Previous Year Paper

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

Held in 2021

200 questions120 minutes
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General Ability (20 questions)

Question 1

Select the option that is related to the third term on the same basis as the second term is related to the first term.

SNJ : QLH :: LAP : ?

  1. AOption (a)

    JYN

  2. BOption (b)

    IYR

  3. COption (c)

    JXN

  4. DOption (d)

    IXN

View answer & explanation

Correct answer

Answer: (a)A.

JYN

Why this answer is correct

The pattern followed is:

Similarly,

Hence, the correct answer is "JYN".

Question 2

In the following Venn Diagram, 'Group A' represents those who study 'Physics', 'Group B' represents those who study 'Chemistry' and 'Group C' represents those who study 'Biology'. The number given in the diagram represents the member of persons of that particular category.

How many persons study exactly two subjects?

  1. AOption (a)

    3

  2. BOption (b)

    12

  3. COption (c)

    21

  4. DOption (d)

    18

View answer & explanation

Correct answer

Answer: (d)D.

18

Why this answer is correct

The given Venn diagram is:

To find out the number of persons studying exactly two subjects,

we have to locate the area of the intersection of two subjects and count the respective numbers and add them.

The number of person studying Physics and Chemistry = 2

The number of person studying Physics and Biology = 5

The number of person studying Biology and Chemistry =11

Therefore, the total number of persons studying exactly two subjects = 11 + 5 + 2

The total number of persons studying exactly two subjects = 18.

Hence, the correct answer is "18".

Question 3

Pointing to Neha's picture, Nikhil said, "Her mother's father's son's wife is the only daughter of my mother-in-law". How is Nikhil related to Neha's mother?

  1. AOption (a)

    Brother

  2. BOption (b)

    Uncle

  3. COption (c)

    Grandfather

  4. DOption (d)

    Father

View answer & explanation

Correct answer

Answer: (a)A.

Brother

Why this answer is correct

The family chart is as follows:

Drawing the family tree as per the given information:

Therefore, it is clear that Nikhil is the brother of Neha's mother.

Hence, the correct answer is Brother.

Question 4

In the question one statement is given, followed by two conclusions, I and II. You have to consider the statement to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statement.

Statement:

G > W = U < T; K ≤ H < W

Conclusions:

I. T > H

II. G ≥ K

  1. AOption (a)

    Either conclusion I or II follow

  2. BOption (b)

     Both conclusion I and II follow

  3. COption (c)

    Only conclusion I follows

  4. DOption (d)

    Only conclusion II follows

View answer & explanation

Correct answer

Answer: (c)C.

Only conclusion I follows

Why this answer is correct

The given statements are:

G > W = U < T; K ≤ H < W

Conclusions:

I. T > H → True (As H < W = U < T, therefore, T > H)

II. G ≥ K → False (As G > W > H ≥ K, therefore G > k and not G ≥ K)

Hence, Only conclusion I follows.

Question 5

A, B, R, D, I, S, and T are sitting around a circular table facing away from the circle. A does not sit adjacent to I and T. B does not sit adjacent to A. R sits fourth to the left of A. D and B sit adjacent to each other. T sits second to the left of I. Who sits exactly between T and A?

  1. AOption (a)

    R

  2. BOption (b)

    S

  3. COption (c)

    B

  4. DOption (d)

    D

View answer & explanation

Correct answer

Answer: (b)B.

S

Why this answer is correct

The logic follows here is:

A, B, R, D, I, S, and T are sitting around a circular table facing away from the circle.

1) R sits fourth to the left of A

2) T sits second to the left of I.

There are three possibilities that are shown below

 or 

 or 

3) A does not sit adjacent to I and T

Therefore, the only possibility that satisfies the given condition is

  1. B does not sit adjacent to A

5) D and B sit adjacent to each other

Therefore, the final sitting arrangement is

Now, from the above sitting arrangement, it is clear that S sits exactly between T and A.

Hence, the correct answer is S.

Question 6

If a mirror is placed on 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: (d)D.

Why this answer is correct

The given image is

The correct mirror image is

Hence, the correct answer is option 4).

Question 7

Out of the given options, three are similar in a certain manner. However, one option is NOT like the other three. Select the option which is different from the rest.

  1. AOption (a)

    LTE

  2. BOption (b)

    TOW

  3. COption (c)

    FEH

  4. DOption (d)

    BAC

View answer & explanation

Correct answer

Answer: (a)A.

LTE

Why this answer is correct

The pattern followed is:

All the given options contain a vowel (A, E, I, O, U) in the middle except option 1).

Here, in option 1) vowel E is placed last.

Hence, the correct answer is "LTE".

Question 8

Out of the given options, three are similar in a certain manner. However, one option is NOT like the other three. Select the option which is different from the rest.

  1. AOption (a)

    Puppy

  2. BOption (b)

    Calf

  3. COption (c)

    Deer

  4. DOption (d)

    Kitten

View answer & explanation

Correct answer

Answer: (c)C.

Deer

Why this answer is correct

The logic follows here is:

Animal NameMeaning
PuppyIt is a baby dog or a young dog
CalfIt is a baby cow or a young cow
KittenIt is a baby cat or a young cat
FawnIt is a baby deer or a young deer

 

All the other animals except deer are baby animals of their respective category.

We called baby deer a fawn.

Hence, the correct answer is Deer.

Question 9

Complete the following letter series:

NAOB, PAQB, RASB, _____.

  1. AOption (a)

    SATB

  2. BOption (b)

    TABU

  3. COption (c)

    TASU

  4. DOption (d)

    TAUB

View answer & explanation

Correct answer

Answer: (d)D.

TAUB

Why this answer is correct

According to the English alphabet series and its positional value

The pattern follows here is:

Similarly,

Hence, the correct answer is "TAUB".

Question 10

Arti deposited equal sum of money in two different banks, one at compound interest, compounded annually and the other at simple interest, both at 10% per annum. If after two years, the difference in the amounts comes to Rs. 400, what are the amounts deposited with each bank?

  1. AOption (a)

    Rs. 45000

  2. BOption (b)

    Rs. 40000

  3. COption (c)

    Rs. 20000

  4. DOption (d)

    Rs. 50000

View answer & explanation

Correct answer

Answer: (b)B.

Rs. 40000

Why this answer is correct

Given:

CI - SI = Rs. 400

Time = 2 years

Formula used:

CI - SI for 2 years = P(R/100)2

Where, P = Principle, R = rate of interest

Calculation:

Let P be the amount deposited in each bank,

CI - SI = Rs. 400

⇒ P(10/100)2 = 400

⇒ P(1/10)2 = 400

⇒ P(1/100) = 400

⇒ P = 400 × 100 = Rs. 40000

∴ The correct answer is option (2).

Question 11

The following question is based on the five three-digit numbers given below. 513 485 625 724 541 If 2 is added to the last digit of each number and then the positions of the first and the third digits are interchanged, which of the following will be the highest number?

  1. AOption (a)

    513

  2. BOption (b)

    625

  3. COption (c)

    724

  4. DOption (d)

    485

View answer & explanation

Correct answer

Answer: (d)D.

485

Why this answer is correct

The given three-digit numbers are 513, 485, 625, 724, 541.

Original numbersNewly formed numbers after adding '2' to the last digit of each numberNewly formed numbers after interchanging first and third digits.
513513 + 2 = 515515
485485 + 2 = 487784
625625 + 2 = 627726
724724 + 2 = 726627
541541 + 2 = 543345

 

The highest number is 784 that we get from the original number 485.

Hence, the correct answer is "485".

Question 12

Find the wrong term in the given series.

144, 288, 576, 1008, 1594, 2304, 3168

  1. AOption (a)

    2304

  2. BOption (b)

    288

  3. COption (c)

    1008

  4. DOption (d)

    1594

View answer & explanation

Correct answer

Answer: (d)D.

1594

Why this answer is correct

The given series is:

144, 288, 576, 1008, 1594, 2304, 3168

The pattern follows here is:

The correct series will be:

 

Hence, the correct answer is "1594".

Question 13

A software company has decided to recruit engineers. The following criteria is to be applied. A candidate must

(i) be an engineering graduate with at least 70% marks in graduation and 80% marks in HSC.

(ii) have work experience of minimum 2 year.

(iii) be ready to sign a bond of three years.

(iv) not be more than 25 years and not less than 22 years as on 1.7.2021. However, if the candidate fulfils all the above criteria except

(a) (i), but has obtained 85% in HSC and has at least three years experience of working, the case may be referred to the Director.

(b) (iii), but is willing to pay an amount of 2 lakh, if he is required to leave- the case may be referred to the HR.

In question below, details one candidate are given. You have to take one of the following courses of action based on the information provided and mark the number of that course of action as your answer. The reference date is 1.7.2021.

Kaushal is a Software Engineer and has been working as an Assistant Engineer for the past three years. He had scored 68% and 85% marks in graduation and HSC respectively. He has just completed 25 years of age. He is ready to sign a bond of three years.

  1. AOption (a)

    The candidate is to be selected.

  2. BOption (b)

    The case is to be referred to the Director.

  3. COption (c)

    The case is to be referred to the HR.

  4. DOption (d)

    The candidate is not to be selected.

View answer & explanation

Correct answer

Answer: (b)B.

The case is to be referred to the Director.

Why this answer is correct

All the conditions are as follows:

Eligibility criteria numberDetailsFulfillment
iBe an engineering graduate with at least 70% marks in graduation and 80% marks in HSCNo, the candidate is a Software Engineer but scored 68% marks in graduation and 85% marks in HSC
iiHave work experience of minimum 2 yearYes, the candidate has past three years of working experience as an Assistant Engineer
iiiBe ready to sign a bond of three yearsYes, the candidate is ready to sign a bond of three years
ivNot be more than 25 years and not less than 22 years as of 1.7.2021. However, if the candidate fulfills all the above criteria exceptYes, the candidate is 25 years old.
a(i), but has obtained 85% in HSC and has at least three years experience of working, the case may be referred to the DirectorYes, the candidate has obtained 85% in HSC and has a past three years of working experience as an Assistant Engineer
b(iii), but is willing to pay an amount of 2 lakh, if he is required to leave- the case may be referred to the HRNo

 

Therefore, the candidate fulfills the eligibility criteria.

Hence, the correct answer is "The case is to be referred to the Director".

Question 14

Three different positions of the same dice are given below. Which symbol is on the face opposite to face showing '@'?

  1. AOption (a)

    !

  2. BOption (b)

    %

  3. COption (c)

  4. DOption (d)

View answer & explanation

Correct answer

Answer: (c)C.

Why this answer is correct

The given positions of the dies are: 

Consider the positions of the dice 1 and 3. Face # is common for both the position, keep that face constant and move in a clockwise direction, we get the faces opposite to each other.

Dice 1#!@
Dice 2#%$

The face opposite to ! is face %, face opposite to @ is face $.

Hence, the correct answer is $$.

Question 15

If each of the odd digits in the number 6482437 is increased by '1' and each of the even digits is decreased by '2', then which of the following will be the sum of the digits of the number?

  1. AOption (a)

    27

  2. BOption (b)

    28

  3. COption (c)

    31

  4. DOption (d)

    26

View answer & explanation

Correct answer

Answer: (d)D.

26

Why this answer is correct

The given number is 6482437

Increase each odd digit number by '1' and decrease each even digit number by '2'.

The number will become 4260248.

Now, the sum of the digits of the number will be:

⇒ 4 + 2 + 6 + 0 + 2 + 4 + 8

⇒ 26

Hence, the correct answer is "26".

Question 16

Following are the criteria to recruit a HR Consultant in an organisation:

The candidate must

(a) be a graduate in any discipline with minimum 70% marks.

(b) be above 25 years and not above 30 years of age as on 01-01-2021.

(c) have done MBA in HR.

(d) have an experience of minimum three years in HR Department.

(e) be ready to be on probation for one year.

If a candidate satisfies all the criteria except

(i) at (c) above, but is a Commerce graduate with minimum 75% marks and has been working in HR department for at least last five years, his/her case is to be referred to the General Manager.

(ii) at (d) above, but has scored minimum 75% in post graduation (MBA-HR) and has a minimum of two years of experience in HR, his/her case is to be referred to the Director.

In question below, details of a candidate are provided. You have to take one of the following courses of action based on the information provided and mark the number of that course of action as your answer.

You are not to assume anything other than the information provided in each question. All these cases are given to you as on 01-07-2021.

Ramesh is a commerce graduate with 76% marks and has completed MBA in HR. He was born on 01-04-1994 and has four years’ experience as a Senior HR Manager. He is ready to join on one-year probation.

  1. AOption (a)

    The candidate is not selected.

  2. BOption (b)

    The candidate is selected.

  3. COption (c)

    The candidate is to be referred to the Director.

  4. DOption (d)

    The candidate is to be referred to the General Manager.

View answer & explanation

Correct answer

Answer: (b)B.

The candidate is selected.

Why this answer is correct

All the conditions are as follows:

Eligibility criteria numberDetailsFulfillment
aBe a graduate in any discipline with minimum 70% marksYes, as the candidate is a commerce graduate
bBe above 25 years and not above 30 years of age as on 01-01-2021Yes, the candidate was born on 01-04-1994.(27 years old)
cHave done MBA in HRYes, the candidate has completed MBA in HR
dHave experience of minimum of three years in the HR DepartmentYes, the candidate has four years of experience as a Senior HR Manager
eBe ready to be on probation for one yearYes, the candidate is ready to join for a one-year probation
i(c) above, but is a Commerce graduate with minimum 75% marks and has been working in HR department for at least last five years, his/her case is to be referred to the General ManagerNo, the candidate has four years of experience as a Senior HR Manager
iiat (d) above, but has scored a minimum 75% in post-graduation (MBA-HR) and has a minimum of two years of experience in HR, his/her case is to be referred to the DirectorNo, the candidate has four years of experience as a Senior HR Manager

Therefore, the candidate fulfills all the eligibility criteria except for the criteria of the general manager and the director.

Hence, the correct answer is "The candidate is selected".

Question 17

From the given answer figures, select the one 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: (a)A.

Why this answer is correct

As we can see that given figure is embedded in Option 1).

The highlighted part is same as given in the question.

Hence, the correct answer is Option 1).

Question 18

Z, Y, X, W, V, and U have different heights. Two persons are either taller or smaller than V. W is taller than Z but not the tallest. Y is taller than only U. If Z is taller than only two persons, then who is the tallest person?

  1. AOption (a)

    W

  2. BOption (b)

    X

  3. COption (c)

    U

  4. DOption (d)

    Z

View answer & explanation

Correct answer

Answer: (b)B.

X

Why this answer is correct

The logic follows here is:

1) Y is taller than only U

This means U will be the last person or the smallest person of all the other person.

Therefore, we can arrange them as

_ > _ > _ > _ > Y > U.

2) Z is taller than only two persons

We know, Y and U are the smallest persons of all.

This means Z is taller than Y and U.

Therefore, we can arrange them as

_ > _ > _ > Z > Y > U.

3) Two persons are either taller or smaller than V.

From the above statements, it is clear that no two person are smaller than V.

Therefore, there is only one possibility of having two persons taller than V.

The order can be formed like this,

_ > _ > V > Z > Y > U.

4) W is taller than Z but not the tallest.

We can arrange W ahead of V which can satisfy the given condition.

_ > W > V > Z > Y > U.

Now, the final arrangement will be

X > W > V > Z > Y > U.

Therefore, X will be the tallest person.

Hence, the correct answer is X.

Confusion PointsDon't confuse in W is taller than Z.

It is not given that W is taller than only Z.

Hence, we can put W ahead of Z anywhere according to the condition given.

Question 19

Find the missing number in the given series: 100, 221, 77, 246, 50, ______.

  1. AOption (a)

    245

  2. BOption (b)

    275

  3. COption (c)

    255

  4. DOption (d)

    265

View answer & explanation

Correct answer

Answer: (b)B.

275

Why this answer is correct

The pattern follows here is:

Hence, the correct answer is 275.

Question 20

Out of the given options, three are similar in a certain manner. However, one option is NOT like the other three. Select the option which is different from the rest.

  1. AOption (a)

  2. BOption (b)

  3. COption (c)

  4. DOption (d)

View answer & explanation

Correct answer

Answer: (d)D.

Why this answer is correct

The logic follows here is:

All the option figures contain 10 triangles each except option figure 4).

In option figure 4), there are 11 triangles present.

Hence, the correct answer is option 4).

General Awareness (20 questions)

Question 21

The approximate height of the World's highest mountain "Mount Everest" is:

  1. AOption (a)

    8,848.86m

  2. BOption (b)

    8,800.86 m

  3. COption (c)

    8,600.00m

  4. DOption (d)

    8,748.76m

View answer & explanation

Correct answer

Answer: (a)A.

8,848.86m

Why this answer is correct

The correct answer is 8,848.86m.

Key Points

  • The World's Highest Peak Mount Everest.
  • It is situated in Nepal.
  • The height of Mount Everest is 8848.86 m (8900 m approx).
  • It is always covered with snow.
  • Nepali name: Sagarmatha.
  • Tibetan name: Chomolungma.
  • It is named after a Surveyor General of India George Everest.
  • The peak is located in the Mahalangur sub-range of the Himalayas.
  • Thus, Mount Everest is a part of Nepal and the height of its peak is 8900 m.

Question 22

Which of the following is not a writer?

  1. AOption (a)

    Chetan Bhagat

  2. BOption (b)

    Maqbool Fida Husain

  3. COption (c)

    Arundhati Roy

  4. DOption (d)

    Ruskin Bond

View answer & explanation

Correct answer

Answer: (b)B.

Maqbool Fida Husain

Why this answer is correct

The correct answer is Maqbool Fida Husain.

Key Points

  • Maqbool Fida Husain (often referred to as M.F. Husain) was a prominent Indian painter and artist.
  • He was born on September 17, 1915, in Pandharpur, Maharashtra, India, and died on June 9, 2011, in London, UK.
  • Chetan Bhagat is an Indian author, columnist, and screenwriter. He was born on April 22, 1974, in New Delhi, India.
  • Bhagat is known for his bestselling novels such as "Five Point Someone," "One Night @ the Call Center," "2 States," "Half Girlfriend," and "The Girl in Room 105."

Additional Information

  • Arundhati Roy is an Indian author, activist, and public intellectual. She was born on November 24, 1961, in Shillong, Meghalaya, India.
  • Roy is best known for her novel "The God of Small Things," which won the Booker Prize in 1997.
  • Ruskin Bond is an Indian author of British descent, known for his contributions to children's literature and Indian English literature.
  • He was born on May 19, 1934, in Kasauli, Punjab (now in Himachal Pradesh), India.

Question 23

SwabSeq is related to the corona virus, it is a:

  1. AOption (a)

    Mini testing kit

  2. BOption (b)

    Vaccine

  3. COption (c)

    Preventive medicine

  4. DOption (d)

    A testing platform

View answer & explanation

Correct answer

Answer: (d)D.

A testing platform

Why this answer is correct

The correct answer is ​A testing platform.

Key Points

  • SwabSeq is a type of diagnostic test for COVID-19 that uses a technology called "barcoded sequencing" to rapidly and accurately identify the presence of the virus in a patient's nasal or throat swab.
  • Developed by researchers at the University of California, San Francisco (UCSF) and Chan Zuckerberg Biohub.
  • SwabSeq can detect the virus even at low levels of infection, making it a powerful tool in the fight against the pandemic.

Additional Information

  • The coronavirus (COVID-19) is a highly infectious respiratory illness caused by a new strain of the coronavirus.
  • It was first identified in December 2019 in Wuhan, China, and has since become a global pandemic.
  • The virus is primarily spread through respiratory droplets when an infected person talks, coughs, or sneezes, and can also be transmitted by touching a surface contaminated with the virus and then touching one's face.
  • The most common symptoms include fever, cough, and difficulty breathing, but some infected individuals may be asymptomatic or experience mild symptoms.

Question 24

Which type of soil is the most fertile?

  1. AOption (a)

    Sand soils

  2. BOption (b)

    Clay soils

  3. COption (c)

    Porous loamy soils

  4. DOption (d)

    Red soils

View answer & explanation

Correct answer

Answer: (c)C.

Porous loamy soils

Why this answer is correct

The correct answer is Porous loamy soils.

 Key Points

  • Porous loamy soils are a type of soil that is characterized by a balance of sand, silt, and clay particles.
  • They are considered to be one of the best types of soils for growing crops, as they have good drainage, aeration, and water-holding capacity.
  • The porous nature of these soils allows air and water to move freely through them, which promotes healthy root growth and helps to prevent waterlogging.
  • Porous loamy soils are commonly found in temperate regions and are ideal for growing a wide range of crops, including fruits, vegetables, and grains.

Additional Information

  • Sand soil is a type of soil that has a high percentage of sand particles in it.
  • It is characterized by its coarse texture and low water-holding capacity.
  • Clay soils are soils that contain a high percentage of clay particles.
  • Clay particles are the smallest particles in the soil, with a diameter of less than 0.002 mm.
  • Clay soils are known for their ability to retain water and nutrients.
  • Red Soils They are poor in lime, magnesia, phosphates, nitrogen, and humus and rich in potash and potassium.
  • The red color of the soil is due to the presence of iron oxide.

Question 25

Last, in which year India won the Cricket World Cup?

  1. AOption (a)

    2019

  2. BOption (b)

    2015

  3. COption (c)

    1995

  4. DOption (d)

    2011

View answer & explanation

Correct answer

Answer: (d)D.

2011

Why this answer is correct

The correct answer is 2011.

Key Points

  • India and Sri Lanka competed in the 2011 Cricket World Cup Final as a One Day International (ODI) game at Mumbai's Wankhede Stadium.
  • On Saturday, April 2, 2011, it was played.
  • India won the game by six wickets, claiming its second World Cup victory since the 1983 competition.
  • The current seating capacity of Wankhede Stadium is 33,108.
  • The final game of Sachin Tendulkar's international career was played at the stadium.

Additional Information

  • Gary Kirsten was the coach of the World Cup-winning Indian Cricket team in 2011.
  • India won the World Cup 2011 for the second time under the captainship of Mahendra Singh Dhoni after 1983 under the captainship of Kapil Dev.
  • Gary Kirsten was the coach of the World Cup-winning Indian Cricket team in 2011.
  • The  ICC World Cup 2023 will be held in India.

Question 26

In India, National Sports Day is celebrated on which day?

  1. AOption (a)

    29th August

  2. BOption (b)

    9th August

  3. COption (c)

    19th August

  4. DOption (d)

    15th August

View answer & explanation

Correct answer

Answer: (a)A.

29th August

Why this answer is correct

The correct answer is 29th August.

Key Points

  • The National Sports Day: 
  • August 29 is the birthday of hockey legend Major Dhyan Chand and is celebrated as the National Sports Day in India.
  • The government of India designated August 29 as the National Sports Day in 2012 to commemorate his birth anniversary.
  • This day aims to spread awareness of the importance of sports in every individual's life.
  • Major Dhyan Chand:
  • He was an Indian hockey player.
  • His autobiography is called Goal.
  • He was honored with the Padma Bhushan in 1956.
  • He is the only Indian hockey player to have a stamp in his honor.
  • During his time Indian hockey team won three Olympic gold medals in 1928, 1932, and 1936.
  • He is also known as 'The Wizard'.

Question 27

Which Legendary actor breathed his last in July 2021 after a long illness?

  1. AOption (a)

    Raj Kaushal

  2. BOption (b)

    Irrfan Khan

  3. COption (c)

    Rinku Singh Nikumbh

  4. DOption (d)

    Dilip Kumar

View answer & explanation

Correct answer

Answer: (d)D.

Dilip Kumar

Why this answer is correct

The correct answer is Dilip Kumar.

Key Points

  • Mohammed Yusuf Khan is known as Dilip Kumar.
  • He was born in Peshwar, North-West Frontier Province, India (present-day Khyber Pakhtunkhwa, Pakistan).
  • His first film was Jwar Bhata in 1944.
  • Dilip Kumar holds the record for most wins of the Filmfare Award for Best Actor.
  • His famous films are Mela (1948) Devdas (1955), the comical Azaad (1955),  Mughal-e-Azam (1960),  Ram Aur Shyam (1967), Naya Daur (1957), Yahudi (1958),  Madhumati (1958), Paigham (1959), etc.
  • He was awarded Padma Bhushan in 1991, Nishan-e-Imtiaz in 1998, and Padma Vibhushan in 2015.
  • Home Minister Rajnath Singh presented Padma Vibhushan to veteran Bollywood actor Dilip Kumar in Mumbai.​

Additional Information

  • Raj Kaushal was an Indian filmmaker, producer, and advertising director, He was born on May 24, 1971, in Mumbai.
  • Irrfan Khan was an Indian actor who appeared in numerous films in India, as well as in Hollywood productions.
  • He was born on January 7, 1967, in Jaipur, India, and passed away on April 29, 2020, at the age of 53 due to a neuroendocrine tumor.
  • Rinku Singh Nikumbh is an Indian professional wrestler and former professional baseball player.
  • He was born on August 8, 1988, in Bhadohi, Uttar Pradesh, India.

Question 28

The headquarter of the International Criminal Court (ICC) is located in:

  1. AOption (a)

    Japan

  2. BOption (b)

    Netherlands

  3. COption (c)

    India

  4. DOption (d)

    Pakistan

View answer & explanation

Correct answer

Answer: (b)B.

Netherlands

Why this answer is correct

The correct answer is the Netherlands.

Key Points

  • International Criminal Court:
  • ​It is a permanent judicial body created by the 1998 Rome Statute of the ICC (its founding and governing document).
  • And began functioning on 1st July 2002 when the Statute came into force.
  • Headquarters: The Hague, Netherlands
  • Members: 
  • ​123 nations are States Parties to the Rome Statute and recognize the ICC’s authority.
  • The USA, China, Russia, and India are not members.
  • The forum was established as a court of last resort to prosecute offenses that would otherwise go unpunished and has jurisdiction over four main crimes: genocide, crimes against humanity, war crimes, and the crime of aggression.

Question 29

Recently, Union Health Minister Harsh Vardhan gave news about the FELUDA paper strip test, this test strips will be used to diagnose:

  1. AOption (a)

    SARS-CoV-2

  2. BOption (b)

    Japanese encephalitis

  3. COption (c)

    Dengue fever

  4. DOption (d)

    H1N1

View answer & explanation

Correct answer

Answer: (a)A.

SARS-CoV-2

Why this answer is correct

The correct answer is SARS-CoV-2.

Key Points

  • SARS-CoV-2 is a virus that causes respiratory illness known as COVID-19.
  • It belongs to the family of viruses called coronaviruses, which also includes the viruses that cause severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS).
  • SARS-CoV-2 was first identified in Wuhan, China in December 2019.
  • It a quickly spread across the globe, causing a pandemic that has had a major impact on public health and the global economy.

Additional Information

  • Japanese encephalitis (JE) is a viral infection caused by the Japanese encephalitis virus (JEV).
  • which is transmitted to humans through the bite of infected mosquitoes, particularly Culex tritaeniorhynchus.
  • Dengue fever is a viral infection caused by the dengue virus, which is transmitted to humans by the bite of infected Aedes mosquitoes.
  • H1N1, also known as swine flu, is a type of influenza virus that can infect pigs, humans, and other animals.
  • In 2009, a new strain of H1N1 influenza virus emerged, which caused a global pandemic.

Question 30

Which of the former Presidents was awarded Bharat Ratna recently?

  1. AOption (a)

    Pranab Kumar Mukherjee

  2. BOption (b)

    A. P. J. Abdul Kalam

  3. COption (c)

    Giani Zail Singh

  4. DOption (d)

    Sarvepalli Radhakrishnan

View answer & explanation

Correct answer

Answer: (a)A.

Pranab Kumar Mukherjee

Why this answer is correct

The correct answer is Pranab Kumar Mukherjee.

Key Points

  • Pranab Kumar Mukherjee was an Indian politician and statesman.
  • He served as the 13th President of India from 2012-2017.
  • He was preceded by Pratibha Patil and was succeeded by Ram Nath Govind.
  • He received Padma Vibhushan in the year 2008 and Bharat Ratna in the year 2019.
  • Books: Challenges Before the Nation: A Saga of Struggle and Sacrifice, Beyond Survival: Emerging Dimensions of the Indian Economy.​

Additional Information

  • Bharat Ratna is the highest civilian award of the Republic of India.
  • Established on 2 January 1954, the award is presented in recognition of "extraordinary service/performance of the highest order" without distinction of race, occupation, status, or gender.
  • A. P. J. Abdul Kalam was a renowned Indian scientist and politician who served as the President of India from 2002 to 2007.
  • He was widely regarded as the "People's President" and was known for his humble and down-to-earth personality.
  • In 1997, A. P. J. Abdul Kalam was awarded the prestigious Bharat Ratna.
  • Giani Zail Singh was a former President of India who served as the seventh President from 1982 to 1987.
  • He was awarded the Bharat Ratna in 1994, seven years after he had completed his term as President.
  • Sarvepalli Radhakrishnan was awarded the Bharat Ratna,  in 1954.

Question 31

What is the minimum age limit to be a Lok Sabha candidate?

  1. AOption (a)

     35 years

  2. BOption (b)

    30 years

  3. COption (c)

    25 years

  4. DOption (d)

    45 years

View answer & explanation

Correct answer

Answer: (c)C.

25 years

Why this answer is correct

The correct answer is ​25 years.

Key Points.

  • To become a member of Lok Sabha, a candidate should have the following eligibility criteria:
  • The candidate should be a citizen of India.
  • The candidate should have at least 25 years of age.
  • The candidate should not hold an office of profit under the Indian government or the government of any other state.
  • The candidate should not be an unstable mind.

Important Points

  • To become a member of Parliament, one should not be less than 30 years of age in the case of Rajya Sabha.

Question 32

The vaccine for Covid -19 was developed by the Bharat Biotech in collaboration with the Indian Council of Medical Research (ICMR) - National Institute of Virology (NIV), which vaccine is this?

  1. AOption (a)

    Covishield

  2. BOption (b)

    Covaxin

  3. COption (c)

    Moderna

  4. DOption (d)

    Covivax

View answer & explanation

Correct answer

Answer: (b)B.

Covaxin

Why this answer is correct

The correct answer is ​Covaxin.

Key Points

  • Covaxin is an inactivated virus-based COVID-19 vaccine developed by Bharat Biotech in collaboration with the Indian Council of Medical Research - National Institute of Virology.
  • Code named - BBV152.
  • The vaccine is similar to CoronaVac in that it uses a completely infective SARS-CoV-2 viral particle consisting of RNA surrounded by a protein shell.
  • They contain dead viruses, incapable of infecting people but still able to instruct the immune system to mount a defensive reaction against an infection.
  • It is a 2-dose vaccination regimen given 28 days apart.

Additional Information

  • Bharat Biotech is a leading biotechnology company in India that specializes in the research and development of vaccines and biotherapeutics.
  • The company was founded in 1996 by Dr. Krishna Ella and has since become a major player in the global biotech industry.

Question 33

As of August 2021, who is the Lieutenant Governor of Delhi?

  1. AOption (a)

    Anil Baijal

  2. BOption (b)

    Najeeb Jung

  3. COption (c)

    Shri P.S. Sreedharan Pillai

  4. DOption (d)

    Bhagat Singh Koshyari

View answer & explanation

Correct answer

Answer: (a)A.

Anil Baijal

Why this answer is correct

The correct answer is Anil Baijal

Key Points

  • Anil Baijal is the Lieutenant Governor of Delhi is the constitutional head of the National Capital Territory of Delhi.
  • ​He is a retired Central Government Civil Servant of the Indian Administrative Service cadre.
  • He is the 21st Lieutenant Governor of Delhi. He took over office on 31st December 2016 after the sudden resignation of Najeeb Jung.
  • He has served as Union Home Secretary under the Atal Bihari Vajpayee government.

Additional Informationl

  • Delhi, officially the National Capital Territory of Delhi (NCT), is a city and a union territory of India containing New Delhi, the capital of India.
  • ​It is situated alongside River Yamuna and bordered by Haryana state on three sides and by Uttar Pradesh state to the east.
  • The States Reorganisation Act, 1956 created the Union Territory of Delhi from its predecessor, the Chief Commissioner's Province of Delhi.
  • The Constitution (Sixty-ninth Amendment) Act, 1991 declared the Union Territory of Delhi to be formally known as the National Capital Territory of Delhi.

Question 34

Which is the second-highest mountain on Earth?

  1. AOption (a)

    Mount Everest

  2. BOption (b)

    K2

  3. COption (c)

    Altai Mountains

  4. DOption (d)

    Hindu Raj

View answer & explanation

Correct answer

Answer: (b)B.

K2

Why this answer is correct

The correct answer is K2.

Key Points

  • K2, a mountain also called Mount Godwin Austen, is the world’s second-highest peak (8,611 meters), second only to Mount Everest.
  • The mountain was discovered in 1856 by Col. T.G. Montgomerie.
  • It was granted the symbol K2 because it was the second peak measured in the Karakoram Range.
  • The name Mount Godwin Austen is for the peak’s first surveyor, Col. H.H. Godwin Austen, a 19th-century English geographer.
  • K2 is prone to frequent and severe storms that make the already treacherous climbing conditions on its slopes even more challenging.

Question 35

Recently, the RBI announced individuals and businesses can opt for loan restructuring options for up to Rs. 25 crore dues under which framework?

  1. AOption (a)

    Resolution framework 3.0

  2. BOption (b)

    Resolution framework 2.0

  3. COption (c)

    Resolution framework 1.0

  4. DOption (d)

    Resolution framework 4.0

View answer & explanation

Correct answer

Answer: (b)B.

Resolution framework 2.0

Why this answer is correct

The correct answer is ​Resolution framework 2.0.

Additional Information

  • The Reserve Bank of India’s (RBI’s) new policy on the restructuring of loans nudges lenders and card issuers to be more transparent and fixes timelines within which financial institutions should act.
  • During the latest monetary policy, the RBI announced Resolution Framework 2.0, which allows lenders to restructure loans of individuals and small businesses.
  • Similar to Resolution Framework 1.0, the new regulations give the power to lenders to accept or reject restructuring applications. Borrowers still have no say in the process. The decision will be based on the board-approved policy of each institution.
  • The policy also allows lenders and card companies to choose the relief they want to offer to borrowers. A lender can reduce the equated monthly installments or EMIs, offer moratorium, convert interest into another credit facility, or even combine two or more of these.
  • Lenders need to restructure the loan or card outstanding in such a way that the tenure extension that borrowers receive is up to two years.

Question 36

Article 14 is related to:

  1. AOption (a)

    Right against exploitation

  2. BOption (b)

    Right to freedom of religion

  3. COption (c)

    Right to equality

  4. DOption (d)

    Right to property

View answer & explanation

Correct answer

Answer: (c)C.

Right to equality

Why this answer is correct

The correct answer is The Right to Equality.

 Key Points

  • Article 14 deals with The Right to Equality.
  • Article 14:
  • ​Articles 14-18 deal with the Right to Equality.
  • Equality before the law.
  • The state shall not deny to any person equality before the law or equal protection of the law within the territory of India.

Question 37

The ozone layer is the common term for the high concentration of ozone that is found in the ____________ around 15–30km above the earth’s surface.

  1. AOption (a)

    mesosphere

  2. BOption (b)

    troposphere

  3. COption (c)

    stratosphere

  4. DOption (d)

    thermosphere

View answer & explanation

Correct answer

Answer: (c)C.

stratosphere

Why this answer is correct

The correct answer is stratosphere

Key Points

  • The stratosphere is a layer of Earth's atmosphere that extends from about 10 kilometers (6 miles) to 50 kilometers (31 miles) above the Earth's surface.
  • It is located above the troposphere, which is the layer closest to the Earth's surface and where most weather occurs.
  • The stratosphere is characterized by a gradual increase in temperature with altitude, due to the absorption of solar radiation by the ozone layer.
  • This warming effect is important because it creates a stable layer of air that prevents vertical mixing between the lower and upper atmosphere, which can limit the distribution of pollutants and other substances.

Question 38

The Jnanpith award is given in which of the following field?

  1. AOption (a)

    Best creative literary writing

  2. BOption (b)

    Best paintings

  3. COption (c)

    Best direction in short Hindi films

  4. DOption (d)

    Best direction in regional films

View answer & explanation

Correct answer

Answer: (a)A.

Best creative literary writing

Why this answer is correct

The correct answer is the best creative literary work.

  • The 57th Jnanpith Award for the year 2022 has also been announced.
  • Awarded to well-known Konkani writer Damodar Mouzo. Damodar Mouzo is a novelist, story writer, critic, and essayist from Goa.

Question 39

Who won the Battle of Plassey?

  1. AOption (a)

    Robert Clive

  2. BOption (b)

    Babur

  3. COption (c)

    Sirāj al-Dawla

  4. DOption (d)

    Akbar

View answer & explanation

Correct answer

Answer: (a)A.

Robert Clive

Why this answer is correct

The correct answer is Robert Clive

Key Points

  • The Battle of Plassey was fought in north-eastern India on 23 June 1757.
  • Troops of the British East India Company, led by Robert Clive, came up against the forces of Siraj-ud-Daulah, the last Nawab of Bengal, and his French allies.
  • Clive's victory eventually led to the British becoming the greatest economic and military power in India.
  • The Battle of Plassey had political significance for it laid the foundation of the British Empire in India.; it has been rightly regarded as the starting point of British rule in India.
  • Result of Battle of Plassey-
  • As a result of this victory, Mir Jafar became the Nawab of Bengal. He gave large sums of money plus the zamindari of 24 Parganas to the English.
  • English rivals, the French were ousted

Question 40

The third battle of Panipat was fought between:

  1. AOption (a)

    Babur and the Lodi Empire

  2. BOption (b)

    Maratha Empire and Akbar

  3. COption (c)

    Samrat Hem Chandra Vikramaditya, popularly called Hemu and Akbar

  4. DOption (d)

    Maratha Empire and Ahmad Shah Durrani

View answer & explanation

Correct answer

Answer: (d)D.

Maratha Empire and Ahmad Shah Durrani

Why this answer is correct

The correct answer is Maratha Empire and Ahmad Shah Durrani

Key Points

  • The Maratha Army and the soldiers of Afghan monarch Ahmad Shah Abdali engaged in combat during the ;Third Battle of Panipat.
  • Ahmad Shah Abdali led the Marathas to victory in the Third Panipat War.
  • The Maratha Empire and the Durrani Empire's invasion force engaged in the Third Battle of Panipat on January 14, 1761.
  • The Pashtun Rohillas under the leadership of Najib ad-Dawlah, the Baloch Khanate of Kalat, the Oudh State under Shuja-ud-Daula, as well as parts of the waning Mughal Empire, were the Afghans' four main allies in India.
  • Sadashivrao Bhau, the third-highest official in the Maratha Empire after the Chhatrapati and the Peshwa, served as the commander-in-chief >of the Maratha army.
  • The Peshwa and the majority of the Maratha army were stationed in the Deccan Plateau.

Additional Information

  • The Durrani Empire, often known as the Afghan Empire, was a sizable nation that at its height encompassed the present-day nations of Afghanistan, Pakistan, northeastern Iran, and western India.
  • Ahmad Shah Durrani, an Afghan military leader, founded it in Kandahar in 1747.
  • The Emirship was passed down to Ahmad Shah's children and grandchildren after his death in 1772.
  • The Ghilzais were the first Pashtun kings >of Kandahar, while Ahmad Shah and his descendants came from the Sadozai line of the Abdali (later called Durrani) Pashtuns.
  • One of the biggest Islamic empires in the globe at the time was the Durrani Empire.
  • The Durrani Empire is frequently cited as the country of Afghanistan's founding, and Ahmad Shah Durrani is credited with creating the country's current nation-state.

Arithmetic Ability (20 questions)

Question 41

If A's salary is 17% more than of B's salary then how many percent is B's salary less than A's?

  1. AOption (a)

    14.53%

  2. BOption (b)

    15.0%

  3. COption (c)

    14.0%

  4. DOption (d)

    13.0%

View answer & explanation

Correct answer

Answer: (a)A.

14.53%

Why this answer is correct

Given:

The salary of A = 17% more than the salary of B

Calculation:

Let us assume the salary of B is X and salary of A is (X + 17% of X)

⇒ The required % = 117X100 − X117X100×100{{117X\over 100}\ -\ {X}\over {117X\over 100} }\times 100 = 14.53%

∴ The required result will be 14.53%.

Question 42

P = 64, Q = 2 and R = 4. If P varies directly as the square of Q and inversely as the square of R then what is the value of P for Q = 4 and R = 8?

  1. AOption (a)

    63

  2. BOption (b)

    16

  3. COption (c)

    64

  4. DOption (d)

    36

View answer & explanation

Correct answer

Answer: (c)C.

64

Why this answer is correct

Given:

P = 64; Q = 2 and R = 4

P is a variable that is dependent on Q and R and changes directly as Q2 and inversely as R2

Calculation:

According to the question:

P ∝ Q2/R2

⇒ P = k(Q2/R2); k = constant

⇒ 64 = k(22/42)

⇒ k = 256

Value of P when, Q = 4 and R = 8 is given by:

P = 256(42/82)

⇒ P = 64

∴ The value of P for Q = 4 and R = 8 is 64

Question 43

Simplify: (5/7 × 2/3 × 9/8 × 3/4 × 7/9)/(8/5 × 6/7 × 7/8 × 5/7)

  1. AOption (a)

    0.36

  2. BOption (b)

    0.37

  3. COption (c)

    0.30

  4. DOption (d)

    0.35

View answer & explanation

Correct answer

Answer: (a)A.

0.36

Why this answer is correct

Given:

The expression = (5/7 × 2/3 × 9/8 × 3/4 × 7/9)/(8/5 × 6/7 × 7/8 × 5/7)

Concept:

Calculation:

⇒ 57×23×98×34×7985×67×78×57{5\over7}\times {2\over3}\times {9\over 8}\times {3\over 4}\times {7\over9}\over {8\over5}\times {6\over7}\times {7\over8}\times {5\over7}

⇒ 51667\frac{\frac{5}{16}}{\frac{6}{7}}

⇒ 516×76\frac{5}{16}\times \frac{7}{6}

⇒ 3596\frac{35}{96} = 0.3645... ≈ 0.36

∴ The required result will be 0.36.

Question 44

Two trains that are 125 m long and 150 m long are travelling towards each other at the parallel tracks. The speed of the trains are 50 kmph and 60kmph. How many seconds will it take for the trains to cross each other?

  1. AOption (a)

    10 secs

  2. BOption (b)

    9 secs

  3. COption (c)

    5 secs

  4. DOption (d)

    6 secs

View answer & explanation

Correct answer

Answer: (b)B.

9 secs

Why this answer is correct

Given:

The length of the first train = 125 m

The length of the second train = 150 m

The speed of the first train = 50 kmph

The speed of the second train = 60 kmph

Formula used:

S = D/T     (Where S = The speed, D = The distance and T = Time)

Calculation:

Let us assume the time taken by both trains to cross each other is S

⇒ The relative speed of the trains = 50 + 60 = 110 kmph = 110 × (5/18) = 550/18 = 275/9 m/s

⇒ S = 125 + 1502759S\ =\ {125\ +\ 150 \over{275\over9}} = 9 seconds

∴ The required result will be 9 seconds.

Question 45

If 81x2 - 126xy + 49y2 = 0 then find the ratio of y : x

  1. AOption (a)

    8 : 7

  2. BOption (b)

    7 : 9

  3. COption (c)

    7 : 8

  4. DOption (d)

    9 : 7

View answer & explanation

Correct answer

Answer: (d)D.

9 : 7

Why this answer is correct

Given:

81x2 - 126xy + 49y2 = 0

Concept:

(a - b)2 = a2 + b2 - 2ab

Calculation:

⇒ 81x2 - 126xy + 49y2 = 0

⇒ (9x)2 - (2 × 7y × 9x) + (7y)2 = 0

⇒ (9x - 7y)2 = 0

⇒ 9x = 7y

⇒ y : x = 9 : 7

∴ The required result will be 9 : 7.

Question 46

P sells to Q an article at 15% profit. Q sells it to R at 20% loss. R sells it to S at 25% profit and finally T receives it at 320896 were S makes 9% profit. What is the amount that P paid for it?

  1. AOption (a)

    Rs. 256000

  2. BOption (b)

    Rs. 25600

  3. COption (c)

    Rs. 256

  4. DOption (d)

    Rs. 2560

View answer & explanation

Correct answer

Answer: (a)A.

Rs. 256000

Why this answer is correct

Given:

The cost price of the article for T = 320896

Concept:

P = SP - CP     (Where P = Profit, SP = Selling price, and CP = Cost price)

Calculation:

Let us assume cost price of the article for P is X

⇒ The cost price of the article for Q = 1.15X

⇒ The cost price of the article for R = (1.15X) × (0.80)

⇒ The cost price of the article for S = (1.15X) × (0.80) × (1.25)

⇒ The cost price of the article for T = (1.15X) × (0.80) × (1.25) × (1.09) = 1.2535X

⇒ 1.2535X = 320896

⇒ X = 256000

∴ The required result will be 256000.

Question 47

The population of a town is 78960000. If it increases at a rate of 8% p.a. then what is the population after 2 years?

  1. AOption (a)

    92098494

  2. BOption (b)

    92098449

  3. COption (c)

    92098495

  4. DOption (d)

    92098944

View answer & explanation

Correct answer

Answer: (d)D.

92098944

Why this answer is correct

Given:

The population of the town = 78960000

Calculation:

⇒ The population of the town after 1 year = 78960000 × (108/100) = 85276800

⇒ The population of the town after 2nd year = 85276800 × (1.08) = 92098944

∴ The required result will be 92098944.

Question 48

A man plays 21 innings of cricket. The average runs of 21 innings is 4 runs more than the average runs of 20 innings. He scored 95 runs in 21st innings. What is the average of all the innings?

  1. AOption (a)

    15

  2. BOption (b)

    50

  3. COption (c)

    14

  4. DOption (d)

    51

View answer & explanation

Correct answer

Answer: (a)A.

15

Why this answer is correct

Given:

The man score run in 21st inning = 95

Formula used:

Average = The sum of all the itemsThe total number of itemsAverage\ =\ {The\ sum\ of\ all\ the\ items\over The\ total\ number\ of\ items}

Calculation:

Let us assume the average run in 20 innings is X

⇒ The sum of the run scored by the man in 20 innings = 20X

⇒ The sum of the runs scored by the man in 21 innings = 21 × (X + 4)

⇒ 20X + 95 = 21 × (X + 4)

⇒ 20X + 95 = 21X + 84

⇒ 21X - 20X = 95 - 84

⇒ X = 11

⇒ The total runs scored  in 20 innings = 20X = 20 × 11 = 220

⇒ The runs scored in 21 innings = 220 + 95 = 315

⇒ The average run scored in 21 innings = 315/21 = 15

∴ The required result will be 15.

Question 49

A shopkeeper increased the price of an article by Rs. 1710. He made a profit of 6% instead of making a loss of 13%. What is the cost price of the article?

  1. AOption (a)

    Rs. 9000

  2. BOption (b)

    Rs. 9540

  3. COption (c)

    Rs. 9300

  4. DOption (d)

    Rs. 9500

View answer & explanation

Correct answer

Answer: (a)A.

Rs. 9000

Why this answer is correct

Given:

The shopkeeper increase the price by 1710

Concept:

Profit = Selling price - Cost price

Calculation:

Let us assume cost price of the article be X

⇒ The selling price of the article before increment = X × (0.87)

⇒ The selling price of the article after increment = (0.87X + 1710)

⇒ 1.06X = 0.87X + 1710

⇒ 0.19X = 1710

⇒ X = 9000

∴ The required result will be 9000.

Question 50

A number 9876X3 is divisible by 3. What are the possible values of X?

  1. AOption (a)

    3, 6, 9

  2. BOption (b)

    0, 3, 6, 9

  3. COption (c)

     0, 3, 6

  4. DOption (d)

    6, 9

View answer & explanation

Correct answer

Answer: (b)B.

0, 3, 6, 9

Why this answer is correct

Given:

The number = 9876X3

Concept:

A number is divisible by 3 if the sum of the digits of the number is divisible by 3

Calculation:

⇒ 9876X3 

⇒ The sum of the digits of the number = 9 + 8 + 7 + 6 + X + 3 = 33 + X

⇒ The possible value of X = 0, 3, 6, and 9

∴ The required result will be "0, 3, 6, and 9".

Question 51

If the average of 4 consecutive even numbers is 55 then what is the largest number?

  1. AOption (a)

    50

  2. BOption (b)

    58

  3. COption (c)

    52

  4. DOption (d)

    54

View answer & explanation

Correct answer

Answer: (b)B.

58

Why this answer is correct

Given:

The average of four consecutive numbers = 55

Concept:

Average = The sum of all the itemsThe total number of itemAverage\ =\ {The\ sum\ of\ all\ the\ items \over The\ total\ number\ of\ item}

Calculation:

Let us assume the four consecutive even numbers are X, (X + 2), (X + 4), (X + 6),

⇒ X + X + 2 + X + 4 + X + 6 4 = 55{X\ +\ X\ +\ 2\ +\ X\ +\ 4\ +\ X\ +\ 6\ \over 4}\ =\ 55

⇒ 4X + 12 = 220

⇒ 4X = 220 - 12

⇒ X = 208/4 = 52

⇒ The largest number = X + 6 = 52 + 6 = 58

∴ The required result will be 58.

Question 52

What is the product of: 0.03 × 0.0003 × 3 × 0.00003 × 0.3

  1. AOption (a)

    0.0000000000243

  2. BOption (b)

    0.000000000243

  3. COption (c)

    0.0000000243

  4. DOption (d)

    0.00000000243

View answer & explanation

Correct answer

Answer: (b)B.

0.000000000243

Why this answer is correct

Given:

The expression = 0.03 × 0.0003 × 3 × 0.00003 × 0.3

Concept:

0.000a = a × 10-4     (Where a = An integer)

Calculation:

⇒ (3 × 10-2) × (3 × 10-4) × (3) × (3 × 10-5) × (3 × 10-1)

⇒ 3 × 3 × 3 × 3 × 3 × (10-2 × 10-4 × 10-5 × 10-1)

⇒ 243 × 10-12

⇒ 0.000000000243

∴ The required result will be 0.000000000243.

Question 53

The shopkeeper marked a good at 34% over it's cost price. After that he gave a 40% discount. Did he make a loss? What is the percentage of such profit or loss?

  1. AOption (a)

    19%

  2. BOption (b)

    19.6%

  3. COption (c)

    20%

  4. DOption (d)

    18%

View answer & explanation

Correct answer

Answer: (b)B.

19.6%

Why this answer is correct

Given:

The shopkeeper marked a price = 34% above the cost price 

Concept:

D%= MP − SPMP×100D\% =\ {MP\ -\ SP \over MP}× 100     (Where D = Discount, MP = marked price, and SP = Selling price)

Calculation:

Let us assume the cost price of the article is X

⇒ The marked price of the article = (134/100) × X

⇒ The selling price of the article = (1.34X) × (0.60) = 0.804X

⇒ The required loss% = X − 0.804XX×100{X\ -\ 0.804X \over X}\times 100 = 19..6% 

∴ The required result will be 19.6%.

Question 54

Find the number of spheres of radius 1.4 cm that can be made from a big sphere of diameter of 42 cm.

  1. AOption (a)

    3753

  2. BOption (b)

    3357

  3. COption (c)

    3375

  4. DOption (d)

    3573

View answer & explanation

Correct answer

Answer: (c)C.

3375

Why this answer is correct

Given:

The radius of the small spheres = 1.4 cm

The diameter of the big sphere = 42 cm

Concept:

When a solid reshape into another solid then volume of the solid remain equal

Formula used:

The volume of the sphere = 43×π ×R3{4\over 3} × \pi\ × R^3     (Where R = The radius of the sphere)

Calculation:

Let be assume the number of the small spheres are N

⇒ The radius of the big sphere = 42/2 = 21 cm

⇒ The volume of a small sphere = 43×π ×(1.4)3{4\over 3} × \pi\ × (1.4)^3

⇒ The volume of the big sphere = 43×π ×213{4\over 3} × \pi\ × 21^3

⇒ 43×π ×(1.4)3{4\over 3} × \pi\ × (1.4)^3 × N = 43×π ×213{4\over 3} × \pi\ × 21^3

⇒ N = 9261/2.744 = 3375

∴ The required result will be 3375.

Question 55

What is the smallest number that leaves a remainder of 7, 17 and 23 when divided by 12, 22 and 28?

  1. AOption (a)

    1843

  2. BOption (b)

    1438

  3. COption (c)

    1483

  4. DOption (d)

    1834

View answer & explanation

Correct answer

Answer: (a)A.

1843

Why this answer is correct

Calculation:

Since there is a difference of 5 in all the divisors and their respective remainders

LCM(12, 22, 28) = 4 × 3 × 7 × 11 = 924

So, the number has to be in the form of (924x - 5); where x is any natural number(Since there is a difference of 5 in all the divisors and their respective remainders)

Then, numbers can be:

924 - 5 = 919

(924 × 2) - 5 = 1843

∴ Required answer = 1843

Question 56

If Rs. 700000 becomes Rs. 824057.5 in sometime at 8.5% p.a. then what is the duration for which the sum has been compounded (in years)?

  1. AOption (a)

    2

  2. BOption (b)

    1

  3. COption (c)

    3

  4. DOption (d)

    4

View answer & explanation

Correct answer

Answer: (a)A.

2

Why this answer is correct

Given:

Principal(P) = 700000

Amount(A) = 824057.5

Rate of interest(R) = 8.5% compounded annually

Formula used:

A = P[1 + (R/100)]T

T = time period

Calculation:

According to the question:

824057.5 = 700000[1 + (8.5/100)]T

⇒ 824057.5/700000 = (217/200)T

⇒ 1.177225 = (1.085)T

⇒ (1.085)2 = (1.085)T

⇒ T = 2

∴ Time duration = 2 years

Question 57

Two numbers are in the ratio 5 : 7 such that their LCM is 175. Find the HCF of those numbers.

  1. AOption (a)

    2

  2. BOption (b)

    5

  3. COption (c)

    4

  4. DOption (d)

    3

View answer & explanation

Correct answer

Answer: (b)B.

5

Why this answer is correct

Given:

The LCM of the two numbers = 175

Formula used:

The product of the two numbers = (LCM of the two numbers) × (HCF of the two numbers)

Calculation:

Let us assume the two numbers is 5x and 7x respectively and the HCF of the two numbers is H

⇒ (5x × 7x) = 175H

⇒ 35x2 = 175H

⇒ x2 = 5H

⇒ Then the possible value of H = 5

∴ The required result will be 5.

Question 58

P and Q can do a work in 6 days. Q and R can do the same work in 8 days while R and P can do it in 10 days. They did the work for 3 days and then P left. How long will Q and R take if they work together?

  1. AOption (a)

    3 days

  2. BOption (b)

    3.3 days

  3. COption (c)

    3.2 days

  4. DOption (d)

    3.1 days

View answer & explanation

Correct answer

Answer: (b)B.

3.3 days

Why this answer is correct

Given:

P and Q together can complete the work = 6 days

Q and R together can complete the work = 8 days

R and P together can complete the work = 10 days

Formula used:

W = E × T     (Where W = The work, E = The efficiency and T = The time)

Calculation:

Let us assume Q and R can complete the remaining work in D days

The efficiency of P and Q = 16{1\over 6}

The efficiency of Q and R = 18{1\over 8}

The efficiency of R and P = 110{1\over 10}

⇒ The efficiency of P, Q, and R together = 47240{47\over 240}

⇒ The P, Q, and R work for 3 days = 3 ×472403\ \times {47\over 240} = 141240{141\over 240}

⇒ The remaining work = (1 − 141240){(1\ -\ {141\over 240})} = 99240{99\over 240} = 3380{33\over 80}

⇒ The Q and R can complete the remaining work = D =  3380 18{33\over 80}\ \over{1\over8} = 3.3 days

∴ The required result will be 3.3 days.

Directions: Study the data carefully and answer the following question.

The Pie-chart given below shows distribution of number of bags sold by five sellers.

Question 59

Based on Passage: View directions & passage

Bags sold by A and B together is how much less than bags sold by C and D together? 

  1. AOption (a)

    660

  2. BOption (b)

    880

  3. COption (c)

    1100

  4. DOption (d)

    770

View answer & explanation

Correct answer

Answer: (b)B.

880

Why this answer is correct

Given:

SellersDegreeConversion of degree into a percentage
A54°15%
B72°20%
C90°25%
D108°30%
E36°10%

 

Calculation:

Required value = [(108° + 90° – 54°  - 72°)/360°] × 4400

⇒ (72°/360°) × 4400

⇒ 880

∴ Bags sold by A and B together is 880 less than bags sold by C and D together.

Question 60

Based on Passage: View directions & passage

D sold three type of bags i.e, X, Y, and Z in the ratio of 3 : 4 : 5. Find the difference between the Z type bags sold to the X type bags sold?

  1. AOption (a)

    440

  2. BOption (b)

    330

  3. COption (c)

    110

  4. DOption (d)

    220

View answer & explanation

Correct answer

Answer: (d)D.

220

Why this answer is correct

Given:

SellersDegreeConversion of degree into percentage
A54°15%
B72°20%
C90°25%
D108°30%
E36°10%

 

Calculation:

Total bags sold by D = (108°/360°) × 4400

⇒ 1320

Required difference = [(5 – 3)/12] × 1320

⇒ 220

∴ Difference between the Z type bags sold to the X type bags sold is 220.

General English (20 questions)

Question 61

Select the most appropriate idiom for the given sentence.

To enjoy yourself very much.

  1. AOption (a)

    A plum job.

  2. BOption (b)

    Have a whale of a time.

  3. COption (c)

    Wallflower

  4. DOption (d)

    Hold your horses.

View answer & explanation

Correct answer

Answer: (b)B.

Have a whale of a time.

Why this answer is correct

The correct answer is "Have a whale of a time"

Key Points

  • In the above question we have to choose the most appropriate idiom for the given sentence.
  • Have a whale of a time" is an idiom that means to have a lot of fun or a good time(

बहुत मज़ा करना).

  • Example: "I had a whale of a time at the party last night."
  • Thus, the most appropriate idiom for the given sentence is "Have a whale of a time"

Correct answer: "Have a whale of a time"

Key Points

  • "A plum job" is an idiom that means a desirable or advantageous job or position(लाभदायक).
  • Example: "He landed a plum job as CEO of the company."
  • "Wallflower" is an idiom that means a shy or socially awkward person who is not actively involved in a social gathering or event(आरक्षित प्रकृति).
  • Example: "She was a wallflower at the dance and didn't talk to anyone."
  • "Hold your horses" is an idiom that means to be patient or to wait a moment before taking action. It can also be used as a way to tell someone to slow down or to stop being overly eager or impulsive(धैर्य रखना).
  • Example: "Hold your horses, we need to think this through before making a decision."

Question 62

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

  1. AOption (a)

    HANDKERCHEIF

  2. BOption (b)

    PHARAOH

  3. COption (c)

    RECOMMEND

  4. DOption (d)

    SCEPTICAL

View answer & explanation

Correct answer

Answer: (a)A.

HANDKERCHEIF

Why this answer is correct

The correct answer is "HANDKERCHEIF"

Key Points

  • HANDKERCHEIF is an incorrect spelling the correct spelling is "HANDKERCHIEF"
  • A handkerchief is a small piece of cloth, usually square, that is used for wiping one's nose or face, or for other purposes.(

रूमाल)

  • Thus, the incorrectly spelt word is "HANDKERCHEIF"

Correct answer: HANDKERCHEIF

Additional Information

  • Pharaoh: (in ancient Egypt) the title of the king or queen who ruled the country.
  • Recommend: To suggest or endorse someone or something as worthy or suitable; to give advice or express a favorable opinion.
  • Sceptical: Doubting or disbelieving, showing a tendency to question or doubt the truth of something; having a mindset of being uncertain or doubtfull of something.

Question 63

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

CAUTIOUS

  1. AOption (a)

    PREDOMINANT

  2. BOption (b)

    PRUDENT

  3. COption (c)

    PRECISE

  4. DOption (d)

    LOOSE

View answer & explanation

Correct answer

Answer: (b)B.

PRUDENT

Why this answer is correct

The correct answer is "PRUDENT"

Key Points

  • The word that is similar in meaning to the word is "CAUTIOUS" is "PRUDENT".
  • CAUTIOUS: Being careful and watchful; taking precautions to avoid danger or mistakes(सतर्क).
  • Example: "He was cautious when crossing the busy street."
  • PRUDENT: Acting with or showing care and thought for the future; having or showing good judgment(विवेकी).
  • Example: "It would be prudent to save some money for a rainy day."
  • Thus, the synonym of the word "CAUTIOUS" is "PRUDENT"

Correct answer: PRUDENT

Additional Information

  • Let's understand the other words given in the options.
  • Predominant: Most common or frequent; having more influence or power than others(प्रबल).
  • Example: "The predominant color in the painting was blue."
  • Precise: Exact and accurate; providing all the necessary details(विधिपूर्वक).
  • Example: "The instructions were precise and easy to follow."
  • Loose: Not tight or fixed in place; not closely controlled or restricted(ढीला).
  • Example: "The rope was loose and the boat began to drift away."

Question 64

Select the word that is opposite in meaning (ANTONYM) to the word given below.

FOOLHARDY

  1. AOption (a)

    INCAUTIOUS

  2. BOption (b)

    RECKLESS

  3. COption (c)

    ENLIGHTENED

  4. DOption (d)

    IMPRUDENT

View answer & explanation

Correct answer

Answer: (c)C.

ENLIGHTENED

Why this answer is correct

The correct answer is "ENLIGHTENED"

Key Points

  • The word that is opposite in meaning to the word "FOOLHARDY" is "ENLIGHTENED"
  • FOOLHARDY: Acting recklessly or without thinking about the potential consequences(उतावला).
  • Example: "It was foolhardy to attempt to climb the mountain in such bad weather."
  • ENLIGHTENED: Having or showing a good understanding of a particular subject or situation; possessing knowledge or understanding(प्रबुद्ध).
  • Example: "He was enlightened about the benefits of meditation and yoga."
  • Thus, the word that best expresses the meaning opposite to the given word is "ENLIGHTENED"

Correct answer: ENLIGHTENED.

Additional Information

  • Let's understand the other words given in the options.
  • RECKLESS: Acting without thinking about the potential consequences; carelessly endangering the well-being of oneself or others(

लापरवाह).

  • Example: "Driving at high speeds on the highway is reckless and dangerous."
  • INCAUTIOUS: Not being careful or taking precautions; acting recklessly(असावधान).
  • Example: "His incautious behavior led to him getting injured."
  • IMPRUDENT: Not showing good judgment or being careful in making decisions(

अविवेकी).

  • Example: "It was imprudent to invest all of his savings in a risky stock."

Question 65

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.

Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a 22-yard pitch with a wicket at each end, each comprising two bails balanced on three stumps.

P When ten batters have been dismissed, the innings ends and the teams swap roles.

Q. Means of dismissal include being bowled, when the ball hits the stumps and dislodges the bails, and by the fielding side either catching the ball after it is hit by the bat and before it hits the ground, or hitting a wicket with the ball before a batter can cross the crease in front of the wicket.

R. The bowling and fielding side tries to prevent this and dismiss each batter (so they are "out").

S. The batting side scores runs by striking the ball bowled at the wicket with the bat.

The game is adjudicated by two umpires, aided by a third umpire and match referee in international matches.

  1. AOption (a)

    RSPQ

  2. BOption (b)

    QRSP

  3. COption (c)

    SRQP

  4. DOption (d)

    PRQS

View answer & explanation

Correct answer

Answer: (c)C.

SRQP

Why this answer is correct

The correct answer is "SRQP"

Key Points

  • The correct sequence for the paragraph is "SRQP".
  • The fist sentence should be that best connects the starting of the paragraph.
  • The paragraph begins by providing a general introduction to the game of cricket, including a description of the field and the 22-yard pitch with a wicket at each end. This serves as the foundation for the rest of the paragraph and sets the context for the following sentences.
  • The next sentence, "S. explains the objective of the game for the batting team. This is an important piece of information as it establishes what the teams are trying to achieve during the game.
  • The following sentence, "R. " explains the objective of the other team, the bowling and fielding side, which is to prevent the batting team from scoring runs and to dismiss each batter. This sentence builds on the previous one by providing more information on how the game is played.
  • The next sentence, "Q. " provides examples of the ways in which a batter can be dismissed. This builds on the previous sentence by providing specific examples of the actions that the bowling and fielding side can take to achieve their objective.
  • The following sentence, "P, This sentence further tells about the how the innings end.
  • The final sentence "The game is adjudicated by two umpires, aided by a third umpire and match referee in international matches." concludes the paragraph by providing information on the officials of the game. This sentence completes the information about the game and provides the reader with a clear understanding of the game of cricket, its objective, methods and officials.
  • Thus, the correct sequence is "SRQP"

Correct arrangement: Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a 22-yard pitch with a wicket at each end, each comprising two bails balanced on three stumps. The batting side scores runs by striking the ball bowled at the wicket with the bat.The bowling and fielding side tries to prevent this and dismiss each batter (so they are "out"). Means of dismissal include being bowled, when the ball hits the stumps and dislodges the bails, and by the fielding side either catching the ball after it is hit by the bat and before it hits the ground, or hitting a wicket with the ball before a batter can cross the crease in front of the wicket. When ten batters have been dismissed, the innings ends and the teams swap roles.The game is adjudicated by two umpires, aided by a third umpire and match referee in international matches.

Question 66

Select the most appropriate 'one word' for the expressions given below.

A large group of fish swimming together, but not in unison or in any coordinated formation.

  1. AOption (a)

    Shoal of fish

  2. BOption (b)

    School of fish

  3. COption (c)

    Bale of fish

  4. DOption (d)

    Parade of fish

View answer & explanation

Correct answer

Answer: (a)A.

Shoal of fish

Why this answer is correct

The correct answer is "Shoal of fish"

Key Points

  • "Shoal of fish" "Shoal" is also a term used to describe a large group of fish swimming together, but not in unison or in any coordinated formation(मछलियों का शोल).
  • A "school" of fish refers specifically to a group of fish that swims together for protection or for the purpose of hunting, while a "shoal" is a general term for any group of fish swimming together.
  • Thus, the correct answer is "Shoal of fish"

Correct answer: Shoal of fish

Question 67

The sentences below are not complete. There are four options for each question. Choose the best words to complete the sentence.

These values are ___________ and ___________ and engage you with the world as it is rather than how you wish it were.

  1. AOption (a)

    rich and sacrifice

  2. BOption (b)

    increasingly and abundant

  3. COption (c)

    immediate and controllable

  4. DOption (d)

    superstitious and clarifying

View answer & explanation

Correct answer

Answer: (c)C.

immediate and controllable

Why this answer is correct

The correct answer is "immediate and controllable"

 Key Points 

  • The best words to complete the sentence are "immediate and controllable".
  • "Immediate and controllable" fits in the context of the sentence as it relates to the idea of engaging with the world as it is because immediate means happening or done without delay, and controllable means capable of being managed or directed.
  • Option 1: "Rich and sacrifice" does not fit in the context of the sentence as it does not relate to the idea of engaging with the world as it is.
  • Option 2: "Increasingly and abundant" does not fit in the context of the sentence as it does not relate to the idea of engaging with the world as it is.
  • Option 4: "Superstitious and clarifying" does not fit in the context of the sentence as it does not relate to the idea of engaging with the world as it is, because superstitious means relating to or involving superstition and clarifying means making something clear or easy to understand.
  • Thus, the correct answer is "immediate and controllable"

Correct answer: These values are immediate and controllable and engage you with the world as it is rather than how you wish it were.

Question 68

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'.

See, its the punching people in the face / that's the problem, not the anger; anger / is merely the messenger.

  1. AOption (a)

    No Error

  2. BOption (b)

    is merely the messenger.

  3. COption (c)

    that's the problem, not the anger; anger

  4. DOption (d)

    See, its the punching people in the face

View answer & explanation

Correct answer

Answer: (d)D.

See, its the punching people in the face

Why this answer is correct

The correct answer is "See, its the punching people in the face".

Key Points

  • The part of the sentence that has an error is "See, its the punching people in the face"
  • The error is the contraction "it's" should be "it's" because it means "it is" instead of "its" which means "belonging to it"(possessive pronoun).

Correct sentence: See, it's the punching people in the face that's the problem, not the anger; anger is merely the messenger.

Question 69

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'.

The extravagant emphasis having laying on purely / intellectual education and the consequent neglect of physical training must / necessarily lead to depressing thoughts in the youth.

  1. AOption (a)

    The extravagant emphasis having laying on purely

  2. BOption (b)

    intellectual education and the consequent neglect of physical training must

  3. COption (c)

    No Error

  4. DOption (d)

    necessarily lead to depressing thoughts in the youth.

View answer & explanation

Correct answer

Answer: (a)A.

The extravagant emphasis having laying on purely

Why this answer is correct

The correct answer is "The extravagant emphasis having laying on purely"

Key Points

  • The part of the sentence that has an error is "The extravagant emphasis having laying on purely"
  • The phrase "having laying" is a grammatical error, it should be  "laid" or "laying emphasis on" to make the sentence grammatically correct.
  • It should be "The extravagant emphasis laid on purely intellectual education and the consequent neglect of physical training must necessarily lead to depressing thoughts in the youth."
  • The use of "having" is superfluous
  • Thus, the first part of the sentence has an error.

Correct sentence: The extravagant emphasis laid on purely intellectual education and the consequent neglect of physical training must necessarily lead to depressing thoughts in the youth.

Question 70

Select the most appropriate meaning of the given idiom.

Shoemaker, stick to your last.

  1. AOption (a)

    Even those who keep postponing their obligations will not let them disappear.

  2. BOption (b)

    Do not criticize anything that you have no idea about. Stick to what you know about.

  3. COption (c)

    Damage caused must be paid for in the same amount.

  4. DOption (d)

    People without similarities appear attractive to each other.

View answer & explanation

Correct answer

Answer: (b)B.

Do not criticize anything that you have no idea about. Stick to what you know about.

Why this answer is correct

The correct answer is "​Do not criticize anything that you have no idea about. Stick to what you know about."

Key Points

  • The proverb "Shoemaker, stick to your last" is a warning against trying to do something that you are not skilled or experienced in, and instead, to stick to what you know and do best.
  • Example: A doctor who is a renowned heart surgeon, but instead of doing surgeries, he starts to invest his money into stock market and ends up losing it all. Friends and colleagues tell him "Shoemaker, stick to your last".
  • Thus, the correct answer is "​Do not criticize anything that you have no idea about. Stick to what you know about."

Correct answer: ​Do not criticize anything that you have no idea about. Stick to what you know about.

Additional Information 

  • It originates from the story of a shoemaker who, instead of sticking to his trade of making shoes, decided to branch out into other areas, such as tailoring or farming, but ended up failing at those pursuits.
  • This proverb is often used to advise people to stick to their profession or expertise, and not to waste their time and resources on things they are not good at.

Question 71

Fill in the blank with the most appropriate choice.

The whole party system as it had ______ existed was not the kind of face that can restore the German nation or repair the damages.

  1. AOption (a)

    scantily

  2. BOption (b)

    sacramentally

  3. COption (c)

    institutionally

  4. DOption (d)

    hitherto

View answer & explanation

Correct answer

Answer: (d)D.

hitherto

Why this answer is correct

The correct answer is "hitherto"

Key Points

  • The most appropriate choice to fill in the blank is "hitherto".
  • Hitherto" means "until now"(अब तक) or "up to this point in time" and it is the most appropriate choice because it fits in the context of the sentence, as the party system as it had existed until now is not the kind of face that can restore the German nation or repair the damages.
  • Example: "Hitherto, we had only heard rumors about the new project, but today we finally got to see it for ourselves."
  • Thus, the most appropriate word is "Hitherto"

Correct sentence: The whole party system as it had hitherto existed was not the kind of face that can restore the German nation or repair the damages.

Additional Information 

  • Scantily: Inadequately or barely(कम).
  • Example: "She was dressed scantily in a top"
  • Sacramentally: Having the nature of a sacrament(पवित्र रूप से).
  • Example: "The bread and wine are sacramentally transformed into the body and blood of Christ in the Catholic Church."
  • Institutionally: Relating to an institution(संस्थागत).
  • Example: "The school has institutionally racist policies."

Question 72

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.

(Building a culture surrounding all idea of freedom) and responsibility, within a framework.

  1. AOption (a)

    Build a culture around the idea of freedom

  2. BOption (b)

    Built a culture around all idea of freedom

  3. COption (c)

    No correction required.

  4. DOption (d)

    Building cultures commiting around all ideas of freedom

View answer & explanation

Correct answer

Answer: (a)A.

Build a culture around the idea of freedom

Why this answer is correct

The correct answer is "Build a culture around the idea of freedom"

Key Points

  • The bracketed word segment "all idea of freedom" is not grammatically correct and doesn't convey a clear meaning. The phrase "the idea of freedom" is more appropriate as it clarifies the type of freedom being referred to and also grammatically correct. The sentence as a whole describes the process of creating a culture that emphasizes individual freedom and responsibility within a specific framework.
  • The corrected sentence would read: "Build a culture around the idea of freedom and responsibility, within a framework."
  • *Thus, the most appropriate substitution is,"*Build a culture around the idea of freedom"

Correct sentence:  Build a culture around the idea of freedom and responsibility, within a framework."

Question 73

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. (

Why do all this talk of hedgehogs) and foxes have to do with good to great?

  1. AOption (a)

    What do all these talk of hedgehogs

  2. BOption (b)

    Why does all this talk of hedgehogs

  3. COption (c)

    No correction required.

  4. DOption (d)

    What does all this talk of hedgehogs

View answer & explanation

Correct answer

Answer: (d)D.

What does all this talk of hedgehogs

Why this answer is correct

The correct answer is "What does all this talk of hedgehogs"

Key Points

  • The correct word segment that substitutes the bracketed word segment correctly and completes the sentence meaningfully is: "What does all this talk of hedgehogs".
  • The bracketed word segment "all this talk of hedgehogs) and foxes" is not grammatically correct as it is not clear what the relationship is between hedgehogs and foxes and it also breaks the sentence in an incomplete way. The phrase "What does all this talk of hedgehogs" is more appropriate as it rephrases the question and it is grammatically correct. The sentence is asking why the topic of hedgehogs is relevant to the concept of good to great.
  • The corrected sentence would read: "Why does all this talk of hedgehogs have to do with good to great?"
  • Thus, the correct answer is "What does all this talk of hedgehogs"

Correct sentence: What does all this talk of hedgehogs and foxes have to do with good to great.

Question 74

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.

Basketball is a team sport

P. opposing one another on a rectangular court,

Q. in which two teams, most commonly of five players each,

R. compete with the primary objective of shooting a basketball through the defender's

S. hoop (a basket 18 inches in diameter mounted 10 feet high to a backboard at each end of the court)

while preventing the opposing team from shooting through their own hoop.

  1. AOption (a)

    SRQP

  2. BOption (b)

    QPRS

  3. COption (c)

    RQSP

  4. DOption (d)

    PSRQ

View answer & explanation

Correct answer

Answer: (b)B.

QPRS

Why this answer is correct

The correct answer is "QPRS"

Key Points

  • The correct sequence is "QPRS"
  • The first sentence will be the one that best connects the Opening of the paragraph.
  • The sentence "Q. In which two teams, most commonly of five players each," provides the context for the game and the number of players on each team.
  • The sentence "P. opposing one another on a rectangular court," describes the location where the game is played and the opposing teams.
  • The sentence "R. compete with the primary objective of shooting a basketball through the defender's hoop (a basket 18 inches in diameter mounted 10 feet high to a backboard at each end of the court)" explains the objective of the game and the target that the teams aim to shoot the ball through.
  • The sentence "S. while preventing the opposing team from shooting through their own hoop," highlights the defensive aspect of the game, where teams work to prevent their opponents from scoring.
  • Thus, the correct sequence is "QPRS"

Correct arrangement: Basketball is a team sport in which two teams, most commonly of five players each,opposing one another on a rectangular court, compete with the primary objective of shooting a basketball through the defender's hoop (a basket 18 inches in diameter mounted 10 feet high to a backboard at each end of the court)while preventing the opposing team from shooting through their own hoop.

Question 75

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

RIVALRY

  1. AOption (a)

    ANTAGONISM

  2. BOption (b)

    COUNTERATTACK

  3. COption (c)

    ASSIMILATE

  4. DOption (d)

    ACCORD

View answer & explanation

Correct answer

Answer: (a)A.

ANTAGONISM

Why this answer is correct

The correct answer is "ANTAGONISM"

 Key Points

  • The word that is similar in meaning to the given word is "ANTAGONISM"
  • RIVALRY: Competitive relationship or situation between two or more parties(विरोध, प्रतिद्वंद्विता)).
  • Example: "The rivalry between the two companies has led to intense competition in the market."
  • ANTAGONISM: Hostility or opposition between two or more parties(प्रतिद्वंद्विता).
  • Example: "The antagonism between the two countries has led to a breakdown in diplomatic relations."
  • Thus, the word best expresses the meaning same as the word "RIVALRY" is "ANTAGONISM"

Correct answer: "ANTAGONISM

Additional Information

  • Counterattack: A military or strategic move in which an attack is launched in response to an earlier attack(

जवाबी हमला).

  • Example: "The enemy launched a surprise attack, but our troops were able to quickly launch a counterattack."
  • Assimilate: To absorb or incorporate something into a larger whole(आत्मसात्‌ करना).
  • Example: "The immigrants were able to assimilate into the new culture over time."
  • Accord: Agreement or harmony between two or more parties(सहमति).
  • Example: "The accord between the two nations was reached after months of negotiations."

A passage is given with 5 questions following it. Read the passage carefully and choose the best answer to each question out of the four alternatives.

Sporadic use of the term for some of the subject matter occurred subsequently, such as the use by Étienne Serres in 1839 to describe the natural history, or palaeontology, of man, based on comparative anatomy, and the creation of a chair in anthropology and ethnography in 1850 at the French National Museum of Natural History by Jean Louis Armand de Quatrefages de Bréau. It is the scientific study of humanity, concerned with human behaviour, human biology, cultures and societies, in both the present and past, including past human species. The major theorists supported the gradual osmosis of anthropology curricula into the major institutions of higher learning. By 1898, 48 educational institutions in 13 countries had some curriculum in anthropology. None of the 75 faculty members were under a department named anthropology.

This meagre statistic expanded in the 20th century to comprise anthropology departments in the majority of the world's higher educational institutions, many thousands in number. Anthropology has diversified from a few major subdivisions to dozens more. Practical anthropology, the use of anthropological knowledge and technique to solve specific problems, has arrived; for example, the presence of buried victims might stimulate the use of a forensic archaeologist to recreate the final scene. The organization has reached global level. For example, the World Council of Anthropological Associations (WCAA), "a network of national, regional and international associations that aims to promote worldwide communication and cooperation in anthropology", currently contains members from about three dozen nations.

Question 76

Based on Passage: View directions & passage

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. World Council of Anthropological Associations (WCAA) currently contains members from about four dozens of nations.

B. The subject of the passage is the study of human animal behaviour, their biology and their evolution.

C. The meagre statistic expanded in the 21th century to comprise palaeontology departments in the majority of the world's higher educational institutions, many thousands in number

  1. AOption (a)

    B & C are correct.

  2. BOption (b)

    A & B are correct.

  3. COption (c)

    All are incorrect.

  4. DOption (d)

    Only A is correct.

View answer & explanation

Correct answer

Answer: (c)C.

All are incorrect.

Why this answer is correct

The correct answer is "All are incorrect".

Key Points

  • Refer to the line:  The World Council of Anthropological Associations (WCAA), "a network of national, regional and international associations that aims to promote worldwide communication and cooperation in anthropology", currently contains members from about three dozen nations.
  • Staement A is incorrect because WCAA currently contains members from about three dozen nations.
  • **Refer to the line:**It is the scientific study of humanity, concerned with human behaviour, human biology, cultures and societies, in both the present and past, including past human species.
  • Statement B is incorrect because the subject of the passage is the study of human behaviour only no human animal behaviour.
  • Refer to the line*: This meagre statistic expanded in the 20th century to comprise anthropology departments in the majority of the world's higher educational institutions, many thousands in number*.
  • Statement C is also incorrect because the meagre statistic expanded in the 20th century not in the 21st century.
  • Thus, All the statements are incorrect.

Correct answer: All are incorrect

Question 77

Based on Passage: View directions & passage

According to the above passage, who was responsible for creation of a chair at the French National Museum of Natural History?

  1. AOption (a)

    Étienne Serres

  2. BOption (b)

    Jean Louis Armand

  3. COption (c)

    Clifford Geertz

  4. DOption (d)

    Adam F. Kollár

View answer & explanation

Correct answer

Answer: (b)B.

Jean Louis Armand

Why this answer is correct

The correct answer is "Jean Louis Armand"

Key Points

  • **Refer to the line: The creation of a chair in anthropology and ethnography in 1850 at the French National Museum of Natural History by Jean Louis Armand de Quatrefages de Bréau.
  • Jean Louis Armand was responsible for creation of a chair at the French National Museum of Natural History.
  • Thus, the correct answer is "Jean Louis Armand"

Correct answer: Jean Louis Armand

Question 78

Based on Passage: View directions & passage

 On the basis of your reading of the above passage, select the most appropriate heading for the same.

  1. AOption (a)

    Anthropology

  2. BOption (b)

    Ethnography

  3. COption (c)

    Palaeontology

  4. DOption (d)

    National Museum of Natural History

View answer & explanation

Correct answer

Answer: (a)A.

Anthropology

Why this answer is correct

The correct answer is "​Anthropology".

Key Points

  • The appropriate title for the passage is "Anthropology".
  • Anthropology refers to the scientific study of humanity, including human behaviour, cultures, societies, and biology, both in the present and the past, including past human species(मनुष्य जाति का विज्ञान).
  • The passage mainly focuses on and discusses the scientific study of humanity, including its history, subdivisions, and current state.
  • Thus, the correct answer is "Anthropology"

Correct answer: Anthropology

Additional Information .

  • Paleontology: the study of prehistoric life, including the fossils of plants, animals, and other organisms, as well as the interpretation of these fossils in terms of the evolution and behavior of ancient life forms(जीवाश्मिकी).
  • Ethnography: The study of the customs, beliefs, and social structures of a particular group or society, typically through participant observation and the gathering of data through interviews and other methods. Ethnography is a research method used in anthropology, but it is also used in other fields such as sociology, cultural studies, and education(नृवंशविज्ञान).

Question 79

Based on Passage: View directions & passage

What is the opposite of the meaning of 'Sporadic' from the above passage?

  1. AOption (a)

    Occasional

  2. BOption (b)

    Scattered

  3. COption (c)

    Frequent

  4. DOption (d)

    Patchy

View answer & explanation

Correct answer

Answer: (c)C.

Frequent

Why this answer is correct

The correct answer is "Frequent"

Key Points

  • Sporadic: occurring at irregular intervals; infrequent and scattered(छिटपुट).
  • Example: "sporadic outbreaks of violence"
  • Frequent: happening often; many times(अक्सर).
  • Example: "frequent visits to the doctor"
  • Thus, as per the above explanation the word opposite to the meaning of "Sporadic" is "Frequent"

Correct answer: Frequent

Additional Information

  • Occasional: happening from time to time; not regular or continuous(आकस्मिक).
  • Example: "an occasional glass of wine with dinner"
  • Scattered: dispersed or distributed over a wide area(छितराया हुआ).
  • Example: "scattered showers throughout the day"
  • Patchy: having spots or patches of a different color or texture(विविध).
  • Example: "a patchy lawn with brown patches"

Question 80

Based on Passage: View directions & passage

From the given options which word can replace the word 'meagre' in the above passage?

  1. AOption (a)

    Relaxed

  2. BOption (b)

    Complex

  3. COption (c)

    Insufficient

  4. DOption (d)

    Abundant

View answer & explanation

Correct answer

Answer: (c)C.

Insufficient

Why this answer is correct

The correct answer is "Insufficient"

Key Points

  • Meagre: having very little of what is needed or desired; scanty(अल्प).
  • Example: "I had a meagre meal there"
  • Insufficient: not enough; lacking**(अपर्याप्त)**.
  • Example: "insufficient evidence to prove the crime"
  • Thus, the word can replace the word "meagre" is "insufficient".

Correct answer: Insufficient

Additional Information

  • Relax: make or become less tense, tight, or stiff(आराम करना).
  • Example: "relax and take a deep breath"
  • Complex: consisting of many interconnected parts; compound(जटिल).
  • Example: "a complex system of government"
  • Abundant: present in great quantity; plentiful(भरपूर).
  • Example: "an abundant supply of fresh water"

General Hindi (20 questions)

Question 81

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

लोलुप

  1. AOption (a)

    अशांत

  2. BOption (b)

    मोक्ष

  3. COption (c)

    समास

  4. DOption (d)

    संतुष्ट

View answer & explanation

Correct answer

Answer: (d)D.

संतुष्ट

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'संतुष्ट' है।

Key Points

  • लोलुप का विलोम शब्द - संतुष्ट।
  • लोलुप का अर्थ - लालची।

 Important Pointsअन्य विकल्प:- 

  • अशांत का विलोम शब्द - शांत
  • मोक्ष का विलोम शब्द - नरक
  • समास का विलोम शब्द - व्यास

Additional Information 

  • ऐसे शब्द जो एक दूसरे के विपरीतार्थक हो या एक दूसरे का उल्टा अर्थ बताते हुए विलोम शब्द कहलाते हैं l
  • अन्य विलोम शब्द युग्म:-
  • हार - जीत,
  • आय - व्यय,
  • आजादी - गुलामी,
  • नवीन - प्राचीन आदि।

Question 82

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

  1. AOption (a)

    स्पष्टवक्ता

  2. BOption (b)

    अनादी

  3. COption (c)

    सर्ग्वासी

  4. DOption (d)

    उरून

View answer & explanation

Correct answer

Answer: (a)A.

स्पष्टवक्ता

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'स्पष्टवक्ता' है।

 Key Points

  • उपरोक्त दिये गए विकल्प शुद्ध शब्द - स्पष्टवक्ता हैं ।
  • स्पष्टवक्ता का अर्थ - जो अपनी बात को स्पष्ट रूप से व्यक्त करें ।
  • ​अन्य विकल्प:- 
  • अनादी का शुद्ध शब्द - अनादि
  • सर्ग्वासी का शुद्ध शब्द - स्वर्गवासी

Additional Information 

  • जो शब्द हिन्दी व्याकरण के बारे में सम्पूर्ण करते हुये वर्ण की दृष्टि से नाम हो, शुद्ध शब्द कहलाते हैं ।
  • उच्चारण से इसकी पुष्टि होती है।
  • ​कुछ महत्वपूर्ण अशुद्ध -  शब्द :- 
  • कंगल - कंगाल
  • प्रदरशन - प्रदर्शन
  • कनिष्ट  - कनिष्ठ
  • ऊघृत   - उद्धृत

Question 83

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

आम में बौर आने पर कोयल कुहकने लगती है।

  1. AOption (a)

    मिश्रित वाक्य

  2. BOption (b)

    सरल वाक्य

  3. COption (c)

    संयुक्त वाक्य

  4. DOption (d)

    विधान वाचक वाक्य

View answer & explanation

Correct answer

Answer: (b)B.

सरल वाक्य

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'सरल वाक्य' है।

Key Points

  • सरल वाक्य:- जिस वाक्य में एक ही मुख्य क्रिया होती है, उसे सरल वाक्य कहते हैं।
  • उदाहरण:- आम में बौर आने पर कोयल कुहकने लगती है |
  • यहाँ 'आम में बौर आने पर' एक पदबंध है और 'कोयल कुहकने लगती है' मुख्य क्रिया है। इसमें एक ही मुख्य क्रिया है, इसलिए यह सरल वाक्य है।

 

Important Pointsरचना के आधार पर वाक्य के अन्य दो भेद:

  • सरल वाक्य:-  ऐसे वाक्य जिनमें एक ही क्रिया एवं एक ही कर्ता होता है या जिस वाक्य में एक ही उद्देश्य एवं एक ही विधेय होता है, वे वाक्य सरल वाक्य कहलाते हैं।
  • इसमें कर्ता एक से अधिक हो सकते हैं लेकिन मुख्य क्रिया एक ही होगी। ​
  • उदाहरण:  'बिजली चमकती है', 'पानी बरसा'।
  • संयुक्त वाक्य:- जिन वाक्यों में दो या दो से अधिक सरल वाक्य योजकों (और, एवं, तथा, या, अथवा, इसलिए, अतः, फिर भी, तो, नहीं तो, किन्तु, परन्तु, लेकिन, पर आदि) से जुड़े हों, उन्हें संयुक्त वाक्य कहते है।  
  • उदाहरण: वह सुबह गया और शाम को लौट आया।

Additional Information

वाक्य
विचार को पूर्णता से प्रकट करनेवाली एक क्रिया से युक्त पद-समूह को 'वाक्य' कहते हैं।
वाक्य के दो भेद होते है-
(1)उद्देश्य 
(2)विद्येय
उद्देश्यवाक्य का वह भाग है, जिसमें किसी व्यक्ति या वस्तु के बारे में कुछ कहा जाए, उसे उद्देश्य कहते हैं।
विद्येयउद्देश्य के विषय में जो कुछ कहा जाता है, उसे विद्येय कहते है।
जैसे- पूनम किताब पढ़ती है। में पूनम उद्देश्य है और किताब पढ़ती है विधेय।
रचना के आधार पर वाक्य के तीन भेद होते है-
(i)साधरण वाक्य या सरल वाक्य 
(ii)मिश्रित वाक्य 
(iii)संयुक्त वाक्य

Question 84

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

प्रीति, जो कल हमारे घर आनेवाली थी, नहीं आई।

  1. AOption (a)

    निषेधवाचक वाक्य

  2. BOption (b)

    संयुक्त वाक्य

  3. COption (c)

    सरल वाक्य

  4. DOption (d)

    मिश्रित वाक्य

View answer & explanation

Correct answer

Answer: (d)D.

मिश्रित वाक्य

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'मिश्रित वाक्य' है।

Key Points

  • मिश्रित वाक्य:- जिस वाक्य में एक से अधिक वाक्य मिले हों, किन्तु एक प्रधान उपवाक्य तथा शेष आश्रित उपवाक्य हों, मिश्रित वाक्य कहलाता है।
  • उदाहरण:- आम में बौर आने पर कोयल कुहकने लगती है | यहा पर दो से अधिक वाक्य हैं । "प्रीति, जो कल हमारे घर आनेवाली थी" एक प्रधान उपवाक्य है तथा नहीं आई आश्रित वाक्य है।

Important Pointsअन्य विकल्प:

  • सरल वाक्य:-  ऐसे वाक्य जिनमें एक ही क्रिया एवं एक ही कर्ता होता है या जिस वाक्य में एक ही उद्देश्य एवं एक ही विधेय होता है, वे वाक्य सरल वाक्य कहलाते हैं। इसमें कर्ता एक से अधिक हो सकते हैं लेकिन मुख्य क्रिया एक ही होगी।
  • उदाहरण:  'बिजली चमकती है', 'पानी बरसा' ।
  • संयुक्त वाक्य:- जिन वाक्यों में दो या दो से अधिक सरल वाक्य योजकों (और, एवं, तथा, या, अथवा, इसलिए, अतः, फिर भी, तो, नहीं तो, किन्तु, परन्तु, लेकिन, पर आदि) से जुड़े हों, उन्हें संयुक्त वाक्य कहते है।
  • ​उदाहरण: वह सुबह गया और शाम को लौट आया।
  • निषेधवाचक वाक्य : जिन वाक्यों से कार्य न होने का भाव प्रकट होता है, उन्हें निषेधवाचक वाक्य कहते हैं।
  • उदाहरण: मैंने दूध नहीं पिया।

 Additional Information

वाक्य
विचार को पूर्णता से प्रकट करनेवाली एक क्रिया से युक्त पद-समूह को 'वाक्य' कहते हैं।
वाक्य के दो भेद होते है-
(1)उद्देश्य 
(2)विधेय
(1)उद्देश्य :-वाक्य का वह भाग है, जिसमें किसी व्यक्ति या वस्तु के बारे में कुछ कहा जाए, उसे उद्देश्य कहते हैं।
(2)विधेय:-उद्देश्य के विषय में जो कुछ कहा जाता है, उसे विधेय कहते है।
रचना के आधार पर वाक्य के तीन भेद होते है- 1. साधरण वाक्य या सरल वाक्य 2. मिश्रित वाक्य 3. संयुक्त वाक्य

Question 85

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

  1. AOption (a)

    पिता जी, आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे

  2. BOption (b)

    पिता जी, आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे।"

  3. COption (c)

    पिता जी आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे।

  4. DOption (d)

    पिता जी, आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे।

View answer & explanation

Correct answer

Answer: (d)D.

पिता जी, आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे।

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'पिता जी, आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे ​' है।

Key Points

  • पिता जी, आप बहुत अच्छे हैं, इस बार जाने का अवसर अवश्य देंगे। - इस वाक्य में सही रूप से विराम चिन्हों का प्रयोग किया गया है।
  • विराम चिन्ह – भाषा के लिखित रूप में विशेष स्थानों पर रुकने का संकेत करने वाले चिन्हों को विराम चिन्ह कहते हैं।​

Additional Information

विराम चिन्ह का नामपरिभाषाउदाहरण
पूर्ण विराम चिन्ह (।)जहाँ एक बात पूरी हो जाये या वाक्य समाप्त हो जाये वहाँ पूर्ण विराम ( । ) चिन्ह लगाया जाता है।बाजार खुल गया।
अर्द्ध विराम चिन्ह (;)जहाँ अल्प विराम से कुछ अधिक ठहरते हैं तथा पूर्ण विराम से कम ठहरते हैं, वहाँ अर्द्ध विराम का चिन्ह ( ; ) लगाया जाता है।मुख्य अतिथि आ गए हैं; वह शीघ्र चले जाएंगे।
अल्प विराम चिन्ह (,)वाक्य में जहाँ थोड़ा रुकना हो या अधिक वस्तुओं, व्यक्तियों आदि को अलग करना हो वहाँ अल्प विराम (,) चिन्ह का प्रयोग किया जाता है।राकेश, मोहन, शीतल और पंकज ने यह चित्र बनाया है।
प्रश्नवाचक चिन्ह (?)बातचीत के दौरान जब किसी से कोई बात पूछी जाती है अथवा कोई प्रश्न पूछा जाता है, तब वाक्य के अंत में प्रश्नसूचक-चिन्ह का प्रयोग किया जाता है।तुम्हारी माताजी का नाम क्या है ?
विस्मयादिबोधक चिन्ह (!)इसका प्रयोग हर्ष, विवाद, विस���मय, घृणा, आश्रर्य, करुणा, भय, संबोधन इत्यादि का बोध कराने के लिए इस चिन्ह का प्रयोग किया जाता है।वाह! कितना सुंदर दृश्य है।
लाघव चिन्ह (०)किसी बड़े तथा प्रसिद्ध शब्द को संक्षेप में लिखने के लिए उस शब्द का पहला अक्षर लिखकर उसके आगे शून्य (०) लगा देते हैं। यह शून्य ही लाघव-चिन्ह कहलाता है।डॉक्टर – डॉ०, प्रोफेसर – प्रो०

Question 86

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

अभ्यागत

  1. AOption (a)

    अभि + गत

  2. BOption (b)

    अभ्या + गत

  3. COption (c)

    अभि + अगत

  4. DOption (d)

    अभि + आगत

View answer & explanation

Correct answer

Answer: (d)D.

अभि + आगत

Why this answer is correct

दिए गए विकल्पों में सही उत्तर विकल्प 'अभि + आगत' है।

Key Points

  • दिए गए विकल्पों में से अभ्यागत का संधि विच्छेद ''अभि + आगत" होगा।
  • अभ्यागत' में यण संधि है।
  • इ, ई, उ, ऊ या ऋ का मेल यदि असमान स्वर से हो तो इ, ई का 'य'; उ, ऊ का 'व' और ऋ का 'र' हो जाता है।
  • जैसे - 
  • यदि + अपि (इ + अ) = यद्यपि,
  • अनु + एषण = अन्वेषण।​

Additional Information

संधि - दो शब्दों के मेल से जो विकार (परिवर्तन) होता है उसे संधि कहते हैं। संधि के तीन प्रकार हैं - 1. स्वर 2. व्यंजन और 3. विसर्ग।
स्वर संधिदो स्वरों के मेल से उत्पन्न होने वाले विकार को स्वर संधि कहते हैं। इसके इसके पाँच भेद हैं- दीर्घ, गुण, वृद्धि, यण, अयादि।स्वार्थ = स्व + अर्थ
व्यंजन संधिव्यंजन के बाद यदि किसी स्वर या व्यंजन के आने से उस व्यंजन में जो विकार / परिवर्तन उत्पन्न होता है वह व्यंजन संधि कहलाता है।दिग्गज = दिक् + गज
विसर्ग संधिविसर्ग के साथ स्वर अथवा व्यंजन के मिलने से जो विकार उत्पन्न होता है, उसे विसर्ग संधि कहते हैं।शिरोमणि = शिर: + मणि

Question 87

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

धन + एषणा

  1. AOption (a)

    धनेषण

  2. BOption (b)

    धनैषणा

  3. COption (c)

    धनीशाणा

  4. DOption (d)

    धनषण

View answer & explanation

Correct answer

Answer: (b)B.

धनैषणा

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'धनैषणा' है।

Key Points

  • दिए गए विकल्पों में से धनैषणा का संधि विच्छेद 'धन + एषणा ' होगा।
  • धनैषणा शब्द में वृद्धि स्वर संधि है।
  • धन + एषणा = धनैषणा
  • धनैषणा शब्द में 'अ + ए = ऐ' का मेल हो रहा है इसलिए यहां वृद्धि स्वर संधि है।

 Additional Information

स्वर संधि
संधिपरिभाषाउदाहरण
दीर्घ संधिदो सवर्ण, ह्रस्व या दीर्घ, स्वरों के मेल होने पर दीर्घ स्वर बन जाता है।जैसे – शिव + आलय (अ + आ) = शिवालय, गिरि + इन्द्र (इ + इ) = गिरीन्द्र।
गुण संधिअ, आ के साथ इ, ई का मेल होने पर 'ए'; उ, ऊ का मेल होने पर 'ओ'; तथा ऋ का मेल होने पर 'अर्' हो जाता है।जैसे – देव + इन्द्र (अ + इ) = देवेन्द्र, देव + ऋषि (अ + ऋ) = देवर्षि।
वृद्धि संधिअ, आ का मेल ए, ऐ के साथ होने पर 'ऐ' तथा ओ, औ के साथ होने पर 'औ' में परिवर्तित हो जाता है।जैसे – एक + एक (अ + ए) = एकैक, परम + ओजस्वी (अ + ओ) = परमौजस्वी।
यण संधिइ, ई, उ, ऊ या ऋ का मेल यदि असमान स्वर से हो तो इ, ई का 'य'; उ, ऊ का 'व' और ऋ का 'र' हो जाता है।जैसे - यदि + अपि (इ + अ) = यद्यपि, अनु + एषण = अन्वेषण।
अयादि संधिए, ऐ तथा ओ, औ का मेल किसी अन्य स्वर के साथ होने से क्रमशः ए का अय्, ऐ का आय, ओ का अव् तथा औ का आव् हो जाता है।जैसे – ने + अन (ए + अ) = नयन, गै + अक (ऐ + अ) = गायक।

Question 88

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

  1. AOption (a)

    पढ़ी - लिखी माँ तो अपने बच्चों की शिक्षा -दीक्षा पर ध्यान देती ही है।

  2. BOption (b)

    पढी - लिखी माँ तो अपने बच्चों की शिक्षा -दीक्षा पर ध्यान देती ही है'

  3. COption (c)

    पढी - लिखी माँ तो अपने बच्चों की शिक्षा दीक्षा पर ध्यान देती ही है।

  4. DOption (d)

    पढी - लिखी माँ तो अपने बच्चों की शिक्षा ;दीक्षा पर ध्यान देती ही है।

View answer & explanation

Correct answer

Answer: (a)A.

पढ़ी - लिखी माँ तो अपने बच्चों की शिक्षा -दीक्षा पर ध्यान देती ही है।

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'पढी - लिखी माँतो अपने बच्चों की शिक्षा -दीक्षा पर ध्यान देती ही है।' है।

Key Points 

  • पढी - लिखी माँ तो अपने बच्चों की शिक्षा -दीक्षा पर ध्यान देती ही है।' - इस वाक्य में सही रूप से विराम चिन्हों का प्रयोग किया गया है।
  • विराम चिन्ह – भाषा के लिखित रूप में विशेष स्थानों पर रुकने का संकेत करने वाले चिन्हों को विराम चिन्ह कहते हैं।​

Additional Information 

विराम चिन्ह का नामपरिभाषाउदाहरण
पूर्ण विराम चिन्ह (।)जहाँ एक बात पूरी हो जाये या वाक्य समाप्त हो जाये वहाँ पूर्ण विराम ( । ) चिन्ह लगाया जाता है।बाजार खुल गया।
अर्द्ध विराम चिन्ह (;)जहाँ अल्प विराम से कुछ अधिक ठहरते हैं तथा पूर्ण विराम से कम ठहरते हैं, वहाँ अर्द्ध विराम का चिन्ह ( ; ) लगाया जाता है।मुख्य अतिथि आ गए हैं; वह शीघ्र चले जाएंगे।
अल्प विराम चिन्ह (,)वाक्य में जहाँ थोड़ा रुकना हो या अधिक वस्तुओं, व्यक्तियों आदि को अलग करना हो वहाँ अल्प विराम (,) चिन्ह का प्रयोग किया जाता है।राकेश, मोहन, शीतल और पंकज ने यह चित्र बनाया है।
प्रश्नवाचक चिन्ह (?)बातचीत के दौरान जब किसी से कोई बात पूछी जाती है अथवा कोई प्रश्न पूछा जाता है, तब वाक्य के अंत में प्रश्नसूचक-चिन्ह का प्रयोग किया जाता है।तुम्हारी माताजी का नाम क्या है ?
विस्मयादिबोधक चिन्ह (!)इसका प्रयोग हर्ष, विवाद, विस्मय, घृणा, आश्रर्य, करुणा, भय, संबोधन इत्यादि का बोध कराने के लिए इस चिन्ह का प्रयोग किया जाता है।वाह! कितना सुंदर दृश्य है।
लाघव चिन्ह (०)किसी बड़े तथा प्रसिद्ध शब्द को संक्षेप में लिखने के लिए उस शब्द का पहला अक्षर लिखकर उसके आगे शून्य (०) लगा देते हैं। यह शून्य ही लाघव-चिन्ह कहलाता है।डॉक्टर – डॉ०, प्रोफेसर – प्रो०

Question 89

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

कसाई के खूँटे से बाँधना -

  1. AOption (a)

    भारी विपत्ति या मुसीबत पड़ना

  2. BOption (b)

    निर्दयी या क्रूर मनुष्य के हाथों में देना

  3. COption (c)

    बेरहम व्यक्ति पर विश्वास न करे

  4. DOption (d)

    सुख-संतोष मिलना

View answer & explanation

Correct answer

Answer: (b)B.

निर्दयी या क्रूर मनुष्य के हाथों में देना

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'निर्दयी या क्रूर मनुष्य के हाथों में देना' है।

Key Points

  • कसाई के खूँटे से बाँधना  मुहावरे का अर्थ है - 'निर्दयी या क्रूर मनुष्य के हाथों में देना' l
  • वाक्य प्रयोग:- मुझे मालूम नहीं था कि मैं बेटी का उससे ब्याह नहीं कर रहा हूँ बल्कि उसे कसाई के खूँटे से बाँध रहा हूँ।
  • दिए गए अन्य विकल्पों का विश्लेषण इस प्रकार है:- 
  • पहाड़ टूट पड़ना मुहावरे का अर्थ है - भारी विपत्ति आना 
  • वाक्य प्रयोग:-  राम जी के वनवास जाते ही सब पर दुःख का पहाड़ सा टूट पड़ा।
  • कलेजा ठंडा पड़ना मुहावरे का अर्थ है - सुख-संतोष मिलना l
  • वाक्य प्रयोग:-  जब से सुरेश ने अपनी कक्षा में प्रथम आने वाले विद्यार्थियों से ज्यादा अंक पाए हैं, तब से उसके कलेजे में ठंडक पड़ गई है l​

Additional Information ​     अन्य प्रचलित मुहावरे और उनके अर्थ:-

  • अंधेर नगरी – कोई नियम कानून न होना।
  • वाक्य प्रयोग– क्या अंधेर नगरी है ! इतनी अधिक महंगाई है।
  • आँखें चार करना– आमना–सामना करना,मुलाकात होना। 
  • वाक्य प्रयोग- एक दिन अचानक मेरी आँखें चार मेरे पुराने मित्र से हो गई।
  • अंग-अंग ढीला होना - थक जाना। 
  • वाक्य प्रयोग- शादी समारोह में कार्य इतना था की शीला का अंग अंग ढीला होने लगा।

Question 90

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

जो दूर की बात पहले से न सोचे -

  1. AOption (a)

    असीम

  2. BOption (b)

    अदूरदर्शी

  3. COption (c)

    दिग्दर्शक

  4. DOption (d)

    दूरदर्शी

View answer & explanation

Correct answer

Answer: (b)B.

अदूरदर्शी

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'अदूरदर्शी' है।

Key Points

  • 'जो दूर की बात पहले से न सोचे' के लिए एक शब्द ‘अदूरदर्शी’ होगा।
  • अदूरदर्शी का पर्यायवाची- विवेकशून्य , विचारशून्य,अल्पदृष्टि, अविचारी,स्थूलबुद्धि, अनग्रसोची आदि।

 Important Pointsअन्य विकल्प:

  • असीम - जिसकी सीमा न हो
  • दिग्दर्शक - दिशा ज्ञान करानेवाला।
  • दूरदर्शी  - दूर की बात सोचनेवाला

Additional Information 

  • वाक्यांश के लिए एक शब्द- भाषा को सुंदर, आकर्षक और प्रभावशाली बनाने के लिए अनेक शब्दों के स्थान पर एक शब्द का प्रयोग किया जाता है तो वह वाक्यांश के लिए एक शब्द कहलाता है।

Question 91

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

चील के घोंसले में मांस कहाँ

  1. AOption (a)

    जाति स्वभाव में परिवर्तन नहीं होता

  2. BOption (b)

    हर तरह से लाभ चाहना

  3. COption (c)

    किसी व्यक्ति से ऐसी वस्तु प्राप्त करने की आशा करना, जो उसके पास न हो।

  4. DOption (d)

    अच्छी चीज और वह भी बहुतायत में

View answer & explanation

Correct answer

Answer: (c)C.

किसी व्यक्ति से ऐसी वस्तु प्राप्त करने की आशा करना, जो उसके पास न हो।

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'किसी व्यक्ति से ऐसी वस्तु प्राप्त करने की आशा करना, जो उसके पास न हो।' है।​

Key Points

  • लोकोक्ति- चील के घोसले में माँस कहाँ, अर्थ- किसी व्यक्ति से ऐसी वस्तु प्राप्त करने की आशा करना, जो उसके पास न हो।
  • वाक्य- मैंने सोचा था कि राजू के घर लड्डू खाने को मिलेंगे, पर चील के घोंसले में मांस कहाँ से मिलता।

अन्य विकल्प -

  • लोकोक्ति-  ​दोनों हाथों में लड्डू होना, अर्थ- हर तरह से लाभ चाहना।
  • वाक्य - जबसे अजय ने नया व्यवसाय शुरू किया तबसे उसके  दोनों हाथों में लड्डू हैं।
  • लोकोक्ति - चपड़ी और दो - दो अर्थ - अच्छी चीज और वह भी बहुतायत में
  • वाक्य - उसकी नौकरी लग गई वो भी उसके ही शहर में । यही तो है चुपड़ी और दो - दो ।

Additional Information 

लोकोक्ति परिभाषाउदाहरण
किसी विशेष स्थान पर प्रसिद्ध हो जाने वाले कथन को 'लोकोक्ति' कहते हैं। जब कोई पूरा कथन किसी प्रसंग विशेष में उद्धत किया जाता है तो लोकोक्ति कहलाता है। इसी को कहावत कहते है।- अकेला चना भाड़ नहीं फोड़ता: अर्थात एक व्यक्ति के करने से कोई कठिन काम पूरा नहीं होता - वाक्य- उस दिन बात-ही-बात में राम ने कहा, हाँ, मैं अकेला ही कुँआ खोद लूँगा। इन पर सबों ने हँसकर कहा, व्यर्थ बकबक करते हो, अकेला चना भाड़ नहीं फोड़ता’ ।

Question 92

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

  1. AOption (a)

    खंडन

  2. BOption (b)

    काजू

  3. COption (c)

    एहसान

  4. DOption (d)

    तमन्ना

View answer & explanation

Correct answer

Answer: (a)A.

खंडन

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'खंडन' है।​

Key Points

  • खंडन विदेशी शब्द नहीं है ।
  • खंडन संस्कृत शब्द हैं ।

अन्य विकल्प:

  • काजू - पुर्तगाली शब्द हैं ।
  • एहसान - फारसी शब्द हैं ।
  • तमन्ना - अरबी शब्द हैं ।

Additional Information 

  • विदेशी शब्द-  अरबी, फारसी, अंग्रजी या अन्य किसी भी दुसरे देश की भाषा के शब्द जिनका हिन्दी भाषा में प्रयोग कर लिया जाता है उन्हें विदेशी शब्द कहते हैं।
  • इन विदेशी भाषाओं में मुख्यतः अरबी, फारसी, तुर्की, अंग्रेजी व पुर्तगाली शामिल है।
  • पुर्तगाली शब्द:-आलपीन, आलमारी, बाल्टी, चाबी, फीता, तम्बाकू, आया, इस्पात, इस्तिरी, कमीज, कनस्टर, कमरा, काजू, गमला।
  • फारसी शब्द:-  जंग, जहर, जोर, जबर, जिन्दगी, जादू, जागीर, जान, जुरमाना, जिगर, जोश, तरकश,  तमाशा, तेज, तीर, तबाह, तनख्वाह, ताजा, दीवार, देहात, दस्तूर, दुकान, दरबार, दंगल, दिल, दिलेर, दरबार, दवा, नाव, नामर्द, नापसन्द।
  • तुर्की शब्द:- उर्दू, मुग़ल, आका, काबू, कालीन, कैंची, कुली, कुर्की, चेचक, चमचा, तोप, तमगा, तलाश, बेगम, बहादुर, लाश।
  • अरबी शब्द:- अदा, अजब, अजीब, अमीर, अक्ल, असर, अल्ला, आसार, आखिर, आदत, आदमी, इनाम, इज्जत, ईमारत, इस्तीफ़ा।
  • अंग्रेजी शब्द:- अफसर, इंजन, डॉक्टर, लालटेन, सिलेट, अस्पताल, टिकस, कप्तान, थेटर/ठेठर, तारपीन, बोतल, मील, अपील, आर्डर।
  • चीनी भाषा से आए विदेशी शब्द:- चाय, चीनी, चीकू, लीची।
  • जापानी भाषा से आए विदेशी शब्द:- रिक्‍शा, सायोनारा, झप्‍पान, सु

Question 93

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

  1. AOption (a)

    कमअक्ल

  2. BOption (b)

    अजर

  3. COption (c)

    दुर्बल

  4. DOption (d)

    दौलतमंद

View answer & explanation

Correct answer

Answer: (d)D.

दौलतमंद

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'दौलतमंद' है।​

Key Points

  • दौलतमंद का अर्थ - धनवान होता हैं ।
  • दौलतमंद शब्द में 'मंद' प्रत्यय हैं ।
  • प्रत्यय : किसी शब्द के अंत में लगकर उसके अर्थ में भेद लाने वाले शब्दों को प्रत्यय कहते हैं। 
  • उदहारण: 
  • इक- सप्ताह + इक = साप्ताहिक
  • अक- लेख+अक = लेखक

अन्य विकल्प:- 

  • कमअक्ल शब्द में कम उपसर्ग लगा हैं । जिसका अर्थ होता हैं - थोड़ा
  • अजर शब्द में अ उपसर्ग लगा हैं । जिसका अर्थ होता है - कभी भी न नष्ट होने वाला ।
  • दुर्बल शब्द मे दुर् उपसर्ग लगा हैं । जिसका अर्थ होता हैं - कठिन/बुरा/विपरीत ।

Additional Information उपसर्ग: 

परिभाषाशब्दउपसर्गअन्य उदाहरण
·वह शब्दांश या अव्यय, जो किसी शब्द के आरंभ में जुड़कर मूल शब्द के अर्थ में विशेषता ला दे या उसका अर्थ ही बदल दे।निकायनि + कायजैसे – अ + छूता = अछूता, कु + चैला = कुचैला इत्यादि।

Question 94

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

राम अभी आया है और मोहन भी अभी गया है।

  1. AOption (a)

    संदिग्ध वर्तमान काल

  2. BOption (b)

    सामान्य भविष्यत्काल

  3. COption (c)

    सामान्य भूतकाल

  4. DOption (d)

    आसन्न भूतकाल

View answer & explanation

Correct answer

Answer: (d)D.

आसन्न भूतकाल

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'आसन्न भूतकाल' है।

Key Points

  • राम अभी आया है और मोहन भी अभी गया है। - आसन्न भूत काल
  • आसन्न भूतकाल :- क्रिया के जिस रूप से कार्य व्यापार की निकट समय में समाप्ति का पता चले उसे आसन्न भूतकाल कहते हैं, जैसे :- मैं अभी हिसार से आया हूँ।

अन्य विकल्प :- 

  • संदिग्ध वर्तमान काल :- क्रिया के जिस रूप से वर्तमान काल क्रिया के होने या करने पर शक हो, उसे संदिग्ध वर्तमान काल कहते है।
  • जिन वाक्यों के अंत में ता होगा, ती होगी, ते होंगे आदि आते हैं, उसे संदिग्ध वर्तमान काल कहते हैं।

जैसे- माँ खाना बना रही होगी।

  • सामान्य भविष्यत् काल:-   भविष्य में होने वाली क्रिया के सामान्य रूप को सामान्य भविष्यत् काल  कहते हैं। जैसे- मैं खेलूँगा।
  • सामान्य भूतकाल:- क्रिया के जिस रूप से काम के सामान्य रूप से बीते समय में पूरा होने का बोध हो, उसे सामान्य भूतकाल कहते हैं। जैसे- मोहन आया।

Additional Information

शब्दपरिभाषाउदाहरण
कालकाल का अर्थ होता है – समय। क्रिया के जिस रूप से कार्य के होने के समय का पता चले उसे काल कहते हैं। अथार्त कार्य – व्यापार के समय और उसकी पूर्ण और अपूर्ण अवस्था के ज्ञान के रूपांतरण को काल कहते हैं। काल के तीन भेद हैं-(i) सुनील गीता पढ़ता है।
(ii) प्रदीप पढ़ रहा है।
भूतकाल - जिस क्रिया से कार्य के समाप्त होने का पता चले उसे भूतकाल कहते हैं। इसकी पहचान वाक्यों के अंत में था , थे , थी आदि से होती है। जैसे - रमेश पटना गया था।
वर्तमान काल  - जिन वाक्यों के अंत में ता , ती , ते , है , हैं आते हैं वो वर्तमान काल कहलाता है। क्रियाओं के होने की निरन्तरता को वर्तमान काल कहते हैं।जैसे :- राम अभी-अभी आया है।
भविष्य काल - क्रिया के जिस रूप से क्रिया के आने वाले समय में पूरा होने का पता चले उसे भविष्य काल कहते हैं। इससे आगे आने वाले समय का पता चलता है। जिन वाक्यों के अंत में गा , गे , गी आदि आते हैं वे भविष्य काल होते हैं। जैसे :- मैं कल विद्यालय जाउँगा।

Question 95

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

अकुल-आकुल

  1. AOption (a)

    बिना अंदाज ,अभिप्राय

  2. BOption (b)

    पर्वत ,संग्रह

  3. COption (c)

    आज, बहुत ज्यादा

  4. DOption (d)

    बिना कुल के, व्याकुल

View answer & explanation

Correct answer

Answer: (d)D.

बिना कुल के, व्याकुल

Why this answer is correct

दिए गए सभी विकल्पों में सही उत्तर 'बिना कुल के, व्याकुल' है।

Key Points

  • अकुल- बिना कुल के,
  • आकुल -व्याकुल
  • शब्द -युग्म​:-  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 शब्द -युग्म या भिन्नार्थक शब्द कहते हैं।

 Additional Information

कुछ शब्द - युग्म:-

  • कुल-कूल = वंश - किनारा
  • कर्म-क्रम = काम - सिलसिला
  • कपि-कपी = बंदर - घिरनी
  • कोष-कोश = खजाना - शब्द-संग्रह
  • गिरी-गिरि = गिरना - पर्वत
  • चिर-चीर = पुराना - कपड़ा

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

मानव की दो मूल प्रवृत्तियां होती हैं। एक तो यह कि लोग हमारे गुणों की क़द्र करें, हमें दाद दें और हमारा आदर करें और दूसरे वे हम पर प्रेम करें, हमारा अभाव महसूस करें, उनके जीवन में हम कुछ महत्त्व रखते हैं- ऐसा अनुभव करें। आपके ज़रा से कार्य की यदि किसी ने सच्चे दिल से प्रशंसा की या कोई आपकी सलाह माँगनेआता है तो आपका दिल कैसा खिल उठता है? ऊपर से कोई बड़ा आदमी कितना भी आत्मविश्वासी और आत्मसंतुष्ट क्यों ना दिखाई दे, भीतर से वह हमारी-आपकी तरह प्रशंसा का, प्रोत्साहन का, स्नेह का भूखा है। यदि आप उसे, प्रमानिकतापूर्वक ले सकें तो आप फ़ौरन उसके ह्रदय के निकट पहुँच जायेंगे। दूसरों की भावनाओं को ठीक-ठाक समझना, उनकी क़द्र करना, उनके साथ सच्चाई और स्नेह का व्यवहार करना यही व्यवहारकुशलता है। इसी से सामाजिक जीवन में लोकप्रियता के दरवाजे खोलने की कुंजी हाथ लगती है। इससे हमारी अपनी सुख-शांति बढती है।

Question 96

Based on Passage: View directions & passage

अनुच्छेद के अनुसार मनुष्य का मन प्रसन्नता से कब भर उठता है ?

  1. AOption (a)

    जब दूसरे लोग उसकी प्रशंसा करते है, या उसकी राय मांगते है

  2. BOption (b)

    जब वह दूसरों की मदद करता है

  3. COption (c)

    जब हम दूसरों की क़द्र या तारीफ़ करते है

  4. DOption (d)

    जब हम अपने जीवन में किसी का अभाव महसूस करते है

View answer & explanation

Correct answer

Answer: (a)A.

जब दूसरे लोग उसकी प्रशंसा करते है, या उसकी राय मांगते है

Why this answer is correct

अनुच्छेद के अनुसार मनुष्य का मन प्रसन्नता से भर उठता है - जब दूसरे लोग उसकी प्रशंसा करते है, या उसकी राय मांगते है

  • अनुच्छेद के अनुसार:-
  • ​हमें दाद दें और हमारा आदर करें और दूसरे वे हम पर प्रेम करें, हमारा अभाव महसूस करें,
  • उनके जीवन में हम कुछ महत्त्व रखते हैं- ऐसा अनुभव करें।
  • आपके ज़रा से कार्य की यदि किसी ने सच्चे दिल से प्रशंसा की या कोई आपकी सलाह माँगने आता है तो आपका दिल कैसा खिल उठता है?

Key Points

  • प्रशंसा- तारीफ़, बड़ाई, गुणों का बखान।

Additional Informationअभाव:-

  • अर्थ: अस्तित्व में न होने की अवस्था, असत।

महसूस:-

  • अर्थ: जिसका अनुभव किया जाए।

क़द्र:-

  • अर्थ: गुण की परख, आदर।

Question 97

Based on Passage: View directions & passage

बड़े से बड़ा आदमी भी किस चीज़ का भूखा होता है?

  1. AOption (a)

    स्नेह एवं प्रोत्साहन का

  2. BOption (b)

    अथाह संपत्ति का

  3. COption (c)

    दूसरों को प्रोत्साहित करने का

  4. DOption (d)

    अच्छे स्वदिष्ट भोजन का

View answer & explanation

Correct answer

Answer: (a)A.

स्नेह एवं प्रोत्साहन का

Why this answer is correct

बड़े से बड़ा आदमी भी स्नेह एवं प्रोत्साहन का भूखा होता है।

  • अनुच्छेद के अनुसार:-
  • ऊपर से कोई बड़ा आदमी कितना भी आत्मविश्वासी और आत्मसंतुष्ट क्यों ना दिखाई दे,
  • ​भीतर से वह हमारी-आपकी तरह प्रशंसा का, प्रोत्साहन का, स्नेह का भूखा है।
  • यदि आप उसे, प्रमानिकतापूर्वक ले सकें तो आप फ़ौरन उसके ह्रदय के निकट पहुँच जायेंगे।

Key Points

  • स्नेह- प्रेम भाव, प्रेम, मुहब्बत।
  • प्रोत्साहन- उत्साह बढ़ाने की क्रिया या भाव, हिम्मत बँधाना।

Additional Informationअथाह:-

  • अर्थ: जिसकी थाह न ली जा सके या जिसकी गहराई न नापी जा सके।

संपत्ति:-

  • अर्थ: धन दौलत, जायदाद।

स्वदिष्ट:-

  • अर्थ: अत्यंत जायकेदार, बहुत स्वादवाला।

Question 98

Based on Passage: View directions & passage

व्यवहार कुशलता का क्या अर्थ है?

  1. AOption (a)

    दूसरों की भावना ओं को समझकर उसके प्रतिकूल व्यवहार करना

  2. BOption (b)

    दूसरों की भावनाओं को समझकर सच्चाई और स्नेह का व्यवहार करना

  3. COption (c)

    अपनी आवश्यकता एवं रुचि के अनुसार कार्य करना

  4. DOption (d)

    दूसरों को समझना एवं अपनी परेशानी बताना

View answer & explanation

Correct answer

Answer: (b)B.

दूसरों की भावनाओं को समझकर सच्चाई और स्नेह का व्यवहार करना

Why this answer is correct

व्यवहार कुशलता का अर्थ है- दूसरों की भावनाओं को समझकर सच्चाई और स्नेह का व्यवहार करना

  • अनुच्छेद के अनुसार:-
  • दूसरों की भावनाओं को ठीक-ठाक समझना, उनकी क़द्र करना,
  • उनके साथ सच्चाई और स्नेह का व्यवहार करना यही व्यवहारकुशलता है।
  • इसी से सामाजिक जीवन में लोकप्रियता के दरवाजे खोलने की कुंजी हाथ लगती है। ​

Key Points

  • स्नेह- प्रेम भाव, प्रेम, मुहब्बत।

Additional Informationप्रतिकूल:-

  • अर्थ: विरुद्ध पक्ष का अवलंबन करनेवाला।

रुचि:-

  • अर्थ: चाह, इच्छा, अभिलाषा, कामना, पसंद, प्रेम, दिलचस्पी।

परेशानी:-

  • अर्थ: परेशान होने की अवस्था या भाव, व्याकुलता, उद्विग्नता, हैरानी।

Question 99

Based on Passage: View directions & passage

इनमें से कौन-सा 'अभाव' का विलोम शब्द है?

  1. AOption (a)

    प्रचुरता

  2. BOption (b)

    व्यापक

  3. COption (c)

    आहार

  4. DOption (d)

    कमी

View answer & explanation

Correct answer

Answer: (a)A.

प्रचुरता

Why this answer is correct

इनमें से 'अभाव' का विलोम शब्द है- प्रचुरता

  • अभाव- अस्तित्व में न होने की अवस्था, असत।
  • प्रचुरता- अत्यधिक होने की अवस्था या भाव।

Key Pointsव्यापक:-

  • अर्थ: चारों ओर फैला हुआ, छाया हुआ।
  • विलोम शब्द - 'संकुचित'
  • अर्थ: ​सिकुड़ा हुआ

आहार:-

  • अर्थ: वह पदार्थ जो खाया गया हो, भोजन।
  • विलोम शब्द - 'निराहार'
  • अर्थ: ​जिसने भोजन नहीं किया।

कमी:-

  • अर्थ: कम होना, अल्पता।
  • विलोम शब्द - 'बेसी'
  • अर्थ: अधिकता, ज़्यादती।​

Additional Informationकुछ अन्य महत्वपूर्ण विलोम शब्द:- 

  • शब्द - विलोम
  • उन्नत - अवनत
  • आदर - अनादर
  • अतिवृष्टि - अनावृष्टि
  • अभिज्ञ - अनभिज्ञ
  • सदोष - अदोष
  • दीर्घायु - अल्पायु
  • पुरातन - अधुनातन
  • बहुज्ञ - अल्पज्ञ
  • अनभ्यस्त - अभ्यस्त
  • कनिष्ठ - वरिष्ठ
  • उदात्त - अनुदात्त
  • उन्नति - अवनति

Question 100

Based on Passage: View directions & passage

अनुच्छेद के लिए उचित शीर्षक दीजिये |

  1. AOption (a)

    मनुष्य की चाह

  2. BOption (b)

    मानव की प्रवृत्तियां 

  3. COption (c)

    जीवन की आवश्यकता

  4. DOption (d)

    मानव मन

View answer & explanation

Correct answer

Answer: (b)B.

मानव की प्रवृत्तियां 

Why this answer is correct

अनुच्छेद के लिए उचित शीर्षक है- मानव की प्रवृत्तियां

  • अनुच्छेद के अनुसार-
  • लेखक ने ​मानव की प्रवृत्तियों का उल्लेख करते हुआ उनके व्यवहार की चर्चा किया है।

Key Points 

  • प्रवृत्ति- सांसारिक भोगों या विषयों के प्रति आसक्ति।

Additional Informationचाह:-

  • अर्थ: इच्छा, आकांक्षा, अभिलाषा, कामना, ईप्सा, मनोरथ, वांछा।

मनुष्य:-

  • अर्थ: इंसान, आदमी, नर, मानव, मानुष, मनुज।

Discipline 1 (20 questions)

Question 101

Which is the example of level surface - 

  1. AOption (a)

    isothermal surface

  2. BOption (b)

    curved surface 

  3. COption (c)

    hyperbolic surface

  4. DOption (d)

    plane surface

View answer & explanation

Correct answer

Answer: (a)A.

isothermal surface

Why this answer is correct

Solution- 

A level surface is the set of points in 3D satisfying 

f(x,y,z)=Cf(x,y,z) = C  for some constant C . is called level surface. 

Here an isothermal surface is level surface. 

Correct Answer is Option 1).

Question 102

A relation is said to be reflexive if ______________. 

  1. AOption (a)

    (a, a) ∉ R, for every A ∈ a

  2. BOption (b)

    (a, b) ∈ R , for every A ∈ a

  3. COption (c)

    (a, a) ∈ R, for every a ∈ b

  4. DOption (d)

    (a, a) ∈ R , for every a ∈ A

View answer & explanation

Correct answer

Answer: (d)D.

(a, a) ∈ R , for every a ∈ A

Why this answer is correct

Solution-

A relation is said to be reflexive if 

(a, a) ∈ R, for every a ∈ A. 

Therefore, Correct Option is  (4).

Question 103

For local maxima sign of first derivative changes from______________.

  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

Solution-

If f'(x) changes sign from positive to negative as x increases through point c,

then c is the point of local maxima, and the f(c) is the maximum value.

 If f'(x) changes sign from negative to positive as x increases through point c,

then c is the point of local minima, and the f(c) is the minimum value

Therefore, Correct Option is Option 1).

Question 104

The curve y = x3 - 2x + 5 has______________ at x = 23\sqrt{\frac{2}{3}}

  1. AOption (a)

    Concave up shape

  2. BOption (b)

    Convex down shape

  3. COption (c)

    Convex up shape

  4. DOption (d)

    Concave down shape 

View answer & explanation

Correct answer

Answer: (a)A.

Concave up shape

Why this answer is correct

Concept:

Concavity Test (Second Derivative):

  • Second derivative (yʺ): tells the local shape of a curve.
  • Concave up: if yʺ(x) > 0, the graph opens upward.
  • Concave down: if yʺ(x) < 0, the graph opens downward.
  • Point of inflection: a point where concavity changes (usually where yʺ = 0 with a sign change).
  • Procedure: find y′, then yʺ; evaluate yʺ at the given x.

 

Calculation:

Given: y(x) = x3 − 2x + 5, x = √(2∕3)

y′(x) = 3x2 − 2

⇒ yʺ(x) = 6x

⇒ yʺ(√(2∕3)) = 6 × √(2∕3)

⇒ 6 × √(2∕3) > 0

⇒ concavity at x = √(2∕3) is upward

∴ The curve is concave up at x = √(2∕3).

Question 105

Which is not a property of equivalence relation?

  1. AOption (a)

    reflexive

  2. BOption (b)

    transitive

  3. COption (c)

    associativity

  4. DOption (d)

    symmetric

View answer & explanation

Correct answer

Answer: (c)C.

associativity

Why this answer is correct

Solution- 

Equivalence Relation holds reflexivity, symmetric, transitivity. 

Therefore, Correct  Option is Option 3).

Question 106

The first derivative tells us about ______________.

  1. AOption (a)

    convexity

  2. BOption (b)

    parabolic property 

  3. COption (c)

    slope

  4. DOption (d)

    concavity

View answer & explanation

Correct answer

Answer: (c)C.

slope

Why this answer is correct

Solution-

Given, The curve y = f(x) 

and dydx=f′(x)\frac{dy}{dx} = f'(x)  = slope 

The first derivative tells about slope 

Therefore, Correct Option is Option 3).

Question 107

Which of the following condition is not satisfied by a matrix in row echelon form?

  1. AOption (a)

    the first non zero element in each row , called the leading entry, is 1.

  2. BOption (b)

    rows with all zero elements , if any, are below rows having a zero element. 

  3. COption (c)

    each leading entry is in the column to the right of leading entry in the previous row. 

  4. DOption (d)

    rows with all zero elements , if any are below rows having a non zero element

View answer & explanation

Correct answer

Answer: (b)B.

rows with all zero elements , if any, are below rows having a zero element. 

Why this answer is correct

Solution-

Any row consisting entirely of zeros occurs at the bottom of the matrix.

For each row that does not contain entirely zeros,

the first non-zero entry is 1 (called a leading 1). 

Therefore, Correct Option is Option 2).

Question 108

Number theory, concerned with the properties of 

  1. AOption (a)

    irrational number 

  2. BOption (b)

    both negative

  3. COption (c)

    positive integer 

  4. DOption (d)

    negative integer 

View answer & explanation

Correct answer

Answer: (c)C.

positive integer 

Why this answer is correct

Explanation:

Number theory is a branch of mathematics which concerned with the properties of positive integers.

(3) is correct

Question 109

An element α of a ring is said to be nilpotent if ______________.

  1. AOption (a)

    α = 1 for some n = 0

  2. BOption (b)

    αm = 2 for some m > 1

  3. COption (c)

    αm = 0 for some m > 1

  4. DOption (d)

    αm = 1 for some m > 1

View answer & explanation

Correct answer

Answer: (c)C.

αm = 0 for some m > 1

Why this answer is correct

Explanation:

An element ����

 of a ring ����

 is called nilpotent if there exists some positive integer ����

, called the index (or sometimes the degree), such that ��=0��=0��=0��=0

.

i.e., an element α of a ring is said to be nilpotent if αm = 0 for some m > 1 

(3) is correct

Question 110

If flux entering any element of space is the same as that of leaving it i.e. Div. v = 0 everywhere, then such a vector point function is called -

  1. AOption (a)

    solenoidal

  2. BOption (b)

    curl

  3. COption (c)

    divergence

  4. DOption (d)

    gradient

View answer & explanation

Correct answer

Answer: (a)A.

solenoidal

Why this answer is correct

Solution-

If flux entering any element of space is the same as that of leaving it i.e

. Div. v = 0 everywhere, then such a vector point function is called  solenoidal.

Therefore, Correct Option is Option 1).

Question 111

The matrix is said to be in reduced row echelon form if the leading coefficient in each row is :-

  1. AOption (a)

    any number 

  2. BOption (b)

    zero

  3. COption (c)

    any variable 

  4. DOption (d)

    only non zero number

View answer & explanation

Correct answer

Answer: (d)D.

only non zero number

Why this answer is correct

Solution-

Reduced row echelon form is a type of matrix used to solve systems of linear equations. Reduced row echelon form has four requirements:

  • The first non-zero number in the first row (the leading entry) is the number 1.
  • The second row also starts with the number 1, which is further to the right than the leading entry in the first row. For every subsequent row, the number 1 must be further to the right.
  • The leading entry in each row must be the only non-zero number in its column.
  • Any non-zero rows are placed at the bottom of the matrix.

Therefore, Correct Option is Option 4).

Question 112

The commutative law for any two complex numbers z1 and z2:

  1. AOption (a)

    z1 + z2 = z1 - z2

  2. BOption (b)

    z1 - z2 = z2 + z1

  3. COption (c)

    z1 - z2 = z2 - z1

  4. DOption (d)

    z1 + z2 = z2 + z1

View answer & explanation

Correct answer

Answer: (d)D.

z1 + z2 = z2 + z1

Why this answer is correct

Solution-

Commutative law means ab = ba 

The commutative law for any two complex numbers z1 and z2:  

z1+z2=z2+z1z_1 + z_2 = z_2+z_1

Therefore, Correct Option is Option 4).

Question 113

Which of the following is not a Peanos postulate? 

  1. AOption (a)

    N\mathbb N is empty.

  2. BOption (b)

    Associated with each natural number n there is a unique natural no. n' called the successor of 

  3. COption (c)

    There is a natural no. n that is not the successor of any natural no.

  4. DOption (d)

    The only subset of N\mathbb N that contains x̅ and the successors of all its elements is N\mathbb N itself

View answer & explanation

Correct answer

Answer: (a)A.

N\mathbb N is empty.

Why this answer is correct

Solution- 

The five Peano axioms are:

 

  • Zero is a natural number.
  • Every natural number has a successor in the natural numbers.
  • Zero is not the successor of any natural number.
  • If the successor of two natural numbers is the same, then the two original numbers are the same.
  • If a set contains zero and the successor of every number is in the set, then the set contains the natural numbers.
  1. Therefore, Correct Option is Option 1).

Question 114

Formula for rotation of curve about x-axis is :-

  1. AOption (a)

    V=∫x1x2πy2dx\rm V=\int_{x_1}^{x_2}\pi y^2 dx

  2. BOption (b)

    V=∫x1x2πx2dy\rm V=\int_{x_1}^{x_2}\pi x^2 dy

  3. COption (c)

    V=∫y2y1πx2dy\rm V=\int_{y_2}^{y_1}\pi x^2 dy

  4. DOption (d)

    V = 0 

View answer & explanation

Correct answer

Answer: (a)A.

V=∫x1x2πy2dx\rm V=\int_{x_1}^{x_2}\pi y^2 dx

Why this answer is correct

Solution- 

Formula for rotation of the curve about the x-axis is 

V=∫x1x2πy2dx\rm V=\int_{x_1}^{x_2}\pi y^2 dx 

Therefore, Correct Option is Option 1).

Question 115

Find the volume of solid generated by revolution of the loop at the curve about x-axis :- 3ay2 =x(x - a)2

  1. AOption (a)

    πa3/6

  2. BOption (b)

    πa/6

  3. COption (c)

    πa/36

  4. DOption (d)

    πa336\pi \frac{a^3}{36}

View answer & explanation

Correct answer

Answer: (d)D.

πa336\pi \frac{a^3}{36}

Why this answer is correct

Solution-

Given, 3ay2 =x(x - a)2 

around x-axis so put y = 0 

we get, x = 0 and a 

now, Volume = π∫0ax(x−a)23adx\pi \int_0^a {\frac{x(x-a)^2}{3a}} dx  

so, Volume = πa336\pi \frac{a^3}{36} 

The required Answer is Option (4).

Question 116

Inflection point for f(x) = x4 - 4x3  is :-

  1. AOption (a)

    x = 0

  2. BOption (b)

    x = 6

  3. COption (c)

    ​x = 4

  4. DOption (d)

    ​x = 1

View answer & explanation

Correct answer

Answer: (a)A.

x = 0

Why this answer is correct

Solution- 

Given, f(x) = x4−4x3x^4-4x^3  

put f" (x) = 0 we get inflection point 

f′′(x)=12x2−24xf''(x) = 12x^2- 24x  = 0 

⇒ x2 - 2x = 0 ⇒ x(x-2) = 0

inflection point at x = 0, 2 

Therefore, Correct Option is Option 1).

Question 117

How many types of inflection points are there in first and second derivatives?

  1. AOption (a)

    3

  2. BOption (b)

    2

  3. COption (c)

    5

  4. DOption (d)

    1

View answer & explanation

Correct answer

Answer: (b)B.

2

Why this answer is correct

Solution-  

There are two types of inflection points in the first and second derivatives. One is stationary point of inflection and other is non-stationary point of inflection.

Therefore, Correct Option is Option 2)

Question 118

The reduced row echelon form of every matrix is 

  1. AOption (a)

    infinite

  2. BOption (b)

    0

  3. COption (c)

    unique

  4. DOption (d)

    1

View answer & explanation

Correct answer

Answer: (c)C.

unique

Why this answer is correct

Solution- 

Reduced row echelon form is a type of matrix used to solve systems of linear equations. Reduced row echelon form has four requirements:

  • The first non-zero number in the first row (the leading entry) is the number 1.
  • The second row also starts with the number 1, which is further to the right than the leading entry in the first row. For every subsequent row, the number 1 must be further to the right.
  • The leading entry in each row must be the only non-zero number in its column.
  • Any non-zero rows are placed at the bottom of the matrix.
  • it is unique

Therefore, Correct Option is Option 3).

Question 119

The polynomial equation of n degree has ______ roots. 

  1. AOption (a)

    4

  2. BOption (b)

    1

  3. COption (c)

    n

  4. DOption (d)

    3

View answer & explanation

Correct answer

Answer: (c)C.

n

Why this answer is correct

Concept Used:

The fundamental theorem of algebra states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

Question 120

Let a, b be integer, not both 0, then there are integers u, v such that :-

  1. AOption (a)

    gcd ( b, a ) =ua - vb 

  2. BOption (b)

    gcd (a, b ) = va - ub

  3. COption (c)

    gcd(a, b) = ua + vb 

  4. DOption (d)

    gcd( a, a ) = ua + vb

View answer & explanation

Correct answer

Answer: (c)C.

gcd(a, b) = ua + vb 

Why this answer is correct

Solution- 

Let a, b be integer, not both 0, then there are integers u, v such that  gcd(a,b) = ua +vb

Therefore, Correct Option is Option 3).

Discipline 2 (20 questions)

Question 121

What is the order of the differential equation y' - 4y = x - 3x2 + 4?

  1. AOption (a)

    0

  2. BOption (b)

    2

  3. COption (c)

    1

  4. DOption (d)

    3

View answer & explanation

Correct answer

Answer: (c)C.

1

Why this answer is correct

Concept Used:

The order of a differential equation is defined as the highest derivative that appears in the equation.

Solution:

In the given differential equation y' - 4y = x - 3x2 + 4, the highest derivative that appears is the first derivative of y, which is y'.

Therefore, the order of the differential equation is 1.

Question 122

Solution of the differential equation d2y/dx2 + dy/dx - 2y = ex is -______________.

  1. AOption (a)

    y = e-2x

  2. BOption (b)

    y = ex + x ex/3

  3. COption (c)

    y = c1 e-2x + c2 ex + xex/3

  4. DOption (d)

    y = xex/ 3

View answer & explanation

Correct answer

Answer: (c)C.

y = c1 e-2x + c2 ex + xex/3

Why this answer is correct

Solution- 

Given, differential equation d2y/dx2 + dy/dx - 2y = ex 

Auxiliary equation is m2+m−2=0m^2+m-2 =0    

⇒ m2 + 2m - m - 2 = 0 ⇒ (m + 2)(m - 1) = 0 ⇒ m = 1, -2 

Hence, CF =  c1e−2x+c2exc_1e^{-2x}+c_2e^{x} 

Now, particular solution 

PI = 1D2+D−2(ex)\frac{1}{D^2+D-2} (e^x)

    = x2D+1(ex)\frac{x}{2D+1}(e^x)  (if f(D) = D2 + D - 2, so f(1) = 0, So we find f'(D))

    = xex3\frac{ xe^x}{3} (replacing D by 1)

Hence general solution is

y = CF + PI = c1e−2x+c2exc_1e^{-2x}+c_2e^{x} + xex3\frac{ xe^x}{3}

Therefore, Correct Option is Option 3).

Question 123

let x ∈ R\mathbb R be non-negative. Then x has a unique non-negative square root, denoted √x, which satisfies

  1. AOption (a)

    (√x)3 = x2

  2. BOption (b)

    (√x)2 = 0

  3. COption (c)

    (√x)2 = x

  4. DOption (d)

    x = 0

View answer & explanation

Correct answer

Answer: (c)C.

(√x)2 = x

Why this answer is correct

Solution- 

let x ∈ R\mathbb R be non-negative. Then x has a unique non - negative square root ,

denoted √x , which satisfies (√x)2 = x 

Therefore, Correct Option is Option 3).

Question 124

A differential equation that incorporates both the threshold population T and carrying capacity. 

  1. AOption (a)

    dp ∕ dt = 0

  2. BOption (b)

    dp ∕ dt = r P(1 - P ∕ K) ( 1 - P ∕ T) 

  3. COption (c)

    dt ∕ dp = r(1 - P ∕ K) ( 1 - P ∕ T) 

  4. DOption (d)

    dp ∕ dt = (1 - P ∕ K) (1 + P ∕ T)

View answer & explanation

Correct answer

Answer: (b)B.

dp ∕ dt = r P(1 - P ∕ K) ( 1 - P ∕ T) 

Why this answer is correct

Solution- 

The differential equation that incorporates both the threshold population T and carrying capacity K is 

dPdt=rP(1−PK)(1−PT)\frac{d P}{ d t} = r P (1 − \frac{P}{ K}) (1 − \frac{P}{ T})

where r represents the growth rate.

Therefore, Correct answer is Option 2).

Question 125

Which is not a property of continuous functions on closed and bounded intervals? 

  1. AOption (a)

    non - uniform continuity criteria

  2. BOption (b)

    divergence criteria

  3. COption (c)

    uniform continuity theorem

  4. DOption (d)

    uniform continuity

View answer & explanation

Correct answer

Answer: (b)B.

divergence criteria

Why this answer is correct

Solution- 

The properties of continuous functions on closed and bounded intervals are non-uniform continuity criteria, uniform continuity theorem, uniform continuity. 

Divergence criteria is on a sequence which not relate to continuity 

Therefore, Correct answer is Option 2).

Question 126

Which of the following is the property of limits?

  1. AOption (a)

    closure

  2. BOption (b)

    monotonicity

  3. COption (c)

    commutativity

  4. DOption (d)

    associativity

View answer & explanation

Correct answer

Answer: (b)B.

monotonicity

Why this answer is correct

Solution- 

Closure , associativity, commutativity its all the property of groups 

Monotonicity is property of limits .

Therefore, Correct answer is Option 2).

Question 127

The constant r > 0 in the exponential growth function - p(t)= p0ert-

  1. AOption (a)

    growth rate

  2. BOption (b)

    phase line 

  3. COption (c)

    carrying capacity

  4. DOption (d)

    threshold population

View answer & explanation

Correct answer

Answer: (a)A.

growth rate

Why this answer is correct

Solution- 

The constant r > 0 in the exponential growth function - p(t)= p0ert 

where , r is growth rate . 

Therefore, Correct answer is Option 1).

Question 128

Every non-empty set that is bounded above has :- 

  1. AOption (a)

    order of supremum 

  2. BOption (b)

    unique least upper bound

  3. COption (c)

    order of infimum

  4. DOption (d)

    order of infimumd

View answer & explanation

Correct answer

Answer: (b)B.

unique least upper bound

Why this answer is correct

Solution:

Every non-empty set that is bounded above has least upper bound.

and it has unique least upper bound.

(2) is correct

Question 129

Sequence whose elements become arbitrary close to each other as the sequence progresses are:-

  1. AOption (a)

    molecule

  2. BOption (b)

    monotone sequence

  3. COption (c)

    direct sequence 

  4. DOption (d)

    cauchy sequence

View answer & explanation

Correct answer

Answer: (d)D.

cauchy sequence

Why this answer is correct

Solution-

sequence of real number say (xn)(x_n) is called a cauchy sequence if for 

every positive real number ϵ\epsilon there is a positive integer n ∈N\in N such 

that for all natural number m,n > N 

∣xm−xn∣<ϵ|x_m-x_n| < \epsilon

Therefore, Correct answer is Option 4).

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xm−xn∣<ϵ

Question 130

Suppose that f(n + 1) exists on an open interval I about x0, and let x be in I. Then the remainder is

  1. AOption (a)

    Rn(x) = f(x) - Tn(x)

  2. BOption (b)

    Rn(x) = f(x)

  3. COption (c)

    Rn(x) = 0

  4. DOption (d)

    Rn(x) = f(x) +Tn(x)

View answer & explanation

Correct answer

Answer: (a)A.

Rn(x) = f(x) - Tn(x)

Why this answer is correct

Solution- 

Suppose that f(n + 1) exists on an open interval I about x0, and let x be in I.

Then the remainder is Rn(x) = f(x) - Tn(x) 

Therefore, Correct Option is Option 1).

Question 131

Solution of differential equation d2y ∕ dx2 - 8 dy ∕ dx +15 y = 0 is -______________.

  1. AOption (a)

    y = e3x - e-3x

  2. BOption (b)

    y = C1 e7x - C1 e6x

  3. COption (c)

    y = C1 e4x - C2 e5x

  4. DOption (d)

    y = C1 e3x + C2 e5x 

View answer & explanation

Correct answer

Answer: (d)D.

y = C1 e3x + C2 e5x 

Why this answer is correct

Concept Used:

for any linear differential equation, if α,β\alpha, \beta are the distinct roots of the ancillary equation, then y=C1eαx+C2eβxy=C_1 e^{\alpha x}+C_2 e^{\beta x} in the solution of differential equation. 

Calculation:

d2y ∕ dx2 - 8 dy ∕ dx +15 y = 0

⇒ r2−8r+15=0r^2-8 r+15=0 is auxiliary equation.

⇒ r2 - 5r - 3r + 15 = 0 

⇒ r(r - 5) - 3(r - 5) = 0 

⇒(r - 5)(r - 3) = 0 

⇒ r = 3, 5 

y=C1e3x+C2e5xy=C_1 e^{3x}+C_2 e^{5 x} is the solution of the given differential equation.

Question 132

Differential equation describing exponential growth is :-

  1. AOption (a)

    (dN ∕ dt) = N

  2. BOption (b)

    dt ∕ dN = rN

  3. COption (c)

    dN ∕ dt = r

  4. DOption (d)

    dN ∕dt = rN

View answer & explanation

Correct answer

Answer: (d)D.

dN ∕dt = rN

Why this answer is correct

Solution-  

Differential equation describing exponential growth is 

dNdt=rN\frac{dN}{dt} = rN

Therefore, Correct Option is Option 4).

Question 133

Every bounded sequence of real numbers has a convergent subsequence.

  1. AOption (a)

    mean value theorem

  2. BOption (b)

    Taylor's theorem

  3. COption (c)

    Bolzano - Weierstrass theorem 

  4. DOption (d)

    theorem of continuity 

View answer & explanation

Correct answer

Answer: (c)C.

Bolzano - Weierstrass theorem 

Why this answer is correct

Solution- 

Bolzano - Weierstrass Theorem-  The theorem states that each infinite bounded sequence in ������

 has a convergent subsequence.

An equivalent formulation is that a subset of ������

 is sequentially compact if and only if it is closed and bounded. 

Therefore, Correct Option is Option 3).

Question 134

Bernoulli equation has the form -______________.

  1. AOption (a)

    y' = a(t) y + b(t) yn

  2. BOption (b)

    y' = a (t) y - b (t) 

  3. COption (c)

    y' = b(t) y -a (t) yn

  4. DOption (d)

    y' = b (t) y

View answer & explanation

Correct answer

Answer: (a)A.

y' = a(t) y + b(t) yn

Why this answer is correct

Explanation -

Differential equations in the form, y′ + p(x)y = q(x)yn

where p(x) and q(x) are continuous functions on the interval and n is a real number. Differential equations in this form are called Bernoulli Equations.

 

So, y' = a(t) y + b(t) yn is Bernoulli equation.

 

Hence, The Correct Option is 1.

Question 135

An alternating series will converge if the terms an converge to _____ monotonically.

  1. AOption (a)

    infinity

  2. BOption (b)

    1

  3. COption (c)

    0

  4. DOption (d)

    -1

View answer & explanation

Correct answer

Answer: (c)C.

0

Why this answer is correct

Solution- 

An alternating series ∑ an will converge if the terms an  converge to 0 (zero) monotonically.

i.e, If a1, a2, a3, . . . is a sequence of positive numbers monotonically decreasing to 0,

then the series a1 − a2 + a3 − a4 + a5 − a6 + . . . converges. 

Therefore, Correct Option is Option 3).

Question 136

If the limit of the summand is undefined or non zero, the series must:- 

  1. AOption (a)

    first diverges then converges

  2. BOption (b)

    converge

  3. COption (c)

    remains constant

  4. DOption (d)

    diverge

View answer & explanation

Correct answer

Answer: (d)D.

diverge

Why this answer is correct

Solution- 

If a series is convergent then its sum must be finite and if it is divergent then its sum is infinite. 

Therefore, Correct Option is Option 4).

Question 137

The golden ratio is :-  

  1. AOption (a)

    ϕ =1 / ϕ 

  2. BOption (b)

    ϕ - 1 = 1 / ϕ 

  3. COption (c)

    ϕ + 2 = ϕ / 2

  4. DOption (d)

    ϕ + 1 =1 / ϕ

View answer & explanation

Correct answer

Answer: (b)B.

ϕ - 1 = 1 / ϕ 

Why this answer is correct

Solution- 

The golden ratio is ϕ−1=1ϕ\phi - 1 = \frac{1}{\phi} 

Therefore, Correct answer is option 2).

Question 138

Solution of differential equation y' + 3y = 6x + 11 is :- 

  1. AOption (a)

    y = e-3x

  2. BOption (b)

    y = e3x + 2x + 3

  3. COption (c)

    y = 2x -3

  4. DOption (d)

    y = e-3x + 2x + 3

View answer & explanation

Correct answer

Answer: (d)D.

y = e-3x + 2x + 3

Why this answer is correct

Concept Used: 

dydx+yP(x)=Q(x)\frac{d y}{d x}+y P(x)=Q(x) is the linear Differential equation in y, and It's solution is

y⋅I.F.=∫I.F.⋅Q(x)dxy \cdot I.F.=\int I.F. \cdot Q(x) d x

where I.F. =e∫P(x)dx=e^{\int P(x) d x}

Calculation:

for  y' + 3y = 6x + 11

P(x) = 3 and Q(x) = 6 x+11

⇒ I.F. =e∫3dx=e3x=e^{\int 3 d x}=e^{3 x}

Hence, the Solution is

ye3x=∫e3x(6x+11)dx y e^{3 x}=\int e^{3 x}(6 x+11) d x  ⇒ ye3x=6∫xe3xdx+11∫e3xdx y e^{3 x}=6 \int x e^{3 x} d x+11 \int e^{3 x} d x

⇒ ye3x=6(xe3x3−e3x9)+11e3x3+c y e^{3 x}=6\left(x \frac{e^{3 x}}{3}-\frac{e^{3 x}}{9}\right)+\frac{11 e^{3 x}}{3}+c  ⇒ ye3x=(2x−23+113)e3x+c y e^{3 x}=\left(2 x-\frac{2}{3}+\frac{11}{3}\right) e^{3 x}+c

⇒ y=2x+3+Ce−3x y=2 x+3+Ce^{-3 x}

where, C is the arbitrary constant,

Hence, only option(4) is the only possible answer.

Question 139

If we have a sequence ynn=1∞{y_n}^∞_{n = 1}, it means for the sequence to have a limit 1 as n tends to infinity. It can be written as ___________.

  1. AOption (a)

    yn → 1 as n → 0

  2. BOption (b)

    yn → n as n → 0

  3. COption (c)

    yn → 1 as n → ∞

  4. DOption (d)

    y1 → n as n → 1

View answer & explanation

Correct answer

Answer: (c)C.

yn → 1 as n → ∞

Why this answer is correct

solution- 

we have a sequence ynn=1∞{y_n}^∞_{n = 1}

If ynn=1∞{y_n}^∞_{n = 1} tends to 1 as n tends to infinity then yn → 1 as n → ∞ 

Therefore, Correct answer is Option 3).

Question 140

The particular solution to the differential equation y' = 2x passing through (2, 7) is ______________. 

  1. AOption (a)

    y = x2 + 2

  2. BOption (b)

    y = 0 

  3. COption (c)

    y = x2 + 1

  4. DOption (d)

    y = x2 + 3

View answer & explanation

Correct answer

Answer: (d)D.

y = x2 + 3

Why this answer is correct

Solution:

y' = 2x

Integrate both sides of the differential equation to get:

⇒ y = ∫ 2x dx ⇒ y = x2 + C , where C is a constant of integration.

Next, we use points (2, 7) to find the value of C. 

⇒ 7 = 22 + C ⇒ C = 7 - 4 = 3

So the particular solution is:

⇒ y = x2 + 3

Therefore the particular solution is y = x2 + 3.

Discipline 3 (20 questions)

Question 141

A vector field in Rn is a function :-

  1. AOption (a)

    F vector → 0

  2. BOption (b)

    F vector → Rn : Rn

  3. COption (c)

    F vector → Rn

  4. DOption (d)

    F vector : Rn → Rn

View answer & explanation

Correct answer

Answer: (d)D.

F vector : Rn → Rn

Why this answer is correct

Solution- 

A vector field in Rn is a function f: Rn→RnR^n \rightarrow R^n 

F vector : Rn → Rn 

Therefore, Correct Option is Option 4).

Question 142

Functions which are either increasing or decreasing in their domain are said to be ______________.

  1. AOption (a)

    non- monotonic 

  2. BOption (b)

    monotonic

  3. COption (c)

    maxima

  4. DOption (d)

    minima

View answer & explanation

Correct answer

Answer: (b)B.

monotonic

Why this answer is correct

Solution-

Functions which are increasing in their domain are said to be monotonicially increasing. 

Functions which are decreasing in their domain are said to be monotonically decreasing 

Functions which are either increasing or decreasing in their domain are said to be monotonic.

 

When both hold we say it's monotonic.

 

Therefore, Correct Option is Option 2).

Question 143

Which of the following is not the property of vector field?

  1. AOption (a)

    radial field

  2. BOption (b)

    electrical field

  3. COption (c)

    gradient field

  4. DOption (d)

    rotational field

View answer & explanation

Correct answer

Answer: (b)B.

electrical field

Why this answer is correct

Solution-

The radial field, gradient field, rotational field are the properties of vector field. 

The electrical field is not a property of vector field 

Therefore, Correct Option is Option 2).

Question 144

A function f(x) is said to be continuous at a point x = c if the following condition hold true:

  1. AOption (a)

    f(x) ≠ 0

  2. BOption (b)

    f(x) is defined at x = c 

  3. COption (c)

    f(x) ≠ f (c) 

  4. DOption (d)

    x = c

View answer & explanation

Correct answer

Answer: (b)B.

f(x) is defined at x = c 

Why this answer is correct

Concept Used:

 a function is continuous at a point if the function has a defined value at that point and the value of the function at that point is equal to the limit of the function as x approaches that point.

i.e., lim⁡x→cf(x)=f(c)\lim_{x\to c}{f(x)} = f(c)

Hence, the function needs to be defined at that point.

Question 145

Evaluate lim⁡x→0x3cot⁡x1−cos⁡x \lim _{x → 0} \frac{x^3 \cot x }{ 1 - \cos x}.

  1. AOption (a)

    1

  2. BOption (b)

    5

  3. COption (c)

    3

  4. DOption (d)

    2

View answer & explanation

Correct answer

Answer: (d)D.

2

Why this answer is correct

Solution- 

lim⁡x→0x3cot⁡x1−cos⁡x \lim _{x → 0} \frac{x^3 \cot x }{ 1 - \cos x}

= lim⁡x→0x3tan⁡x.2sin⁡2x2 \lim _{x → 0} \frac{x^3 }{\tan x .2\sin^2\frac x2}

= lim⁡x→02tan⁡xx.(sin⁡x2x2)2 \lim _{x → 0} \frac{2 }{\frac{\tan x}{x} .\left(\frac{\sin\frac x2}{\frac x2}\right)^2}  = 2

∵  lim⁡x→0tan⁡xx \lim _{x→ 0} \frac{\tan x }{x}  = 1 and lim⁡θ→0sin⁡θθ \lim _{\theta → 0} \frac{\sin \theta }{\theta}  = 1

Hence, The Correct option is 4

Question 146

Taylor's theorem is not used to study the properties of ______________.

  1. AOption (a)

    evaluating definite integral

  2. BOption (b)

    understanding the growth of functions

  3. COption (c)

    on solving quadratic eqn.

  4. DOption (d)

    understanding asymptotic behaviour

View answer & explanation

Correct answer

Answer: (c)C.

on solving quadratic eqn.

Why this answer is correct

Solution- 

Taylor's theorem is used to study evaluating definite integral,  understanding the growth of functions, and understanding asymptotic behaviour.

Therefore, Correct answer is Option 3).

Question 147

Which is not the property of Riemann integral?

  1. AOption (a)

    additivity

  2. BOption (b)

    Linearity

  3. COption (c)

    Associativity

  4. DOption (d)

    monotonicity

View answer & explanation

Correct answer

Answer: (c)C.

Associativity

Why this answer is correct

Solution-

Riemann integral is the property of additivity , linearity, 

monotonicity . whereas associativity is property of group .

Therefore, Correct Option is Option 3).

Question 148

The triple integral of a function f(x) over a three dimensional solid w is written as ______________. 

  1. AOption (a)

    ∫w f.dv 

  2. BOption (b)

    ∫∫∫_w f. dv

  3. COption (c)

    ∫∫∫f.dv 

  4. DOption (d)

    ∫∫f.dv

View answer & explanation

Correct answer

Answer: (b)B.

∫∫∫_w f. dv

Why this answer is correct

Explanations:

The triple integral of a function f(x, y, z) over a three-dimensional solid W is written as:

∫∫∫_W f(x, y, z) dV

Where dV = dx dy dz is a differential volume element in xyz-coordinates, and the integral sign ∫∫∫_W represents integration over the region W. This integration computes the volume-weighted sum of f(x, y, z) over the entire region W.

Hence, The Correct Answer is ∫∫∫_w f. dv

Question 149

The surface integral of a vector field A over a closed surface is equal to the volume integral of the divergence of a vector field A over the volume (v) enclosed by the closed surface, is ______________. 

  1. AOption (a)

    Green's theorem

  2. BOption (b)

    Gauss's theorem

  3. COption (c)

    Taylor's theorem

  4. DOption (d)

    Stoke's theorem 

View answer & explanation

Correct answer

Answer: (b)B.

Gauss's theorem

Why this answer is correct

Concept Used:

Gauss's theorem, also known as the divergence theorem, is a statement in vector calculus that relates the flux of a vector field through a closed surface to the volume density of the vector field's divergence.

Formally, Gauss's theorem states that for a vector field F and a closed surface S that encloses a volume V:

∬SFdS=∭Vdiv⁡(F)dV\iint_S F dS = \iiint_V\operatorname{div}(F) dV

where F dS is the flux of the vector field F through the surface S, div(F) is the divergence of the vector field F, and dV is an infinitesimal volume element.

Hence, the given statement is for Gauss's theorem.

Question 150

Suppose that f(x) has a derivative on the interval (a, b) , is continuous on the interval [a, b] then at some value cє (a, b).

F'(c) =[f(b) - f(a)]/(b - a)

  1. AOption (a)

    Mean value theorem

  2. BOption (b)

    Rolle's theorem 

  3. COption (c)

    Taylor's theorem

  4. DOption (d)

    Newton's theorem

View answer & explanation

Correct answer

Answer: (a)A.

Mean value theorem

Why this answer is correct

Concept Used:

The mean value theorem is a statement in calculus that states that for any function that is continuous on a closed interval, there exists at least one value in the interval at which the function's average rate of change is equal to its instantaneous rate of change at that point.

In other words, for a function f(x) that is continuous on the interval [a, b] and differentiable in (a, b ), there exists at least one value, c, such that:

f'(c) = (f(b) - f(a)) / (b - a)

where f'(c) is the derivative of f(x) evaluated at the point c, and (f(b) - f(a)) / (b - a) is the average rate of change of f(x) over the interval [a, b].

Question 151

If z = x4 e3y. Find dz.

  1. AOption (a)

    dz = 4x3e3y dx + 3x4e3y dy

  2. BOption (b)

    dz = 3x4e3ydy

  3. COption (c)

    dz = 4x³e3ydy - 3x4e3ydy

  4. DOption (d)

    dz = 4x3e3y dx

View answer & explanation

Correct answer

Answer: (a)A.

dz = 4x3e3y dx + 3x4e3y dy

Why this answer is correct

Concept Used:

For any z = f(x, y) 

dz=∂z∂xdx+∂z∂ydy \mathrm{d} z=\frac{∂ \mathrm{z}}{∂ \mathrm{x}} \mathrm{dx}+\frac{∂ \mathrm{z}}{∂ \mathrm{y}} \mathrm{dy}

Solution:

Given,  z = x4 e3y

⇒  ∂z/∂x = 4x3 e3y

⇒ ∂z/∂y = 3x4 e3y

So, the differential of z is given by:

⇒ dz = (4x3 e3y)dx + (3x4 e3y)dy

Question 152

The multivariable chain rule is ______________.

  1. AOption (a)

    df/dx = ( df/dt).( dt/dx) 

  2. BOption (b)

    dx/dt = ( df/dt).( dt/dx )

  3. COption (c)

    df/dx = ( dx/df ).( df/dt ) 

  4. DOption (d)

    dy/df = (df/dt).(dt/dy)

View answer & explanation

Correct answer

Answer: (a)A.

df/dx = ( df/dt).( dt/dx) 

Why this answer is correct

Explanation:

If f is a function of x only, then we revert back to the single-variable chain rule:

df/dx = df/dt × dt/dx

In this scenario, f depends on x indirectly through an intermediate variable t.

This expression is saying the derivative of f with respect to x is equal to the derivative of f with respect to t multiplied by the derivative of t with respect to x.

Question 153

Green's theorem relates a double integral over a region to a ______________. 

  1. AOption (a)

    indefinite integral

  2. BOption (b)

    surface integral

  3. COption (c)

    volume integral

  4. DOption (d)

    line integral 

View answer & explanation

Correct answer

Answer: (d)D.

line integral 

Why this answer is correct

Explanations:

Green's theorem relates a double integral over a region to a line integral around the boundary of the region.

More specifically, it relates a flux double integral to a circulation line integral, or a circulation double integral to a flux line integral.

This is a fundamental theorem in vector calculus and serves as a higher-dimensional version of the Fundamental Theorem of Calculus for line integrals in the plane.

Question 154

Green's theorem says that the total "microscopic circulation" in D is equal to the circulation around the boundary c = dD̅

  1. AOption (a)

    ∫ -F.ds

  2. BOption (b)

    ∫ F.ds 

  3. COption (c)

    F.ds

  4. DOption (d)

    ∫c F.ds

View answer & explanation

Correct answer

Answer: (d)D.

∫c F.ds

Why this answer is correct

Explanation:

Green's theorem states that the circulation form of the double integral over a plane region D is equal to the line integral around the boundary curve C of D (often noted as ∂D). To put it quantitatively:

∫∫_D (curl F) × da = ∮_C F ×  ds

Where:

The left side is a double integral over the region D of the curl of a vector field F dotted with da, the area element. This represents the total "microscopic circulation" in D.

The right side is a line integral around the closed curve C (the boundary of D, ∂D) of F dotted with ds, the line element. This represents the circulation around the boundary C.

Question 155

A continuous function v is said to be negative definite, if ______________.

  1. AOption (a)

    v is negative definite 

  2. BOption (b)

    (-v is negative definite) 

  3. COption (c)

    (-v is positive definite)

  4. DOption (d)

    v is positive definite 

View answer & explanation

Correct answer

Answer: (c)C.

(-v is positive definite)

Why this answer is correct

Explanation:

A function v is said to be negative definite if, for all non-zero vectors x in its domain, the quadratic form v(x) < 0.

Take option 3

if -v is positive definite, then for any non-zero vector x, -v(x) > 0.

By multiplying by -1, we obtain that for all non-zero vectors x, v(x) < 0,

which indicates that v is negative definite.

Thus, the correct statement is (3) (-v is positive definite).

Question 156

Which is not the property of double integrals?

  1. AOption (a)

    linearity

  2. BOption (b)

    area property

  3. COption (c)

    commutativity

  4. DOption (d)

    additivity

View answer & explanation

Correct answer

Answer: (c)C.

commutativity

Why this answer is correct

Solution:

  • Commutativity is not a property of double integrals. Commutativity refers to the property of being able to swap the order of the integration variables without changing the result, but in double integrals, the order of integration does matter, and changing the order of integration can change the result.
  • The other properties you listed, Linearity, Area Property, and Additivity are properties of double integrals.
  • Linearity means that the integral of a sum of functions is equal to the sum of the integrals of the individual functions.
  • The Area Property states that the double integral of a non-negative function over a region represents the area of the region.
  • Additivity means that the integral of a function over a region can be computed by breaking the region into smaller regions and adding up the integrals over the smaller regions.

Question 157

The surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the particular vector function around that surface, is ______________. 

  1. AOption (a)

    Gauss's theorem

  2. BOption (b)

    Green's theorem

  3. COption (c)

    Stoke's theorem 

  4. DOption (d)

    Taylor's theorem

View answer & explanation

Correct answer

Answer: (c)C.

Stoke's theorem 

Why this answer is correct

Concept Used:

Stoke's Theorem relates the surface integral of the curl of a vector field over a closed surface to the line integral of the vector field around the boundary of that surface. More specifically, it states that:

∫curl F dS = ∫F dr

Where F is a vector field, S is a closed surface, and the path integral is taken around the boundary of S.

Hence, the given statement is Stoke's Theorem.

Question 158

A continuous function v : Rn → R is said to bev radially unbounded if ______________.

  1. AOption (a)

    v(0) ≠ 0 

  2. BOption (b)

    v(0) =0

  3. COption (c)

    v(0) = ∞

  4. DOption (d)

    v(0) = 1

View answer & explanation

Correct answer

Answer: (b)B.

v(0) =0

Why this answer is correct

Explanation:

it is common for many functions that are radially unbounded to also satisfy v(0) = 0,

especially in the field of machine learning and optimization, given that many loss/objective functions coincide with this property.

Question 159

The Maclaurin series are used to approximate the ______________.

  1. AOption (a)

    momentum

  2. BOption (b)

    Lorentz factor ϐ

  3. COption (c)

    Lorentz factor ϒ 

  4. DOption (d)

    Lorentz factor α

View answer & explanation

Correct answer

Answer: (c)C.

Lorentz factor ϒ 

Why this answer is correct

Explanation:

 The Lorentz factor γ (gamma) in special relativity can indeed be approximated using a Maclaurin series when v/c is very small.

The Lorentz factor γ is defined as 1/√(1 − v²/c²), wherein it can be difficult to calculate for v close to zero.

Using a Maclaurin series, γ can be approximated as 1 + ½(v/c)² for small values of v/c.

Hence, the answer is option 3: Lorentz factor γ.

Question 160

All of computational science is built on ______________.

  1. AOption (a)

    Taylor's theorem

  2. BOption (b)

    Rolle's theorem 

  3. COption (c)

    remainder theorem

  4. DOption (d)

    mean value theorem

View answer & explanation

Correct answer

Answer: (a)A.

Taylor's theorem

Why this answer is correct

Explanation:

Taylor's theorem is indeed significant in computational science

Taylor's Theorem is often applied in numerical analysis – a branch of mathematics that deals with algorithms for numerical approximation. 

It is extensively used in computational science because it provides a way to approximate complex systems that can't be solved with more straightforward methods.

Discipline 4 (20 questions)

Question 161

A function from one metric space to another f : A → B is continuous at p if for all Є > 0, there exist ∂ > 0 such that ______________. 

  1. AOption (a)

    d(x, p) < ∂

  2. BOption (b)

    d(x, p) = 1

  3. COption (c)

    d(x, p) > ∂ 

  4. DOption (d)

    d(x, p) = 0

View answer & explanation

Correct answer

Answer: (a)A.

d(x, p) < ∂

Why this answer is correct

Explanation:

A function from one metric space to another f: A → B is continuous at p ∈ A if for all Є > 0, there exists ∂ > 0 such that dA(x,p)<∂d_A(x, p) < ∂ implies dB(f(x),f(p))<Єd_B(f(x), f(p)) < Є.

In this case, the distance of x to the point p in A is less than ∂, and the distance of the image of x under f to the image of p under f in B would need to be less than Є.

Question 162

Find the power series representation for the following function g(x) = 1/(1 + x3)

  1. AOption (a)

    g(x)=Σn=1∞(1)nx3n\rm g(x)=\Sigma^{\infty}_{n=1}(1)^nx^{3n}

  2. BOption (b)

    g(x)=Σn=1∞(−1)n\rm g(x)=\Sigma^{\infty}_{n=1}(-1)^n

  3. COption (c)

    g(x) = 0

  4. DOption (d)

    g(x)=Σn=0∞[(−x)3]n\rm g(x)=\Sigma^{\infty}_{n=0}[(-x)^3]^n

View answer & explanation

Correct answer

Answer: (d)D.

g(x)=Σn=0∞[(−x)3]n\rm g(x)=\Sigma^{\infty}_{n=0}[(-x)^3]^n

Why this answer is correct

Concept:

(1 + x)-1 = 1 - x + x2 - x3 + ...

Explanation:

g(x) = 1(1+x3)1\over (1 + x^3) = (1+x3)−1(1+x^3)^{-1}

⇒ g(x) = 1−x3+(x3)2−(x3)3+...1-x^3+(x^3)^2-(x^3)^3+... 

⇒ g(x)=Σn=0∞[(−x)3]n\rm g(x)=\Sigma^{\infty}_{n=0}[(-x)^3]^n

(4) is correct

Question 163

A function f : A → B is continuous if and only if ______________.

  1. AOption (a)

    f(G) is closed if G is closed

  2. BOption (b)

    G is closed then f(G) is closed

  3. COption (c)

    G is open in B then f-1(G) is open in A

  4. DOption (d)

    G = 0 

View answer & explanation

Correct answer

Answer: (c)C.

G is open in B then f-1(G) is open in A

Why this answer is correct

Explanation:

A function f : A → B is continuous if and only if the inverse image of open set is open

i.e., if G is an open set in B then f-1(G) is open in A

(3) is correct

Question 164

Which topology is called the metric topology induced by d?

  1. AOption (a)

    {B(x, Є|XЄx, Є > 0}

  2. BOption (b)

    {Bd(x, ∈)|x ∈ X, ∈ > 0}

  3. COption (c)

    {(xd, ∈) | x, ∈ > 0}

  4. DOption (d)

    {(xd, ∈) x, ∈ > 0}

View answer & explanation

Correct answer

Answer: (b)B.

{Bd(x, ∈)|x ∈ X, ∈ > 0}

Why this answer is correct

Explanation:

{Bd(x, ∈) | x ∈ X, ∈ > 0} :

The notation Bd(x, ∈) typically accommodates the "ball" in a given space X centred at "x" and of radius "∈". It indicates all points whose distance to x is less than ∈

According to the metric "d". The collection of all these balls for all points x in X and all real numbers ∈ > 0 forms the basis for the metric topology induced by the metric "d".

The definition of the basis for the metric topology induced by a metric d on set X is: { B_d(x, ε) | x ∈ X, ε > 0 } where B_d(x, ε) = { y ∈ X | d(x, y) < ε } , the open ball centered at x with radius ε.

Question 165

Find the value of improper integral  ∫ e-x dx  upper limit as ∞ and lower limit as 0

  1. AOption (a)

    0

  2. BOption (b)

    -1

  3. COption (c)

    1

  4. DOption (d)

    2

View answer & explanation

Correct answer

Answer: (c)C.

1

Why this answer is correct

Calculation:

The value of improper integral  ∫ e-x dx  upper limit as ∞ and lower limit as 0  

⇒  ∫0∞e−xdx=[−e−x]0∞=−e−∞+e0=0+(1)=1 ∫_0^{\infty} e^{-x} dx =[-e^{-x} ]_0^{\infty}= -e^{-∞} + {e^0} = 0 + (1) = 1

Hence, The Correct Answer is option 3.

Question 166

If a finite subcover of S is contained in each open cover of any set S, then S is called ______________. 

  1. AOption (a)

    compact set 

  2. BOption (b)

    finite set 

  3. COption (c)

    equivalent set

  4. DOption (d)

    empty set 

View answer & explanation

Correct answer

Answer: (a)A.

compact set 

Why this answer is correct

Explanation:

Compact set: A set is compact if every open cover of the space has a finite subcover.

Finite set: A set is called a finite set if it has finite number of elements.

Equivalent set: equivalent sets are sets that contain the same number of elements, although the elements themselves may be different.

Empty set: A set is called an empty set if it has no element.

Hence If a finite subcover of S is contained in each open cover of any set S, then S is called compact set

(1) is correct

Question 167

Every open cover of a closed and bounded subset S of real numbers contains a finite subcover of S, i.e., every closed and bounded subset of R\mathbb R is compact, is known as ______________.

  1. AOption (a)

    De Moivre's theorem

  2. BOption (b)

    Fundamental theorem 

  3. COption (c)

    Heine - burel theorem 

  4. DOption (d)

    Four squares theorem

View answer & explanation

Correct answer

Answer: (c)C.

Heine - burel theorem 

Why this answer is correct

Explanation:

Heine - burel theorem: every closed and bounded subset of R\mathbb R is compact i.e., Every open cover of a closed and bounded subset S of real numbers contains a finite subcover of S.

(3) is correct

Question 168

If there is at least one geodesic path between every pair of points in x. Then (x , d) is called ______________. 

  1. AOption (a)

    geodesic space

  2. BOption (b)

    Brownian bridge

  3. COption (c)

    path length

  4. DOption (d)

    geodesic segment

View answer & explanation

Correct answer

Answer: (a)A.

geodesic space

Why this answer is correct

Explanation -

If there is at least one geodesic path between every pair of points in a metric space (X, d), then (X, d) is called a geodesic metric space, or geodesic space.

A "geodesic" is the shortest path between two points in a space that respects the metric of the space. For example, on a flat plane, the geodesic path between two points is a straight line, while on a sphere (like the surface of the Earth), the geodesic path is a great circle path.

Hence option (1) is correct.

Question 169

Let X = R² and d : X × x → R is defined by d [ (x1, x2) (y1, y2) ]1/2. Then points inside the circle centred at ______________.

  1. AOption (a)

    (1, 1)

  2. BOption (b)

    (2, 0)

  3. COption (c)

    (1, 0)

  4. DOption (d)

    (0, 0)

View answer & explanation

Correct answer

Answer: (d)D.

(0, 0)

Why this answer is correct

Explanation:

The standard Euclidean metric, which measures the distance from the origin to the points in the plane. In that case, a circle centered at the origin contains all the points that are a certain distance (the radius of the circle) or less from the origin (0, 0)

Question 170

A sequence of functions is a sequence with functions as elements. fn : D → R is defined on set ______________.

  1. AOption (a)

    D ⊆ R 

  2. BOption (b)

    R ⊂ D 

  3. COption (c)

    D ⊂ R

  4. DOption (d)

    D ∩ R

View answer & explanation

Correct answer

Answer: (a)A.

D ⊆ R 

Why this answer is correct

Explanation:

A sequence of functions is a sequence with functions as elements. fn : D → R is defined on set D ⊆ R 

(1) is correct

Question 171

The bounded function f : (a, b) → R is Riemann integrable if and only if for every Є > 0 there exist a partition P [a, b] which may depend on Є , such that ______________. 

  1. AOption (a)

    u(f;P) > L(f;P) 

  2. BOption (b)

    u(f;p) - L(f;P ) < Є

  3. COption (c)

    u(f;P) - L(f;P) = 0 

  4. DOption (d)

    u(f;P) - L(f;P) > Є

View answer & explanation

Correct answer

Answer: (b)B.

u(f;p) - L(f;P ) < Є

Why this answer is correct

Explanation:

The correct answer is: u(f;P) - L(f;P ) < Є

This is a statement of the Riemann condition for integrability. For a bounded function f over the interval [a, b] to be Riemann integrable, it must be the case that for any ε > 0, there exists a partition P of [a, b] such that the difference between the upper sum (u(f;P)) and lower sum (L(f;P)) is less than ε.

The lower sum is the sum of areas of inscribed rectangles under the curve of the function, and the upper sum is the sum of areas of circumscribed rectangles over the curve. The function is Riemann integrable if and only if we can make these two sums arbitrarily close to each other, i.e., if the difference can be made less than any positive number ε.

Question 172

Let W ⊂ c be a domain and suppose {fn} is a sequence of analytic functions on W to f, then f is analytic on ______________. 

  1. AOption (a)

    fn

  2. BOption (b)

    c and W 

  3. COption (c)

    c

  4. DOption (d)

    W

View answer & explanation

Correct answer

Answer: (d)D.

W

Why this answer is correct

Explanation:

If {fn} is a sequence of analytic (or holomorphic) functions on the domain W that converges to a function f, then according to the theory of complex analysis, the limit function f will also be analytic on W.

Alternate Method

The set of analytic functions on a given domain is closed under the limit operation, assuming uniform convergence on compact sets.

Question 173

Suppose a closed interval [a, b] Є R . The partition of this interval is said to be a sequence of the following form: 

  1. AOption (a)

    a = x0 + x1 + x2 ------- xn

  2. BOption (b)

    a = x0 > x2 > ---------- xn

  3. COption (c)

    a = x0 < x1 < x2 < ------- xn

  4. DOption (d)

    a = x0 - x1 + ---------- xn

View answer & explanation

Correct answer

Answer: (c)C.

a = x0 < x1 < x2 < ------- xn

Why this answer is correct

Explanation:

A partition of an interval [a, b] in real numbers is a finite sequence of numbers that starts at 'a' and ends at 'b' where each subsequent number is greater than the previous one. Hence, the correct choice as per your question would be:

a = x0 < x1 < x2 < ------- xn <= b

Here, x0, x1, x2, ..., xn are points in the interval [a, b] with x0 = a and xn = b. Each xi for 1 <= i <= n - 1 divides the interval into smaller subintervals.

Question 174

Let X be a topological space. Which of the following condition does not hold?

  1. AOption (a)

    finite unions of closed sets are closed. 

  2. BOption (b)

    ϕ and X are closed

  3. COption (c)

    finite unions of closed sets are not closed.

  4. DOption (d)

    arbitrary intersections of closed sets are closed. 

View answer & explanation

Correct answer

Answer: (c)C.

finite unions of closed sets are not closed.

Why this answer is correct

Explanation:

X is said to be a topological space if it satisfies the following properties

(i) ϕ and X are closed  

(ii) finite unions of closed sets are closed

(iii) arbitrary intersections of closed sets are closed. 

Hence (3) does not hold

Question 175

Which property is not satisfied by metric space?

  1. AOption (a)

    non - negativeness

  2. BOption (b)

    symmetry

  3. COption (c)

    monotonicity

  4. DOption (d)

    identification

View answer & explanation

Correct answer

Answer: (c)C.

monotonicity

Why this answer is correct

Explanation -

Metric spaces satisfy several properties These properties include:

The distance between any point and itself is zero. (d(x,x) = 0)

The distance between two distinct points is always greater than zero. (If x ≠ y, then d(x,y) > 0)

The distance from point x to point y is the same as the distance from point y to point x. (d(x,y) = d(y,x))

The triangle inequality is satisfied. (d(x,z) ≤ d(x,y) + d(y,z) for any points x, y, z)

The concept of monotonicity isn't inherently part of its basic structure. 

So, monotonicity is not inherently a property satisfied or not satisfied by a metric space.

Hence option (iii) is correct.

Question 176

Which of the following condition is correct for a mapping f : G → G is called automorphism of G is ______________.

  1. AOption (a)

    f(a, b) = f(b)

  2. BOption (b)

    f is a bijection

  3. COption (c)

    f(b, a) = f(a)

  4. DOption (d)

    f(a, b) = 0 

View answer & explanation

Correct answer

Answer: (b)B.

f is a bijection

Why this answer is correct

Explanation:

The correct condition for a mapping f: G → G to be an automorphism of G is: f is a bijection

More than just being a bijection, an automorphism of a group is a bijective map f: G → G that preserves the group operation, meaning, for any elements a, b, in G, we have f(ab)=f(a).f(b)f(ab) = f(a).f(b)

So, while "f is a bijection" is a necessary condition for f to be an automorphism

Question 177

If either limit of a definite integral is infinite or if the integrand is infinite anywhere inside the range of integration , the integral is said to be ______________. 

  1. AOption (a)

    lower Riemann integral

  2. BOption (b)

    proper integral 

  3. COption (c)

    improper integral

  4. DOption (d)

    upper Riemann integral

View answer & explanation

Correct answer

Answer: (c)C.

improper integral

Why this answer is correct

Explanation:

Improper integral: An improper integral is one of two types of definite integrals, where either the interval of integration is unbounded (one or both limits are infinite)

The integrand function has one or more singularities in the range of integration.

Question 178

Every continuous real - valued function on each closed bounded interval is ______________.

  1. AOption (a)

    lower Riemann integral

  2. BOption (b)

    upper Riemann integral 

  3. COption (c)

    Riemann sums

  4. DOption (d)

    Riemann integrable 

View answer & explanation

Correct answer

Answer: (d)D.

Riemann integrable 

Why this answer is correct

Explanation:

Every continuous real-valued function on each closed bounded interval is Riemann integrable.

So, the answer is Riemann integrable

Question 179

A function f : A → B between two metric spaces is uniformly continuous on A if for all Є > 0 there exist ∂:

  1. AOption (a)

    d(x, y) = 0

  2. BOption (b)

    d(x, y) > ∂

  3. COption (c)

    d(x, y) < ∂ 

  4. DOption (d)

    d(x, y) = ∂

View answer & explanation

Correct answer

Answer: (c)C.

d(x, y) < ∂ 

Why this answer is correct

Explanation -

A function f : A → B between two metric spaces is uniformly continuous on A if for all ε > 0 there exists δ > 0 such that for all x, y in A, if the distance between x and y is less than δ [ d(x, y) < δ ]  (i.e., if ρ(x, y) < δ where ρ is the metric on A) then the distance between f(x) and f(y) is less than ε (i.e., τ(f(x), f(y)) < ε, where τ is the metric on B).

Uniform continuity is a stronger condition than continuity. It means that the function behaves in a similar manner throughout the space A, and not just at individual points.

Hence option (iii) is correct.

Question 180

A series of functions of form Σ an (x - c)n is called a ______________.

  1. AOption (a)

    Weierstrass criterion

  2. BOption (b)

    uniform convergence

  3. COption (c)

    alternating series 

  4. DOption (d)

    power series

View answer & explanation

Correct answer

Answer: (d)D.

power series

Why this answer is correct

Explanation:

A series of functions of a particular form, typically of the form Σ an (x - c)n

(where "Σ" indicates a summation over n, an are the coefficients of the series, x is the variable, c is a constant, and n is a non-negative integer running from 0 to infinity), is called a power series.

Discipline 5 (10 questions)

Question 181

Which is not the property of external direct product ?

  1. AOption (a)

    (a , b) ЄG1 × G2

  2. BOption (b)

    (e, e') is identity element of G1 * G2

  3. COption (c)

    (a, b)∉( G1 × G2)

  4. DOption (d)

    |G1 × G2| = | G1|.|G2|

View answer & explanation

Correct answer

Answer: (c)C.

(a, b)∉( G1 × G2)

Why this answer is correct

Explanation:

The tuple (a , b) belongs to the external direct product of G1 and G2, signifying that a is an element of G1 and b is an element of G2.

Identity Element: The tuple (e, e') is the identity element of G1 × G2 which implies e is the identity element of G1 and e' is the identity element of G2. That is, for any (a,b) in G1 × G2, (a,b)(e,e') = (a,b) and (e,e')(a,b) = (a,b).

Non-Membership: The tuple (a, b) is not an element of G1 × G2. It seems contradictory to point 1 above, Hence, Option 3 is incorrect

Order of the Group: The order (or size) of the group formed by the direct product G1 × G2 is the product of the orders (or sizes) of G1 and G2.

That is, if G1 has |G1| elements and G2 has |G2| elements, then G1 × G2 has |G1|.|G2| elements.

Question 182

Every finite group G can be embedded in a symmetric group is ______________. 

  1. AOption (a)

    Gauss divergence theorem

  2. BOption (b)

    Taylor's theorem 

  3. COption (c)

    Cayley theorem

  4. DOption (d)

    Green's theorem

View answer & explanation

Correct answer

Answer: (c)C.

Cayley theorem

Why this answer is correct

Explanation:

Cayley's theorem states that every group G (finite or not) is isomorphic to a subgroup of the symmetric group acting on G

.In other words, every group can be embedded in a symmetric group.

Question 183

Let G be a finite group and G has only two normal subgroups {e} and G itself then it is a ______________. 

  1. AOption (a)

    normal P- subgroup

  2. BOption (b)

    P - group

  3. COption (c)

    simple group 

  4. DOption (d)

    sylow P- subgroup

View answer & explanation

Correct answer

Answer: (c)C.

simple group 

Why this answer is correct

Explanation:

G is a simple group.

A simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.

By this definition, if G has only two normal subgroups {e} (the trivial group containing only the identity element) and G itself, then G is a simple group

Question 184

Which of the following is not the property of continuous function if f(z) and g(z) are continuous on a region A, then ______________.

  1. AOption (a)

    f(z) g(z) is continuous on A. 

  2. BOption (b)

    f(z) ∕g(z) is continuous on A except at points where g(z) = 0 

  3. COption (c)

    f(z) - g(z) is continuous on A .

  4. DOption (d)

    f(z) + g(z) is continuous on A . 

View answer & explanation

Correct answer

Answer: (c)C.

f(z) - g(z) is continuous on A .

Why this answer is correct

Calculation:

f(z) = z, which is a continuous function (identity function), and g(z) = |z|, which is also a continuous function (absolute value function).

However, the function h(z) = z - |z|, h(0) = 1 is not a continuous function at z = 0

This is because for z < 0, h(z) = 2z, but for z > 0, h(z) = 0.

At z = 0, the function h(z) "jumps" from 0 to 0, the left-hand limit and the right-hand limit at z = 0 not being the same, 

so the function is not continuous at z = 0.

Hence, Option 3 is correct.

Question 185

Let G be a finite group and P be a prime factor of |G|. Then some element of G has order P is ______________. 

  1. AOption (a)

    Green's theorem

  2. BOption (b)

    Cayley theorem

  3. COption (c)

    Cauchy theorem

  4. DOption (d)

    Taylor's theorem

View answer & explanation

Correct answer

Answer: (c)C.

Cauchy theorem

Why this answer is correct

Explanations:

"Let G be a finite group and P be a prime factor of |G|. Then there is an element of order P in G."

So, The Correct Answer is: Cauchy's Theorem.

Question 186

In a group G , the mapping f : G → G , defined by f(x) = x-1 for every XєG is an automorphism if G is ______________.

  1. AOption (a)

    alternating

  2. BOption (b)

    abelian

  3. COption (c)

    sporadic

  4. DOption (d)

    cyclic

View answer & explanation

Correct answer

Answer: (b)B.

abelian

Why this answer is correct

Explanation:

The map f : G → G defined by f(x) = x⁻¹ (where x⁻¹ denotes the inverse of x in the group G), is an automorphism if G is an Abelian group.

Here's why: An automorphism is a bijective map from a group to itself that preserves the group structure.

If G is an Abelian group, then for any elements a, b in G we have ab = ba, or equivalently, (ab)⁻¹ = a⁻¹b⁻¹.

Our map f preserves the group operation under this condition: f(ab) = (ab)⁻¹ = b⁻¹a⁻¹ = f(a)f(b) for all a, b in G, since in an Abelian group, b⁻¹a⁻¹ = a⁻¹b⁻¹.

Therefore, the correct answer is: Abelian

Question 187

Let G be a finite group of order n = pkm, where p is a prime and p does not divide m. A subgroup H of order pk is called______________.

  1. AOption (a)

    P - group 

  2. BOption (b)

    sylow P - subgroup

  3. COption (c)

    normal subgroup

  4. DOption (d)

    simple subgroup 

View answer & explanation

Correct answer

Answer: (b)B.

sylow P - subgroup

Why this answer is correct

Explanation:

A subgroup H of a finite group G, having order pk, is called a Sylow p-subgroup.

Sylow theorem stated:

"If G is a finite group with |G| = pk m, where p is a prime number, p does not divide m, then G contains a subgroup of order pk, which is a Sylow p-subgroup."

So the correct answer is: Sylow p-subgroup.

Question 188

Which statement is not correct when H acts on G by left multiplication?

  1. AOption (a)

    there are no fixed points ( if H ≠ G).

  2. BOption (b)

    staba = { h :ha = a } = {e} is trivial. 

  3. COption (c)

    the orbits are the right H - cosets.

  4. DOption (d)

    there are no fixed points {if [H] > 1} 

View answer & explanation

Correct answer

Answer: (a)A.

there are no fixed points ( if H ≠ G).

Why this answer is correct

Explanation:

There are no fixed points (if H ≠ G).

In the context of group actions,

a fixed point is an element that is left unchanged by the action of any group element. If H acts on G by left multiplication, there may be fixed points under certain conditions.

 For example, if H contains the identity element of G, then the action of the identity element does not change any element of G, so every element of G is a fixed point under the action of the identity.

If G = H, even in this case, every element of G = H acts as a fixed point, because for each g in G = H, we have hg = g for all h in H = G.

Question 189

Which is the correct option for internal direct product? 

  1. AOption (a)

    If G = G1 × G2 then G is an internal direct product of two normal subgroups  G1 and  G2  and Each element of the group G can be uniquely expressed as the product of an element in G1 and an element in G2

  2. BOption (b)

    H1 ⊂ H2

  3. COption (c)

    S3 × Z4

  4. DOption (d)

    K4 × Z3

View answer & explanation

Correct answer

Answer: (a)A.

If G = G1 × G2 then G is an internal direct product of two normal subgroups  G1 and  G2  and Each element of the group G can be uniquely expressed as the product of an element in G1 and an element in G2

Why this answer is correct

Explanations:

Let's consider a group G and two subgroups H and K.

We say that group G is the internal direct product of H and K if the following conditions are met:

Each element of the group G can be uniquely expressed as the product of an element in H and an element in K.

Both H and K are normal subgroups of G.

The intersection of H and K is trivial, i.e., includes only the identity element of G.

Hence, Option 1 is true.

Question 190

If A , B ⊂ X and A × B ≅ X, then we say that X is ______________.

  1. AOption (a)

    an internal direct product 

  2. BOption (b)

    antisymmetric product

  3. COption (c)

    an external direct product

  4. DOption (d)

    cartesian product

View answer & explanation

Correct answer

Answer: (c)C.

an external direct product

Why this answer is correct

Explanation:

when A and B are separate groups themselves (not subgroups of a group X) and the Cartesian product of these groups is isomorphic to X, this is referred to as an "external direct product".

Hence, The Correct option is 3.

Teaching Methodology (10 questions)

Question 191

Why do children tend to imitate and internalise what they see and then repeat those patterns in their own lives? 

  1. AOption (a)

    Because they are strongly influenced by parental generations.

  2. BOption (b)

    Because Children learn vicariously through their observation and imitation of what they see their primary caregivers are doing 

  3. COption (c)

    Because they were taught that certain traits or activities are appropriate or inappropriate for them to engage

  4. DOption (d)

    Because they more likely to take on those roles themselves as adults than are peers whose parents were less stereotyped. 

View answer & explanation

Correct answer

Answer: (b)B.

Because Children learn vicariously through their observation and imitation of what they see their primary caregivers are doing 

Why this answer is correct

Key Points

  • Children are naturally inclined to imitate the people around them, especially their parents and other caregivers. This is because they see their caregivers as role models and want to be like them.
  • Children also learn by observing the consequences of their caregivers' actions. For example, if a child sees their parent being kind and helpful to others, they are more likely to be kind and helpful themselves.
  • This process of vicarious learning is a powerful way for children to learn about the world and how to behave. It is also a key reason why children tend to imitate and internalize what they see in their own lives.

Thus, it is concluded that option 2 is the correct answer.

Question 192

Which learning will collaborative projects on teaching methods promote?

  1. AOption (a)

    Indirect learning

  2. BOption (b)

    Secondary learning

  3. COption (c)

    Direct learning

  4. DOption (d)

    Primary learning

View answer & explanation

Correct answer

Answer: (a)A.

Indirect learning

Why this answer is correct

Collaborative projects on teaching methods can provide students with opportunities to learn indirectly in a number of ways. For example, students can learn from each other by observing and discussing their different teaching methods. They can also learn from their own experiences of teaching and reflecting on their successes and failures.

Key Points

  • Collaborative projects on teaching methods can promote indirect learning.
  • Indirect learning is a type of learning that occurs through observation, experience, and reflection. It is often contrasted with direct learning, which is a type of learning that occurs through explicit instruction.
  • Here are some specific examples of indirect learning that can occur during collaborative projects on teaching methods:
  • Students can learn about different teaching strategies and philosophies by observing and discussing each other's teaching methods.
  • Students can learn about the importance of planning and preparation by working together to develop and implement their teaching projects.
  • Students can learn about the challenges and rewards of teaching by reflecting on their own experiences of teaching.

Thus, it is concluded that indirect learning is the correct answer.

Question 193

In Language as a school Subject which is not Methodology of teaching ?

  1. AOption (a)

    Form focused

  2. BOption (b)

    Teacher oriented 

  3. COption (c)

    Function oriented

  4. DOption (d)

    Product oriented 

View answer & explanation

Correct answer

Answer: (b)B.

Teacher oriented 

Why this answer is correct

In teaching language as a school subject, different methodologies are applied to develop communication skills and language competence.

  • These methodologies are designed to focus on structure, function, and production of language. However, not every approach qualifies as a recognized methodology of language teaching.

Key PointsIn Language as a school Subject, methodology of teaching includes:

  • Form focused methodology emphasizes grammar rules, sentence structures, and accuracy in usage.
  • Function oriented methodology stresses the communicative purpose of language, enabling learners to use it in real-life contexts.
  • Product oriented methodology focuses on the final outcome of learning, such as essay writing or creating texts, highlighting learners’ ability to produce language effectively.

Hint

  • Teacher oriented is not considered a methodology of language teaching. This is because language learning must remain learner-centered, where students acquire skills through practice, interaction, and usage.
  • A teacher-centered approach limits learners to passive listening and imitation, reducing opportunities for active participation and real language use.

Hence, the approach that is not a methodology of language teaching is teacher oriented.

Question 194

The RTE Act provides for the right of children to free and compulsory education to the children of ____ years age group including children with special needs. 

  1. AOption (a)

    6 to 14

  2. BOption (b)

    3 to 14 

  3. COption (c)

    6 to 18

  4. DOption (d)

    3 to 18

View answer & explanation

Correct answer

Answer: (a)A.

6 to 14

Why this answer is correct

Key Points

  • The RTE Act provides for the right of children to free and compulsory education to the children of 6 to 14 years age group including children with special needs.
  • This means that all children in India have the right to free and compulsory education from the age of 6 to 14, regardless of their caste, creed, religion, or gender.
  • Children with special needs are also included in this provision.
  • The RTE Act is an important piece of legislation that has helped to imove access to education for millions of children in India.
  • It has also helped to reduce the dropout rate and improve the quality of education.

Thus, it is concluded that The RTE Act provides for the right of children to free and compulsory education to the children of 6 to 14 years age group including children with special needs.

Question 195

Effectiveness of teaching has to be judged in terms of ____.

  1. AOption (a)

    Students’ interest 

  2. BOption (b)

    Use of teaching aids in the classroom

  3. COption (c)

    efficiency of the candidate in securing good marks

  4. DOption (d)

    Course coverage

View answer & explanation

Correct answer

Answer: (a)A.

Students’ interest 

Why this answer is correct

The effectiveness of teaching can be judged in terms of multiple factors, and different stakeholders may prioritize different aspects.  

Key Points

  • Students’ interest: This is an important factor in evaluating teaching effectiveness.
  • When students are engaged and interested in the subject matter, they are more likely to learn and retain information.
  • A teacher who can generate interest and curiosity among students is often considered effective.

Thus, it is concluded that Effectiveness of teaching has to be judged in terms of student's interest.

Question 196

_____ involves students providing feedback to other students on the quality of their work.

  1. AOption (a)

    Self-assessment

  2. BOption (b)

    Collaborative assessment

  3. COption (c)

    Peer assessment

  4. DOption (d)

    Group assessment 

View answer & explanation

Correct answer

Answer: (c)C.

Peer assessment

Why this answer is correct

Key Points

  • Peer assessment is a process in which students provide feedback to other students on the quality of their work. It is a collaborative process that can help students to improve their work and to develop their critical thinking skills.
  • Peer assessment can be used in a variety of ways, such as:
  • Students can review and provide feedback on each other's essays, presentations, or projects.
  • Students can work in pairs or small groups to solve problems or complete assignments, and then provide feedback to each other on their individual contributions.
  • Students can use peer assessment rubrics to evaluate each other's work based on specific criteria.

Thus, it is concluded that peer assessment is the correct answer.

 

 

Hint

  • Self-assessment is the process of evaluating one's own work.
  • Collaborative assessment is a type of assessment that involves students working together to complete an assignment or project.
  • Group assessment is a type of assessment that is given to a group of students as a whole.

Question 197

______ is a branch of learning or scholarly investigation that provides a structure for the students’ (program of study,) especially in the graduate and post-graduate levels.

  1. AOption (a)

    Non academic discipline

  2. BOption (b)

    Academic Discipline

  3. COption (c)

    Unitary discipline 

  4. DOption (d)

    Multi discipline 

View answer & explanation

Correct answer

Answer: (b)B.

Academic Discipline

Why this answer is correct

Key Points

  • Academic disciplines are important because they provide a framework for organizing and understanding the vast amount of knowledge that exists in the world. They also help to train students to think critically and solve problems in a systematic way.
  • An academic discipline is a branch of learning or scholarly investigation that provides a structure for the students' (program of study,) especially in the graduate and post-graduate levels. Academic disciplines are typically defined by their own unique sets of theories, methods, and research questions.

Here are some examples of academic disciplines:

  • Humanities: English, history, philosophy, religious studies, etc.
  • Social sciences: anthropology, economics, political science, psychology, sociology, etc.
  • Natural sciences: biology, chemistry, physics, earth science, etc.
  • Formal sciences: mathematics, computer science, logic, etc.
  • Applied sciences: engineering, medicine, agriculture, business, etc.

​Thus, it is concluded that Academic Discipline is the correct answer.

Question 198

Some boys and girls are born with a condition called congenital adrenal hyperplasia (CAH),which cause them which of the following? 

  1. AOption (a)

    to care less about their physical appearance than the others

  2. BOption (b)

    to have significantly higher levels of androgens than their non-affected peers

  3. COption (c)

    to strongly influence girls to behave as though they were boys or vice versa. 

  4. DOption (d)

    to avoid having girl or boy playmates; do not play games revolving around stereotypical feminine events 

View answer & explanation

Correct answer

Answer: (b)B.

to have significantly higher levels of androgens than their non-affected peers

Why this answer is correct

CAH is a group of genetic disorders that affect the adrenal glands. The adrenal glands are responsible for producing a variety of hormones, including cortisol, aldosterone, and androgens. Androgens are male sex hormones that are also present in females, but at lower levels.

Key Points

  • In people with CAH, the adrenal glands do not produce enough cortisol or aldosterone, and they produce too much androgens. This can lead to a variety of health problems, including ambiguous genitalia in newborns, early puberty, and fertility problems.

The other options are not accurate descriptions of CAH.

  • to care less about their physical appearance than the others
  • to avoid having girl or boy playmates; do not play games revolving around stereotypical feminine events are not specific to CAH and could apply to anyone.
  • to strongly influence girls to behave as though they were boys or vice versa is a harmful and outdated stereotype. There is no evidence that CAH causes people to change their gender identity.

Thus, option 2 is the correct answer.

Question 199

Which knowledge is dependent on experience or empirical evidence, as with most aspects of science and personal knowledge? 

  1. AOption (a)

    Priori Knowledge 

  2. BOption (b)

    Communicating knowledge

  3. COption (c)

    Practitioner knowledge

  4. DOption (d)

    Posteriori Knowledge

View answer & explanation

Correct answer

Answer: (d)D.

Posteriori Knowledge

Why this answer is correct

Key Points

  • Posteriori knowledge is knowledge that is gained through experience or empirical evidence. It is the type of knowledge that is most commonly associated with science. For example, the statement "water boils at 100 degrees Celsius at sea level" is a piece of posteriori knowledge. It is based on the results of repeated experiments.
  • Priori knowledge, communicating knowledge, and practitioner knowledge are all types of knowledge that can be acquired without direct experience.
  • Priori knowledge is knowledge that is gained through reason and deduction, rather than experience. It is often thought of as being self-evident or true by definition. For example, the statement "all bachelors are unmarried" is a piece of a priori knowledge.
  • Communicating knowledge is the process of sharing knowledge with others. It can be done through a variety of means, such as writing, speaking, or teaching.
  • Practitioner knowledge is the knowledge that is gained through practice and experience in a particular field. It is often tacit, meaning that it is difficult to articulate or explain. For example, a skilled surgeon has a deep understanding of human anatomy and physiology, as well as the skills necessary to perform complex operations. However, this knowledge is largely tacit and difficult to teach to others.

 Thus it is concluded that Posteriori knowledge is dependent on experience or empirical evidence, as with most aspects of science and personal knowledge.

Question 200

In a classroom, translanguaging may not involve which of the following ?

  1. AOption (a)

    translation between languages 

  2. BOption (b)

    using school language compulsorily in whole part of the activity 

  3. COption (c)

    mixing words and expressions from different languages in the same spoken or written utterance

  4. DOption (d)

    comparing and being playful with different languages 

View answer & explanation

Correct answer

Answer: (b)B.

using school language compulsorily in whole part of the activity 

Why this answer is correct

Translanguaging is an approach to language learning and teaching that encourages the flexible and strategic use of multiple languages in the classroom.

Key Points

  • Translanguaging allows for a fluid and dynamic language practice that incorporates elements from different languages.
  • It includes activities like translation between languages, mixing words and expressions from different languages in the same spoken or written utterance, and comparing and being playful with different languages.
  • These practices support language development and cultural understanding among students.

Hint

  • Using the school language compulsorily in the whole part of the activity, does not align with the principles of translanguaging.
  • Translanguaging encourages the use of multiple languages, and it recognizes the value and richness of students' linguistic backgrounds.
  • It does not impose restrictions on the use of specific languages but rather embraces the diversity of languages present in the classroom.

Hence, in a classroom, translanguaging may not involve using school language compulsorily in whole part of the activity.

200 questions in the full paper