curl \vec F. d\vec r = \int \int 0. d\vec r = 0

Hence Option(3) is correct.

Question 144

The function f(x) = x for every x in R which is continuous in R is called

  1. AOption (a)

    Riemann function

  2. BOption (b)

    Constant function

  3. COption (c)

    Identity function

  4. DOption (d)

    Dirichlet function

View answer & explanation

Correct answer

Answer: (c)C.

Identity function

Why this answer is correct

Explanation:

The function f(x) = x for x ∈ R is called identity function which is continuous everywhere.

An example of the identity function would be �(�)=��(�)=��(�)=�

Code
f(x) = x where ���

x belongs to the set of real numbers ���

R. For instance, if you plug in �=5�=5�=5

x = 5, the function would output �(5)=5�(5)=5�(5)=5

f(5) = 5.<br>

Similarly, for any other real number input, the output will be the same as the input due to the nature of the identity function.

Option (3) is true.

Question 145

Which condition is not required in checking for Taylor's theorem?

  1. AOption (a)

    It's (n -1)th derivative is derivable on (a, b)

  2. BOption (b)

    It's (n - 1)th derivative is continuous on [a, b]

  3. COption (c)

    f is necessarily bounded

  4. DOption (d)

    there exists a real number between a and b

View answer & explanation

Correct answer

Answer: (c)C.

f is necessarily bounded

Why this answer is correct

Concept -

Taylor's theorem -

Let  f(x) be a function that is n times differentiable on an interval containing [a, b], and let x = c be a point within that interval. Then, there exists a real number ξ  between a and b such that the Taylor polynomial of degree n  for f(x) centered at c can be expressed as:

f(x)=Pn(x)+Rn(x)f(x) = P_n(x) + R_n(x)

where:

Pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!(x−c)2+f′′′(c)3!(x−c)3+…+f(n)(c)n!(x−c)n P_n(x) = f(c) + f'(c)(x - c) + \frac{f''(c)}{2!}(x - c)^2 + \frac{f'''(c)}{3!}(x - c)^3 + \ldots + \frac{f^{(n)}(c)}{n!}(x - c)^n

 is the Taylor polynomial of degree n for  f(x) centered at c,

  

Rn(x) is the remainder term, given by Rn(x)=f(n+1)(ξ)(n+1)!(x−c)n+1R_n(x) = \frac{f^{(n+1)}(ξ)}{(n+1)!}(x - c)^{n+1} .

The remainder term Rn(x) quantifies the difference between the actual function f(x) and its Taylor polynomial approximation Pn(x). The presence of ξ ensures that Taylor's theorem guarantees an exact equality at some point between a and b, assuming the function f(x) satisfies the conditions of the theorem.

Explanation:

According to Taylor's theorem, f is not necessarily to be bounded

Hence condition (3) is not required

Question 146

When will be matrix of derivative of f given by f(x, y) = (x - y, xy) will be singular?

  1. AOption (a)

    if x = y

  2. BOption (b)

    if x = 0

  3. COption (c)

    if x = -y

  4. DOption (d)

    if y = 0

View answer & explanation

Correct answer

Answer: (c)C.

if x = -y

Why this answer is correct

Explanation:

f(x, y) = (x - y, xy)

i.e., f1 = x - y and f2 = xy

∂f1∂x{\partial f_1\over \partial x} = 1, ∂f1∂y{\partial f_1\over \partial y} = -1, ∂f2∂x{\partial f_2\over \partial x} = y, ∂f2∂y{\partial f_2\over \partial y} = x

matrix of derivative of f will be zero if

\(\begin{vmatrix}{\partial f_1\over \partial x}&{\partial f_1\over \partial y}\{\partial f_2\over \partial x}&{\partial f_2\over \partial y}\end{vmatrix}\) = 0

⇒ \(\begin{vmatrix}1&-1\y&x\end{vmatrix}\) = 0

⇒ x + y = 0

⇒ x = -y

Option (3) is true.

Question 147

The oscillation of a bounded function f on an interval [a, b] is the ______ of the set {|f(x) - f(y)|} of the numbers.

  1. AOption (a)

    supremum

  2. BOption (b)

    infimum

  3. COption (c)

    maximum

  4. DOption (d)

    minimum

View answer & explanation

Correct answer

Answer: (a)A.

supremum

Why this answer is correct

Concept -

The oscillation of a bounded function on an interval measures how much the function can vary within that interval. It is defined as the supremum (least upper bound) of the set of absolute differences between the function values at different points within the interval. In simpler terms, it represents the maximum distance between any two points on the graph of the function within the given interval.

Explanation:

The oscillation of a bounded function f on an interval [a, b] is the supremum of the set {|f(x) - f(y)|} of the numbers.

(1) is correct

Question 148

What is the interval of Taylor series expansion of tan(x)?

  1. AOption (a)

    (-π, π)

  2. BOption (b)

    (0, 90)

  3. COption (c)

    (-90, 90)

  4. DOption (d)

    Infinite field

View answer & explanation

Correct answer

Answer: (c)C.

(-90, 90)

Why this answer is correct

Concept -

tan(x)=x+x33+2x515+17x7315+⋯tan(x) = x + \frac{x^3}{3} + \frac{2x^5}{15} + \frac{17x^7}{315} + \cdots

Explanation -

The Taylor series expansion of tan(x) is centered around x = 0 and it is given by:

tan(x)=x+x33+2x515+17x7315+⋯tan(x) = x + \frac{x^3}{3} + \frac{2x^5}{15} + \frac{17x^7}{315} + \cdots

This Taylor series expansion is valid for all x such that |x| < π2\frac{\pi}{2} , which means it converges within the interval .

Beyond this interval, the tangent function has singularities (vertical asymptotes) at x=π2+nπ x = \frac{\pi}{2} + n\pi where n is an integer,

so the Taylor series does not converge beyond (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right).

Hence Option (3) is correct.

Question 149

The functions which are present on one side of Green's theorem are of which kind?

  1. AOption (a)

    Continuous partial derivative

  2. BOption (b)

    only partial derivatives

  3. COption (c)

    discrete derivatives

  4. DOption (d)

    complete derivatives

View answer & explanation

Correct answer

Answer: (a)A.

Continuous partial derivative

Why this answer is correct

Explanation:

Let C be the positively oriented, smooth, and simple closed curve in a plane, and D be the region bounded by the C. If P and Q are the functions of (x, y) defined on the open region, containing D and have continuous partial derivatives, then Green’s theorem is stated as

∫C(Pdx+Qdy)\int_C (Pdx+Qdy) = ∫∫D(∂Q∂x−∂P∂y)dxdy\int\int_D\left({\partial Q\over \partial x}-{\partial P\over \partial y}\right)dxdy

i.e., the functions which are present on one side of Green's theorem are Continuous partial derivative

Option (1) is true.

Question 150

Which theorem is valid in calculating integral for a multiple connected domain R?

  1. AOption (a)

    Green's theorem

  2. BOption (b)

    Stokes theorem

  3. COption (c)

    Iterated integrals

  4. DOption (d)

    Gauss divergence theorem

View answer & explanation

Correct answer

Answer: (a)A.

Green's theorem

Why this answer is correct

Explanation:

Let C be the positively oriented, smooth, and simple closed curve in a plane, and D be the region bounded by the C. If P and Q are the functions of (x, y) defined on the open region, containing D and have continuous partial derivatives, then Green’s theorem is stated as

∫C(Pdx+Qdy)\int_C (Pdx+Qdy) = ∫∫D(∂Q∂x−∂P∂y)dxdy\int\int_D\left({\partial Q\over \partial x}-{\partial P\over \partial y}\right)dxdy

Therefore, Green's theorem is valid in calculating integral for a multiple connected domain R.

Option (1) is true.

Question 151

While finding maximum value of a function what will we get in the case if it's second derivative becomes zero?

  1. AOption (a)

    we get maxima at that point

  2. BOption (b)

    we get minima at that point

  3. COption (c)

    we get possible inflection point

  4. DOption (d)

    we get both maxima and minima

View answer & explanation

Correct answer

Answer: (c)C.

we get possible inflection point

Why this answer is correct

Explanation:

Let f(x) be a function. Then we get the critical points from f'(x) = 0.

If f''(x) < 0 at the critical point then we get maxima at that point.

If f''(x) > 0 at the critical point then we get minima at that point.

If f''(x) = 0 at the critical point then we get possible inflection point.

Hence while finding maximum value of a function, if it's second derivative becomes zero we get possible inflection point.

Option (3) is true.

Question 152

Let a lie in the domain of a function f such that for all x in the domain, f(x) < f(a)

  1. AOption (a)

    f is said to have a minimum value at x = a.

  2. BOption (b)

    f is said to have a maximum value at x = a.

  3. COption (c)

    f is unbounded

  4. DOption (d)

    f has both a maximum and a minimum value at x = a.

View answer & explanation

Correct answer

Answer: (b)B.

f is said to have a maximum value at x = a.

Why this answer is correct

Explanation:

A function f(x) is said to have a maximum at a point x = a if f(x) < f(a) for all x and said to have a minimum at a point x = a if f(x) > f(a) for all x.

Hence option (2) is true.

Question 153

The sequence given by interval [0,1] is ______.

  1. AOption (a)

    Bounded

  2. BOption (b)

    unbounded

  3. COption (c)

    connvergent

  4. DOption (d)

    divergent

View answer & explanation

Correct answer

Answer: (a)A.

Bounded

Why this answer is correct

Explanation:

The sequence given by interval [0,1] is bounded with lower bound 0 and upper bound 1 because all the elements of the sequence belongs to [0,1].

Hence the sequence is bounded.

The sequence is need not be convergent if you take an={0n  is  odd 1n  is  even a_n = \begin{cases} 0 & n\ \ is \ \ odd\ 1 & n\ \ is \ \ even\ \end{cases}

(1) is correct

Question 154

If y is expressed in terms of a variable x as y = f(x), then y is called what?

  1. AOption (a)

    explicit function

  2. BOption (b)

    convergent function

  3. COption (c)

    implicit function

  4. DOption (d)

    divergent function

View answer & explanation

Correct answer

Answer: (a)A.

explicit function

Why this answer is correct

Explanation:

An explicit function is an algebraic function in which the output variable (dependent variable) can be written explicitly only in terms of the input variable (independent variable).

Hence, The Correct Option is 1.

Question 155

How do we find the volume of a solid surface?

  1. AOption (a)

    By finding its line integral

  2. BOption (b)

    By double integrating it

  3. COption (c)

    By integrating over the surface

  4. DOption (d)

    By integrating it threefold over the surface

View answer & explanation

Correct answer

Answer: (d)D.

By integrating it threefold over the surface

Why this answer is correct

Concept -

The volume of a solid surface, we integrate over the surface. This involves calculating the triple integral of the function representing the surface over the region it occupies in three-dimensional space.

The integration process considers the infinitesimal volume elements throughout the surface to determine the total volume enclosed by the surface.

Explanation:

To find the volume of a solid surface we integrate the threefold over the surface.

Option (4) is true.

Question 156

The necessary and sufficient condition for a function f to be Riemann integrable is that for every partition P for every ε > 0; which of the following condition must occur?

  1. AOption (a)

    Upper and lower sum vanishes

  2. BOption (b)

    |U(f, P) - L(f, P)| > ε

  3. COption (c)

    |U(f, P) - L(f, P)| = ε

  4. DOption (d)

    |U(f, P) - L(f, P)| < ε

View answer & explanation

Correct answer

Answer: (d)D.

|U(f, P) - L(f, P)| < ε

Why this answer is correct

Concept -

Theorem -

f(x) is integrable on [a,b] if and only if for every ϵ > 0 there exist a partition P such that U(P,f) - L(P,f) < ϵ 

Explanation:

The necessary and sufficient condition for a function f to be Riemann integrable is that for every partition P for every ε > 0, |U(f, P) - L(f, P)| < ε where U(P, f) is upper Reimann sum and L(P. f) is Reimann sum.

(4) is correct

Question 157

Pick the correct statement.

  1. AOption (a)

    If function is increasing in interval it is not increasing in each of its subinterval

  2. BOption (b)

    Every continous function is not Riemann integrable

  3. COption (c)

    Every monotonic increasing function f is not Riemann integrable

  4. DOption (d)

    Every continuous function is Riemann integrable

View answer & explanation

Correct answer

Answer: (d)D.

Every continuous function is Riemann integrable

Why this answer is correct

Concept -

(i) Every continuous function is Riemann Integrable because it has 0 discontinuous points.  

(ii) Every monotone function has at most countable discontinuity.

(iii) If the function has countable discontinuity then the function is Riemann Integrable.

Explanation:

For option (1) - 

If function is increasing in interval then it is increasing in each of its subinterval.

So, it's a false option.

Hence by using above concept we get -

option(4) is correct.

Question 158

Find the simultaneous limit of function y sin(1/x) ?

  1. AOption (a)

    1

  2. BOption (b)

    0

  3. COption (c)

    3

  4. DOption (d)

    2

View answer & explanation

Correct answer

Answer: (b)B.

0

Why this answer is correct

Explanation:

Simultaneous limit of the function 

= lim⁡x→0lim⁡y→0ysin⁡(1/x)\lim_{x\to0}\lim_{y\to0}y\sin(1/x) 

= lim⁡x→00×sin⁡(1/x)\lim_{x\to0}0\times\sin(1/x)

= lim⁡x→00×sin⁡(1/x)\lim_{x\to0}0\times\sin(1/x)

= 0

Option (2) is true.

Question 159

Which of the following is not the application of Taylor's series?

  1. AOption (a)

    It is used in optimization techniques

  2. BOption (b)

    It reduces mathematical proofs

  3. COption (c)

    It is used to find value of whole function

  4. DOption (d)

    It fails to solve power flow analysis

View answer & explanation

Correct answer

Answer: (d)D.

It fails to solve power flow analysis

Why this answer is correct

Explanation:

It is used in optimization techniques: True. Taylor series expansions are often used in optimization algorithms, especially in numerical optimization methods, to approximate functions and iteratively find optimal solutions.

It reduces mathematical proofs: True. Taylor's series can be used to simplify mathematical proofs by providing accurate approximations of functions and enabling easier manipulation of expressions.

It is used to find the value of the whole function: True. Taylor series can be used to approximate the value of a function at a point based on its derivatives at that point, providing a way to estimate the behavior of the entire function.

It fails to solve power flow analysis: False. Taylor series expansions can be used in power flow analysis and related engineering applications to linearize complex nonlinear systems and make them more manageable for analysis and simulation.

Hence, The option that does not represent a typical application of Taylor's series is (4) It fails to solve power flow analysis.

Question 160

If r = 2xyi + j + kl then the value of curl(r) is 

  1. AOption (a)

    -2yk

  2. BOption (b)

    -2xk

  3. COption (c)

    0

  4. DOption (d)

    -2zk

View answer & explanation

Correct answer

Answer: (b)B.

-2xk

Why this answer is correct

Concept - 

The curl of a vector field

F(x,y,z)=P(x,y,z)i+Q(x,y,z)j+R(x,y,z)k \mathbf{F}(x, y, z) = P(x, y, z)\mathbf{i} + Q(x, y, z)\mathbf{j} + R(x, y, z)\mathbf{k} is given by:

 curl(F)=(∂R∂y−∂Q∂z)i+(∂P∂z−∂R∂x)j+(∂Q∂x−∂P∂y)k\text{curl}(\mathbf{F}) = \left( \frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z} \right)\mathbf{i} + \left( \frac{\partial P}{\partial z} - \frac{\partial R}{\partial x} \right)\mathbf{j} + \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right)\mathbf{k}

Explanation -

We have, r=2xyi+j+lk\mathbf{r} = 2xy\mathbf{i} + \mathbf{j} + l\mathbf{k} , so:

P(x, y, z) = 2xy 

Q(x, y, z) = 1

R(x, y, z) = l

Now, let's compute the partial derivatives:

∂P∂y=2x\frac{\partial P}{\partial y} = 2x

∂Q∂z=0\frac{\partial Q}{\partial z} = 0

∂R∂x=0\frac{\partial R}{\partial x} = 0

∂Q∂x=0 \frac{\partial Q}{\partial x} = 0

∂R∂y=0\frac{\partial R}{\partial y} = 0

∂P∂z=0\frac{\partial P}{\partial z} = 0

Now, plug these derivatives into the curl formula:

curl(r)=(0−0)i+(0−0)j+(0−2x)k\text{curl}(\mathbf{r}) = \left( 0 - 0 \right)\mathbf{i} + \left( 0 - 0 \right)\mathbf{j} + \left( 0 - 2x \right)\mathbf{k}

= −2xk-2x\mathbf{k}

So, the value of curl(r)\text{curl}(\mathbf{r}) is −2xk-2x\mathbf{k} .

Discipline 4 (20 questions)

Question 161

Every element of a group G when expressed as internal Direct product of a, b, c, ... z if and only of every element is uniquely expressed as ?

  1. AOption (a)

    G = a. b. c ... z

  2. BOption (b)

    G = a - b - c ... -z

  3. COption (c)

    G = a + b - c. .. z

  4. DOption (d)

    G = a + b + c +.... + z

View answer & explanation

Correct answer

Answer: (a)A.

G = a. b. c ... z

Why this answer is correct

Explanation:

To express a group G as an internal direct product of subgroups a, b, c, ... z, you typically mean that each element of G can be represented uniquely as a product of elements from each of these subgroups.

This implies that every element g in G can be expressed uniquely as g = a . b . c . ... . z, where a is from subgroup a, b is from subgroup b, and so forth.

So the correct option is:

G = a . b . c ... z

This expression represents the unique product from each subgroup. Note that the operation here isn't necessarily numerical multiplication— it's the group operation, whatever that might be in the specific context of the group in question.

Question 162

The expansion of power series having R as the radius of convergence and x, a be any two points in R, converges if ______.

  1. AOption (a)

    |x - a| > R

  2. BOption (b)

    |x - a❘ = R

  3. COption (c)

    nowhere convergent

  4. DOption (d)

    |x - a| < R

View answer & explanation

Correct answer

Answer: (d)D.

|x - a| < R

Why this answer is correct

Explanation:

The expansion of power series ∑an(x−a)n\sum a_n(x-a)^n having R as the radius of convergence and x, a be any two points in R, converges if |x - a| < R

(4) is correct

Question 163

If we are given two overlapping sets A and B in metric space then what can we say about d(A, B)?

  1. AOption (a)

    infinity

  2. BOption (b)

    doesn't exist

  3. COption (c)

    zero

  4. DOption (d)

    finite

View answer & explanation

Correct answer

Answer: (c)C.

zero

Why this answer is correct

Explanation -

In a metric space, the distance between two sets A and B, denoted as d(A, B), is defined as d(A, B) = inf{d(a, b) : a ∈ A, b ∈ B}

In other words, the distance between A and B is the infimum (greatest lower bound) of the distances between each element of A and each element of B.

However, when the sets A and B overlap, meaning they have at least one common element, the distance between them is 0. This is because there exists at least one pair (a,b) such that a = b and both are in A and B. And as per the properties of metric space, the distance between identical points is 0 (d(a, b) = d(a, a) = 0), hence d(A, B) = 0.

Hence option(iii) is correct.

Question 164

Find the limit point of the sequence <1, 2, 1/2, 3, 1/3..... >

  1. AOption (a)

    3

  2. BOption (b)

    0

  3. COption (c)

    2

  4. DOption (d)

    1

View answer & explanation

Correct answer

Answer: (b)B.

0

Why this answer is correct

Concept use:

The limit of a sequence is a point such that every neighborhood around it contains infinitely many terms of the sequence

Explanation:

<1, 2, 1/2, 3, 1/3..... > 

 

The Sequence having even terms as 1/2, 1/3, 1/4, ..... which tends towards 0 

Hence, Zero is the Limit point of the Sequence because it Contains infinitely many terms in the neighborhood.

The Sequence has odd terms such as 1, 2, 3, 4, ..... which goes to infinity 

Hence, The Limit point of the Sequence is Zero

Hence, The correct Answer is option 2.

Question 165

If f is a continuous function from X to Y, then this property is called?

  1. AOption (a)

    completeness of metric space

  2. BOption (b)

    distance variant

  3. COption (c)

    continuous invariant

  4. DOption (d)

    continous variant

View answer & explanation

Correct answer

Answer: (c)C.

continuous invariant

Why this answer is correct

Explanation -

If f is a continuous function from one metric space X to another metric space Y, then the property being referred to is typically called the "Continuity of f". In more precise terms, a function f: X → Y is continuous if for any open set O in Y, the preimage f−1(O)f^{-1}(O) is an open set in X. This use of open sets is a standard way to define continuity in topology and metric spaces then the property being referred  the "Continuous invariant of f".

Hence option (iii) is correct.

Question 166

A group is called abelian if it satisfies ______ property.

  1. AOption (a)

    associative property

  2. BOption (b)

    existence of identity

  3. COption (c)

    existence of inverse

  4. DOption (d)

    commutative property

View answer & explanation

Correct answer

Answer: (d)D.

commutative property

Why this answer is correct

Concept -

An abelian group is a set, G, with an operation (commonly denoted as '+'), satisfying these properties:

Closure: If a and b are in G, then a+b is in G.

Associativity: For all a, b, c in G, (a+b)+c equals a+(b+c).

Identity: There's an element '0' in G, such that for all a in G, 0+a and a+0 equals a.

Inverse: For every a in G, there exists a '-a' in G, such that a + (-a) and (-a) + a equals 0.

Commutativity: For all a, b in G, a+b equals b+a.

Explanation-

A group satisfy all four property like closure, Associativity, Identity and Inverse. In question we have a group so if we add the commutative property then it will be Abelian group.

Hence option (iv) is correct.

Question 167

Every absolutely convergent improper integral is ______.

  1. AOption (a)

    infinite

  2. BOption (b)

    oscillatory

  3. COption (c)

    divergent

  4. DOption (d)

    convergent

View answer & explanation

Correct answer

Answer: (d)D.

convergent

Why this answer is correct

Concept -

Every absolutely convergent improper integral is always convergent but converse is not true in general.

Explanation:

Every absolutely convergent improper integral is convergent.

(4) is correct

Question 168

Which statement states that "Every complete metric space is of second category"?

  1. AOption (a)

    Baire category theorem

  2. BOption (b)

    Cantor Theorem

  3. COption (c)

    Fundamental theorem

  4. DOption (d)

    Baire sandwich theorem

View answer & explanation

Correct answer

Answer: (a)A.

Baire category theorem

Why this answer is correct

Explanation -

The statement given in the question is known as the Baire Category Theorem. In its simplest form, it states that:

"Every complete metric space is of second category."

In the context of topology, a space is said to be of second category (or a "Baire space") if it cannot be expressed as a countable union of nowhere dense sets (sets whose closure has empty interior). So, the Baire Category Theorem verifies that complete metric spaces are "large" in the sense that they are not the countable union of "small" sets, which are in this context the nowhere dense sets. This theorem is a fundamental result in topology and has significant implications in various fields of mathematics.

Hence option (i) is correct.

Question 169

If f = <1/n>, then what can you say about monotonic nature of f?

  1. AOption (a)

    monotonically decreasing

  2. BOption (b)

    both increasing and decreasing

  3. COption (c)

    monotonically increasing

  4. DOption (d)

    monotonic

View answer & explanation

Correct answer

Answer: (a)A.

monotonically decreasing

Why this answer is correct

Concept -

(i) A sequence is monotonically increasing if an ≤ an+1

(ii) A sequence is monotonically decreasing if an ≥ an+ 1

Explanation:

f = <1/n> = {1, 12\frac12, 13\frac13, 14\frac14, ...} and 1 > 1/2 > 1/3 ... 

So we can see that sequence is monotonically decreasing

(1) is correct

Question 170

Inner automorphism corresponding to every element of an abelian group is?

  1. AOption (a)

    trivial

  2. BOption (b)

    infinite

  3. COption (c)

    bounded

  4. DOption (d)

    non trivial

View answer & explanation

Correct answer

Answer: (a)A.

trivial

Why this answer is correct

Explanation -

In an abelian group (also known as a commutative group), the operation of the group commutes. This means that for any two elements a and b in the group, the equation ab = ba holds true. Because of the commutative property, the inner automorphism corresponding to any element of an abelian group is the identity function.

let (G, *) be an abelian group, and let's denote by ϕa(x)ϕ_a(x) the inner automorphism of G defined by some element a, where 'x' is an element of G. Thenϕa(x)=axa−1ϕ_a(x) = a x a⁻¹

However, since the group operation is commutative, we can rearrange the terms to obtain: ϕa(x)=aa−1x=ex=xϕ_a(x) = a a⁻¹ x = e x = x  where 'e' is the identity element of the group.

Since ϕa(x)=xϕ_a(x) = x for any element x in the group,  the inner automorphism of an element of the Abelian group is the identity map for any element a in an abelian group G.

Hence option (i) is true.

Question 171

Every uniformly continuous function on an interval is ______ on that interval.

  1. AOption (a)

    continuous

  2. BOption (b)

    convergent

  3. COption (c)

    divergent

  4. DOption (d)

    oscillatory

View answer & explanation

Correct answer

Answer: (a)A.

continuous

Why this answer is correct

Concept -

Every uniformly continuous function is continuous on any domain.

Explanation:

Every uniformly continuous function on an interval is always continuous on that interval.

(1) is correct

Question 172

If a group G is internal Direct product of its subgroups A, B, C, .... Z then G is isomorphic to ______.

  1. AOption (a)

    A, B, C, ... Z

  2. BOption (b)

    external direct product of A, B, C... Z

  3. COption (c)

    internal Direct product of A, B, C... Z

  4. DOption (d)

    it is not isomorphic

View answer & explanation

Correct answer

Answer: (b)B.

external direct product of A, B, C... Z

Why this answer is correct

Concept -

If a group G is the internal direct product of its subgroups A, B, C, ..., Z then G is isomorphic to the external direct product of the groups A, B, C, ..., Z.

Explanation -

If a group G is the internal direct product of its subgroups A, B, C, ..., Z then G is isomorphic to the external direct product of the groups A, B, C, ..., Z.

Formally, if G = A x B x C x ... x Z for subgroups A, B, C, ..., Z of G, then G is isomorphic to the group A * B * C * ... * Z where * is the direct product operation.

In more precise terms, the fundamental theorem of finitely generated abelian groups states that every finitely generated abelian group G is isomorphic to a direct product of cyclic groups of prime power order.

Hence option(ii) is correct.

Question 173

Let (X, d) be a metric space then what can you say about X and d?

  1. AOption (a)

    d is called metric and X is called ground set

  2. BOption (b)

    both are called ground sets

  3. COption (c)

    d is called metric but can't say about X

  4. DOption (d)

    X is called metric and d is called ground set

View answer & explanation

Correct answer

Answer: (a)A.

d is called metric and X is called ground set

Why this answer is correct

Concept -

In a metric space (X, d):

  1. ( d ) is called the metric, which is a function that measures the distance between elements of the set ( X ).

  2. ( X ) is the set of elements, sometimes referred to as the ground set or the underlying set.

Explanation -

Let (X, d) be a metric space then d is called metric and X is called ground set

Hence option (1) is correct.

Question 174

Which of the following metric space is not complete?

  1. AOption (a)

    set of complex numbers

  2. BOption (b)

    set of rationals

  3. COption (c)

    set of irrationals

  4. DOption (d)

    set of real numbers

View answer & explanation

Correct answer

Answer: (b)B.

set of rationals

Why this answer is correct

Explanation:

An incomplete metric space is one where there exist Cauchy sequences that do not converge within the space. For instance, the set of rational numbers (ℚ, d), where d is the standard absolute difference, is an example of an incomplete metric space. This is because there are Cauchy sequences of rational numbers that converge to irrational numbers not in ℚ for example: sequence that approximates the square root of 2.

Hence option (2) is correct.

From the direct theorem we know that the set of real numbers is complete.

The set of complex numbers ℂ is complete, i.e., every Cauchy sequence in ℂ converges in ℂ.

(1) and (4) are complete

The set of irrational numbers is not complete when considered as a subspace of the real numbers with the standard Euclidean metric; this means that a Cauchy sequence of irrational numbers can converge to a rational number, which is not in the set of irrationals. 

(3) is also correct.

But in official answer (2) is correct only.

Question 175

Let (X, d) be a complete metric space and let B be a subset of X then if B is closed then B is also ______.

  1. AOption (a)

    Unbounded

  2. BOption (b)

    Complete

  3. COption (c)

    Dense

  4. DOption (d)

    Bounded

View answer & explanation

Correct answer

Answer: (b)B.

Complete

Why this answer is correct

Explanation -

Let (X, d) be a complete  metric space  and let B be a subset of X, then if B is compact, then B is complete.

Every Cauchy sequence in B is also a Cauchy sequence in X (because the metrics agree). Since X is complete, the sequence converges to some limit in X. Because B is closed, that limit point lies in B. Hence the sequence converges in B, so B is complete.

The correct option is Complete.

Question 176

Let (X, d) be a metric space and Pn be the Cauchy sequence defined then {Pn} is ______.

  1. AOption (a)

    divergent

  2. BOption (b)

    cauchy

  3. COption (c)

    bounded

  4. DOption (d)

    convergent

View answer & explanation

Correct answer

Answer: (d)D.

convergent

Why this answer is correct

Explanation -

Let (X, d) be a metric space and Pn be a Cauchy sequence. Then, by definition, the sequence {Pn} is said to be Cauchy.

A sequence {Pn} in a metric space is called a Cauchy sequence if for every positive real number ε > 0, there is a positive integer N such that for all natural numbers m, n > N, the distance d(Pm, Pn) < ε.

Basically, a Cauchy sequence is one where the terms of the sequence become arbitrarily close to each other as the sequence progresses.  If (X, d) is a complete metric space, then every Cauchy sequence converges to some limit in X. If the space is not complete, a Cauchy sequence may not have a limit within the space.

Hence option (iv) is true.

Question 177

What powers of x does expansion of sin(x) contains?

  1. AOption (a)

    all powers of x

  2. BOption (b)

    even powers of x

  3. COption (c)

    any alternate powers of x

  4. DOption (d)

    odd powers of x

View answer & explanation

Correct answer

Answer: (d)D.

odd powers of x

Why this answer is correct

Explanation:

The Maclaurin series expansion for Sin (x) is given by the summation from n=0 to infinity of (-1)n ×  x(2n+1)/(2n+1)!

The Expansion of Sinx = x -x3/3! + x5/5! -............

Hence, The Expansion of Sinx contains all the odd powers of x.

Hence, The Correct option is 4.

Question 178

In metric space which function is always continuous?

  1. AOption (a)

    bounded function

  2. BOption (b)

    distance function

  3. COption (c)

    continuous function

  4. DOption (d)

    discrete function

View answer & explanation

Correct answer

Answer: (b)B.

distance function

Why this answer is correct

Explanation -

Constant functions are always continuous in any space, including metric spaces. A constant function is a function for which the value of the function is the same for every input in the domain. Additionally, "identity function" is also always continuous in a metric space. Here, the output value is always equal to the input value, i.e., the function f: X -> X, where X is a metric space, defined by f(x) = x is always continuous.

the distance function in a metric space is also always continuous.

Formally, the distance function d: X × X -> R (where X is a metric space and R is the set of real numbers) is continuous.  This is the definition of the distance function for a metric space X: for any two points a, b in X, the distance function d(a, b) gives the distance between a and b.

Hence option (ii) is correct.

Question 179

If f is the derivative of some function on [a, b], then there exists a number c in (a, b) such that Integral of f with respect to x =

  1. AOption (a)

    f(c)

  2. BOption (b)

    f(c) . (b - a)

  3. COption (c)

    (b + a - c) f(c)

  4. DOption (d)

    f(c) . (b + a)

View answer & explanation

Correct answer

Answer: (b)B.

f(c) . (b - a)

Why this answer is correct

Concept use:

The Mean Value Theorem for Integrals states that if f is continuous on the closed interval [a, b], then there exists at least one number c in the open interval (a, b) such that:

∫from a to b f(x) dx = f(c) · (b - a)

This theorem guarantees the existence of at least one point c in the interior of the interval [a, b] where the value of the function f(c) multiplied by the length of the interval (b - a) gives the integral of f(x) over that interval

Explanation:

In the given statement, if f is the derivative of some function on the interval [a, b], then the Mean Value Theorem for Integrals applies.

According to this theorem, there exists a number c in the open interval (a, b) such that the integral of f(x) over the interval [a, b] is equal to f(c) multiplied by the length of the interval (b - a).

Hence, the correct option is: f(c) · (b - a)

Hence, The Correct Option is 2.

Question 180

Let (X, d) be a metric space and E is contained in X, E is called nowhere dense set if ______.

  1. AOption (a)

    closure of E is empty

  2. BOption (b)

    closure of E terminate after some steps

  3. COption (c)

    closure of E is not defined

  4. DOption (d)

    closure of E is finite

View answer & explanation

Correct answer

Answer: (a)A.

closure of E is empty

Why this answer is correct

Explanation -

In a metric space (X, d), a subset E is called a "nowhere dense" set if its closure has empty interior.

This means that for any point in X and for any radius, no matter how small, the open ball centered at that point with that radius always contains a point not in the closure of E.

In simpler terms, a set is nowhere dense if it is not dense in any neighborhood - it doesn't "fill up" any portion of the space.

Hence option (i) is correct.

Discipline 5 (10 questions)

Question 181

Which theorem states that "An integral function attains every finite value with atmost one possible exception"?

  1. AOption (a)

    Picard's theorem

  2. BOption (b)

    Jensen's inequality

  3. COption (c)

    Jensen's formula

  4. DOption (d)

    Schwartz' lemma

View answer & explanation

Correct answer

Answer: (a)A.

Picard's theorem

Why this answer is correct

Concept -

Picard's theorem states that a complex function, if analytic near an essential singularity, will attain every complex value, except possibly one, in any

neighborhood of that singularity.

Explanation:

Picard's theorem states that An integral function attains every finite value with atmost one possible exception.

Option (1) is true.

Question 182

What is order of convergence of cosh√z?

  1. AOption (a)

    0

  2. BOption (b)

    infinite

  3. COption (c)

    one

  4. DOption (d)

    two

View answer & explanation

Correct answer

Answer: (b)B.

infinite

Why this answer is correct

Explanation:

We know that the order of convergence of cosh z is infinity

So order of convergence of cosh√z is infinite

(2) is correct

Question 183

Which of the following group is not normal under usual ring operation?

  1. AOption (a)

    3 ssg

  2. BOption (b)

    2 ssg

  3. COption (c)

    7 ssg

  4. DOption (d)

    5 ssg

View answer & explanation

Correct answer

Answer: (b)B.

2 ssg

Why this answer is correct

Explanation -

For Option (1) - 3Z(the multiples of 3)3\mathbb{Z} (the \ multiples \ of \ 3 )

This subset consists of all integers that are multiples of 3. 

we need to verify that for every element h ∈ 3Z3\mathbb{Z}  and every element r in Z\mathbb{Z}, the product rh is also in 3Z3\mathbb{Z} .

Since multiplying any integer by 3 yields a multiple of 3, 3Z3\mathbb{Z}  is closed under multiplication and thus normal under the usual ring operation.

For Option (2) - 2Z2\mathbb{Z} (the multiples of 2):

2Z2\mathbb{Z}  is not normal under the usual ring operation because there exist elements h and r such that rh is not in 2Z2\mathbb{Z} .

For example, if we take h = 2  and r = 3, then rh = 3 x 2 = 6, which is not in 2Z2\mathbb{Z} .

For Option (3) - 7Z7\mathbb{Z}  (the multiples of 7):

Similar to 3Z3\mathbb{Z} , 7Z7\mathbb{Z}  is also normal under the usual ring operation because multiplying any integer by 7 yields a multiple of 7.

For Option (4) - 5Z5\mathbb{Z}  (the multiples of 5):

Like 3Z3\mathbb{Z} and 7Z7\mathbb{Z} , 5Z5\mathbb{Z} is normal under the usual ring operation because multiplying any integer by 5 yields a multiple of 5.

Hence Option (2) is correct.

Question 184

Name the smallest non cyclic group.

  1. AOption (a)

    abelian group of p order

  2. BOption (b)

    Q8Q_8

  3. COption (c)

    Matrix group

  4. DOption (d)

    K4K_4

View answer & explanation

Correct answer

Answer: (d)D.

K4K_4

Why this answer is correct

Concept -

(i) every prime order group is always cyclic.

(ii) every cyclic group is always abelian.

Explanation -

(i) Abelian group of p order is cyclic. Hence option (i) is false

(ii) Q8Q_8  group is non abelian non cyclic but it is not  smallest non cyclic group. Hence option (ii) is false.

(iii) Matrix group is non abelian non cyclic but it is not  smallest non cyclic group. Hence option (iii) is false.

(iv) K4K_4 group is abelian non cyclic but it is smallest non cyclic group. Hence option (iv) is true.

Question 185

Does C-R equations are necessary and sufficient for a function to be analytic?

  1. AOption (a)

    FALSE

  2. BOption (b)

    can't say about nature of equations

  3. COption (c)

    TRUE

  4. DOption (d)

    depend on range of functions

View answer & explanation

Correct answer

Answer: (a)A.

FALSE

Why this answer is correct

Explanation:

u(x,y)=xyu(x,y) = \sqrt{xy} , v(x,y)=0v(x,y) = 0

CR equation states that

 ∂u∂x=∂v∂y,∂v∂x=−∂u∂y,\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}, \frac{\partial v}{\partial x} = -\frac{\partial u}{\partial y},

Here \(\begin{align*} u_x(0,0) &= \lim_{h\to 0} \frac{u(0+h,0) - u(0,0)}{h} = 0, \ u_y(0,0) &= \lim_{k\to 0} \frac{u(0,0+k) - u(0,0)}{k} = 0. \end{align*}\)

vx(0, 0) = 0 and vy(0, 0) = 0 

Hence, CR  Equation is satisfied but Function is not Analytic 

Since, Limit of this function along y = mx not Exist 

∴ CR equation is only Necessary Condition but Not Sufficient 

Hence, Option 1 is Correct.

Question 186

The external direct product of two cyclic groups is ______.

  1. AOption (a)

    not abelian

  2. BOption (b)

    always cyclic

  3. COption (c)

    never cyclic

  4. DOption (d)

    need not cyclic

View answer & explanation

Correct answer

Answer: (d)D.

need not cyclic

Why this answer is correct

Concept -

if you have two cyclic groups of order m and n, the external direct product of these two groups will form a new group of order mn. If m and n are coprime, this group is cyclic. If m and n are not coprime , then the resulting group is not cyclic.

Explanation - 

For example, let's consider two cyclic groups, one of order 2 and one of order 3. Their external direct product will be a cyclic group of order 6, because 2 and 3 are coprime. However, if you take two cyclic groups both of order 2, their external direct product will be a group of order 4, but it won't be cyclic, it will rather be isomorphic to the Klein four-group, which is not a cyclic group.

Hence option(iv) is correct.

Question 187

Let k be the number of p-ssg of a finite group G. Then ______.

  1. AOption (a)

    k does not divide O(G)

  2. BOption (b)

    k divides O(G)

  3. COption (c)

    k does not exist

  4. DOption (d)

    k bipolars

View answer & explanation

Correct answer

Answer: (b)B.

k divides O(G)

Why this answer is correct

Concept -

If k is the number of p - ssg (subgroups of order p) of a finite group G, then k necessarily divides the order of G.

This means that the number of p - ssg evenly divides the total number of elements in the group.

Explanation -

Consider the cyclic group G=ZpG = \mathbb{Z}_p, where p is a prime number.

In this group, every nontrivial subgroup has order p, so the number of p - ssg is p - 1.

However, p - 1 does divide the order of G, which is p.

Therefore, the correct Option is (2).

Question 188

If f(z) is analytic function whose real part is constant then f(z) is ______.

  1. AOption (a)

    constant

  2. BOption (b)

    Function of x and y both

  3. COption (c)

    Function of y only

  4. DOption (d)

    Function of x only

View answer & explanation

Correct answer

Answer: (a)A.

constant

Why this answer is correct

Concept:

If f(z) = u + iv is an analytic function, then it must satisfy the Cauchy-Riemann equations,

ux = vy , uy= -vx

Calculations:

Let the real part of f(z) be a, where a is a constant.

f(z) = a + iv

ux = 0 and uy = 0 implies vy = 0 and vx = 0 (Using Cauchy-reimann equation)

So, f'(z) = ux + ivx = 0

Integraing both sides we get,

f(z) = constant

Hence, option (1) is correct.

Question 189

Multiply (1 2 3) and (5 6 4 1)?

  1. AOption (a)

    (1 5 6 4 2 3)

  2. BOption (b)

    (2 3 4 5 6 7)

  3. COption (c)

    (1 2 3 4 5 6)

  4. DOption (d)

    (3 6 3 7 3 8)

View answer & explanation

Correct answer

Answer: (a)A.

(1 5 6 4 2 3)

Why this answer is correct

Explanation:

The symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group 

 defined over a finite set of 

 symbols consists of the permutations that can be performed on the 

 symbols. Since there are 

 such permutation operations, the order (number of elements) of the symmetric group 

 is 

.

Multiplication of Symmetric Group :

 (1 2 3) 

Images of the first Permutation element

1 --> 2, 2 --> 3, 3 --> 1, 4 --> 4, 5 --> 5, 6 --> 6

(5 6 4 1)

Images of the Second Permutation element

1 --> 5, 2 --> 2, 3 --> 3, 4 --> 1, 5 --> 6, 6 --> 4

For Multiplying the Element of the Group 

we have to process from backward to forward

1 --> 5, 5 --> 5 so, The Image of 1 under Permutation is 5

2 --> 2, 2 --> 3 so, The image of 2 under Permutation is 3

3 --> 3, 3 --> 1 so, The image of 3 under Permutation is 1

4 --> 1, 1 --> 2 so, The image of 4 under Permutation is 2

5 --> 6, 6 --> 6 so, The image of 5 under Permutation is 6

6 --> 4, 4 --> 4 so, The image of 6 under Permutation is 4

So, The multiplication of (1 2 3)(5 6 4 1) = (1 5 6 4 2 3)

Question 190

What is the number of elements of order 100 in Z(200)?

  1. AOption (a)

    40

  2. BOption (b)

    120

  3. COption (c)

    80

  4. DOption (d)

    160

View answer & explanation

Correct answer

Answer: (a)A.

40

Why this answer is correct

Concept -

 Number of elements of order m in Zn is ϕ(n)\phi(n).

Explanation -

The number of elements of order 100 in Z(200) = 

ϕ(100)=22×52=100×(1−12)(1−15)1ˉ0×1×4=40\phi(100) = 2^2 \times 5^2 = 100 \times (1- \frac{1}{2})(1-\frac{1}{5})\=10 \times 1 \times 4 = 40

Teaching Methodology (10 questions)

Question 191

"What type of family allows a woman to marry more than one man?"

  1. AOption (a)

    Extended family

  2. BOption (b)

    Polygamous family

  3. COption (c)

    Monogamous family

  4. DOption (d)

    Polyandry family

View answer & explanation

Correct answer

Answer: (d)D.

Polyandry family

Why this answer is correct

There are various types of family structures, and they can vary based on cultural, societal, and personal factors.

Key Points

  • Polyandry is a form of marriage in which a woman is married to more than one man at the same time.
  • Polyandrous families are relatively rare, but they can be found in some traditional societies.

Hint

  • Extended family: An extended family is a family that includes multiple generations of relatives, such as grandparents, parents, children, grandchildren, aunts, uncles, and cousins.
  • Monogamous family: A monogamous family is a family in which a person is married to one spouse at a time.
  • Polygamous family: A polygamous family is a family in which a person is married to more than one spouse at the same time. However, polygamy is usually in the form of polygyny, where a man is married to multiple women. Polyandry is a rarer form of polygamy.

Hence, polyandry family is correct.

Question 192

Which of the following skill is a sociological term relating to a person's "EQ"?

  1. AOption (a)

    Hard skills

  2. BOption (b)

    People skills

  3. COption (c)

    Soft skills

  4. DOption (d)

    Social skills

View answer & explanation

Correct answer

Answer: (c)C.

Soft skills

Why this answer is correct

Soft skills are a set of personal attributes that enable someone to interact effectively and harmoniously with other people.

Key Points

  • Soft skills are often seen as complementary to hard skills, which are the technical skills and knowledge required to perform a specific job or task.
  • Emotional intelligence (EQ) is the ability to perceive, use, understand, manage, and handle emotions. EQ is an important soft skill that can help people to build relationships, communicate effectively, and resolve conflict.
  • Soft skills are important for success in both personal and professional life. They can help people to get along with others, to work effectively as part of a team, and to achieve their goals.
  • EQ is a particularly important soft skill for success in the workplace. People with high EQ are able to manage their own emotions and the emotions of others.
  • This can help them to build strong relationships with colleagues and customers, to resolve conflict effectively, and to lead teams successfully.

Hence, soft skills are a sociological term relating to a person's EQ.

Question 193

The school should aim at developing ______.

  1. AOption (a)

    Social, moral and spiritual values.

  2. BOption (b)

    Political and spiritual values.

  3. COption (c)

    Economic, political and social values.

  4. DOption (d)

    Emotional, Moral and political values.

View answer & explanation

Correct answer

Answer: (a)A.

Social, moral and spiritual values.

Why this answer is correct

A school is an educational institution designed to provide learning spaces and learning environments for the teaching of students under the direction of teachers. 

Key Points

  • The school should aim at developing social, moral, and spiritual values in students.
  • These values are essential for living a happy and fulfilling life. They also help students to become responsible and productive members of society.
  • Social values include things like cooperation, respect, and tolerance. Moral values include things like honesty, fairness, and justice. Spiritual values include things like compassion, forgiveness, and gratitude.
  • Schools can develop social, moral, and spiritual values in students through a variety of ways, such as teaching about different cultures and religions, encouraging students to participate in community service, providing opportunities for students to learn about ethics and moral reasoning, etc.

Hence, the school should aim at developing social, moral and spiritual values.

Question 194

From the following strategies which strategy can not be employed to make students conscious of gender issues which would result in developing an attitude of gender equality?

  1. AOption (a)

    Film analysis

  2. BOption (b)

    Society analysis

  3. COption (c)

    Analysis of data collected from Interview

  4. DOption (d)

    Analysis of Biographies

View answer & explanation

Correct answer

Answer: (d)D.

Analysis of Biographies

Why this answer is correct

Gender issues are the social, economic, and political challenges that people face due to their gender. Gender issues can impact both men and women, but they disproportionately impact women and girls.

Key Points

Effective strategies for making students conscious of gender issues and developing an attitude of gender equality:

  • Film analysis: Film analysis can be used to examine how gender roles and stereotypes are portrayed in films. Students can discuss how these portrayals can impact their own attitudes and beliefs about gender.
  • Society analysis: Society analysis can be used to examine how gender roles and stereotypes are perpetuated in society. Students can discuss how these roles and stereotypes impact the lives of both men and women.
  • Analysis of data collected from interviews: Analysis of data collected from interviews can be used to learn about the experiences and perspectives of people of different genders. This can help students to understand the challenges and barriers that people face due to their gender.

Hint

  • Analysis of biographies is a strategy that can be used to teach students about the lives of individuals, but it is not an effective strategy for making students conscious of gender issues and developing an attitude of gender equality. In fact, some biographies may reinforce traditional gender roles and stereotypes.

Hence, Analysis of Biographies is correct.

Question 195

Piaget's learning theory does not revolve around which pillars of schemas?

  1. AOption (a)

    Equilibration

  2. BOption (b)

    Assimilation

  3. COption (c)

    Assessment

  4. DOption (d)

    Accommodation

View answer & explanation

Correct answer

Answer: (c)C.

Assessment

Why this answer is correct

Piaget's learning theory revolves around the four pillars of schemas: assimilation, accommodation, equilibration, and organization. Assessment is not a pillar of Piaget's learning theory.

Key PointsHere is a brief explanation of each of the four pillars of Piaget's learning theory:

  • Assimilation: When a child encounters new information, they try to fit it into their existing schemas. For example, a child who has only seen small dogs may assimilate a large dog into their schema of "dog" by thinking that it is just a very large dog.
  • Accommodation: If new information does not fit into an existing schema, the child must modify the schema to accommodate it. For example, the child who has only seen small dogs may accommodate the new information of a large dog by creating a new schema for "large dog."
  • Equilibration: Piaget believed that children strive for cognitive equilibrium, which is a state of balance between assimilation and accommodation. When a child encounters new information that challenges their existing schemas, they experience cognitive disequilibrium. To restore cognitive equilibrium, the child must assimilate or accommodate the new information.
  • Organization: Schemas are organized into a hierarchical structure, with more general schemas at the top and more specific schemas at the bottom. For example, the child's schema of "dog" may be organized under the more general schema of "animal."

Hint

  • Assessment is the process of gathering and analyzing data to evaluate student learning. It is an important part of the educational process, but it is not a pillar of Piaget's learning theory.

Hence, Piaget's learning theory does not revolve around assessment.

Question 196

Often referred to as the skin sense, the ______ involves touch, movement and body positions in space.

  1. AOption (a)

    Sense of Hearing

  2. BOption (b)

    Kinesthetic Sense

  3. COption (c)

    Sense of Smell

  4. DOption (d)

    Tactual Sense

View answer & explanation

Correct answer

Answer: (b)B.

Kinesthetic Sense

Why this answer is correct

A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli.

Key Points

  • The kinesthetic sense is the sense of touch, movement, and body positions in space.
  • It is mediated by specialized nerve receptors located in the muscles, tendons, and joints.
  • These receptors send signals to the brain about the position and movement of the body's limbs.
  • The kinesthetic sense is essential for many everyday activities, such as walking, running, and eating. It also plays a role in balance, coordination, and athletic performance.

Hint

  • The sense of hearing is mediated by the ears.
  • The sense of smell is mediated by the nose.
  • The tactile sense is mediated by the skin.

Hence, often referred to as the skin sense, the Kinesthetic Sense involves touch, movement and body positions in space.

Question 197

Which one is correct Objective of teaching English?

  1. AOption (a)

    Develop the ability of appreciation of ideas

  2. BOption (b)

    Develop knowledge

  3. COption (c)

    Develop self-study habit

  4. DOption (d)

    Literacy development

View answer & explanation

Correct answer

Answer: (d)D.

Literacy development

Why this answer is correct

Literacy development is the process of learning to read and write. It is an essential skill for success in school and in life. Teaching English should help students develop their literacy skills in both English speaking and writing.

Key Points

Here are some of the specific objectives of teaching English that are related to literacy development:

  • Develop phonemic awareness: Phonemic awareness is the ability to hear and manipulate the individual sounds in a word. It is an essential foundation for learning to read and write.
  • Develop fluency: Fluency is the ability to read smoothly and accurately. It is important for students to develop fluency in order to comprehend what they are reading.
  • Develop vocabulary: Vocabulary is the knowledge of the meaning of words. Teaching vocabulary helps students to understand what they are reading and to express themselves effectively in writing.
  • Develop comprehension skills: Comprehension is the ability to understand what one is reading. Teaching comprehension skills helps students to get the most out of what they are reading.
  • Develop writing skills: Writing skills include the ability to generate ideas, to organize thoughts, and to use grammar and mechanics correctly. Teaching writing skills helps students to communicate effectively in writing.

Hence, literacy development is the objective of teaching English.

Question 198

Who decides textbook curriculum?

  1. AOption (a)

    the government

  2. BOption (b)

    the education minister

  3. COption (c)

    the State Board of Education

  4. DOption (d)

    the principal of school

View answer & explanation

Correct answer

Answer: (c)C.

the State Board of Education

Why this answer is correct

The textbook curriculum is the set of topics and skills that are covered in a textbook. It is typically aligned with the state standards, which are the academic standards that all students in the state are expected to meet.

Key Points

  • The State Board of Education is responsible for setting the curriculum. This includes deciding which textbooks will be used in the classroom.
  • The State Board of Education is typically made up of appointed or elected officials, as well as educators and community members.
  • Once the State Board of Education set the textbook curriculum, school districts are responsible for selecting the textbooks that will be used in the classroom. School districts typically select textbooks through a bidding process.

Here are some of the factors that State Boards of Education consider when setting the textbook curriculum:

  • State standards: State Boards of Education must ensure that the textbook curriculum meets the state standards. State standards are the academic standards that all students in the state are expected to meet.
  • Input from educators: State Boards of Education typically solicit input from educators when setting the textbook curriculum. This input can come from teachers, administrators, and curriculum experts.
  • Input from parents and the community: State Boards of Education also typically solicit input from parents and the community when setting the textbook curriculum. This input can be gathered through public hearings, surveys, and other methods.

Hint

  • The government does not have a direct role in determining the textbook curriculum.
  • The education minister may have some influence on the textbook curriculum, but this influence varies from state to state.
  • The principal of a school does not typically have a role in determining the textbook curriculum.

Hence, the correct answer is the State Board of Education.

Question 199

Teachers comprehend the relationship between different concepts through ______ which visually illustrate the relationships between concepts and ideas.

  1. AOption (a)

    Concept diagrams

  2. BOption (b)

    Concept maps

  3. COption (c)

    Concept graph

  4. DOption (d)

    Concept charts

View answer & explanation

Correct answer

Answer: (b)B.

Concept maps

Why this answer is correct

Concept maps are visual representations of concepts and the relationships between them.

Key Points

  • They can be used to organize and represent knowledge, to identify gaps in understanding, and to develop new ideas.
  • Concept maps are a powerful tool for teachers to use to comprehend the relationship between different concepts.
  • By looking at how students have organized their concept maps, teachers can see which concepts students understand well and which concepts they need more support with.
  • Concept maps can be used to develop new ideas. By brainstorming and organizing their ideas in a visual format, teachers can generate new insights and ideas.

Hence, the correct answer is concept maps.

Hint

  • Concept diagrams are similar to concept maps, but they are typically more simplified and focused on a specific topic.
  • Concept graphs are a more formal type of concept representation. They are based on graph theory and use nodes and edges to represent concepts and relationships, respectively.
  • Concept charts are a type of concept diagram that uses a tabular format to organize concepts and relationships.

Question 200

What is the importance of discussion method in teaching?

  1. AOption (a)

    Initiate Talking

  2. BOption (b)

    Stimulate critical thinking

  3. COption (c)

    Guided Conversation

  4. DOption (d)

    Activate Learning

View answer & explanation

Correct answer

Answer: (b)B.

Stimulate critical thinking

Why this answer is correct

The discussion teaching method is a teaching strategy that involves a group of students and a teacher exchanging ideas and opinions on a particular topic. It is a collaborative learning process that encourages students to think critically, listen actively, and communicate effectively.

Key Points

  • Discussion is an important teaching method because it encourages students to think critically about the material they are learning.
  • When students discuss a topic with their peers, they are forced to consider different perspectives and to defend their own ideas.
  • This process helps students to develop their critical thinking skills, which are essential for success in school and in life.

Hint

  • Initiate Talking: Discussion can be a way to get students talking about a topic, but this is not the only purpose of discussion.
  • Guided Conversation: Discussion can be guided by the teacher, but it is important to give students the freedom to explore their own ideas and to come to their own conclusions.
  • Activate Learning: Discussion can be a way to activate students' learning, but it is important to note that it is not the only way to do this.

Hence, stimulate critical thinking is correct.

200 questions in the full paper