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

- AOption (a)

- BOption (b)

- COption (c)

- DOption (d)

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





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

C and G
G and I
I, D, C and B
C and D
Correct answer
C and G
Why this answer is correct
As per the given information,
The shaded part i.e. 'C and G' represents →mammals that are human or female but not male
Hence, the correct answer is "C and G".
Find the wrong term in the given series.
111, 100, 87, 71, 55, 36
71
36
87
55
Correct answer
71
Why this answer is correct
Given: 111, 100, 87, 71, 55, 36
The logic follows here is:
The next term in the series is obtained by subtracting consecutive odd numbers starting from 11.
Thus, the wrong term in the series is '71'.
Hence, the correct answer is "71".
The following are the criteria for the selection of a management trainee.
to candidate -
a - Graduation in any subject with a minimum of 72% marks.
b - Age should not be less than 21 years and not more than 25 years.
c - Must have passed written examination and interview with minimum 70% marks.
d - Be prepared to pay a deposit of Rs 50,000 which is to be refunded on completion of the training.
However, if all the above criteria are satisfied, except –
I- As in (a) above, but have completed post-graduation with a minimum of 65% marks, the case will be referred to the Director.
II -In (d) above, but has experience of working in this area for more than one year, may be referred to Case Manager.
Sumit has done BBA from a government college with 74% marks and his marks in written tests and interviews are 75%. He is 25 years old and has 2 years of experience in this field. He is not willing to pay the deposit amount of Rs 50,000.
The candidate has been selected.
The candidate is referred to the Director.
The candidate has not been selected.
The candidate has been referred to the manager.
Correct answer
The candidate has been referred to the manager.
Why this answer is correct
As per the given information,
Sumit has done BBA from a government college with 74% marks and his marks in written tests and interviews are 75%. He is 25 years old and has 2 years of experience in this field. He is not willing to pay the deposit amount of Rs 50,000.
→ Here, the candidate fulfills all the above criteria except (d) but has experience of working in this area for more than one year. Thus, the candidate has to be referred to Case Manager.
Hence, the correct answer is "option (4)".
How many such letters are there in the word BLOKEISH, each of which is as far from the beginning of the word as it is from the beginning of the English alphabet?
Four
Two
One
Three
Correct answer
Two
Why this answer is correct
The logic follows here is:
Given word: BLOKEISH
As per the question,
Words which are as far from the beginning of the word as it is from the beginning of the English alphabet are :
Clearly, there are 'Two' words.
Hence, the correct answer is "Two"
A reputed educational establishment is going to select meritorious students for scholarships for higher studies abroad who fulfill the following criteria:
However, if the candidate fulfills all the above criteria except
You have to study the information provided for the candidate in the following question and decide the course of action.
Chirag who will be 23 years old on 1.1.2021 has passed B.com. with 92% marks. Her father, a government employee, has been working in Delhi since 1989, with a current monthly income of Rs 30,000. Chirag got 1st prize in the state essay competition.
The candidate is referred to the Secretary.
The candidate has been selected.
The candidate is referred to the Chairman.
The candidate has not been selected.
Correct answer
The candidate is referred to the Chairman.
Why this answer is correct
As per the given information,
Chirag who will be 23 years old on 1.1.2021 has passed B.com. with 92% marks. Her father, a government employee, has been working in Delhi since 1989, with a current monthly income of Rs 30,000. Chirag got 1st prize in the state essay competition.
→ Here, the candidate fulfills all the above criteria except (4) as his annual family income is Rs 360000 which is more than Rs 2,50,000 but he has obtained 92% marks in graduation, so the case may be referred to the Chairman of the Establishment.
Thus, the candidate is referred to the Chairman.
Hence, the correct answer is "option (3)".
The following questions are based on five three-digit numbers given below.
283 395 768 534 187
If the positions of the first and second digits in each number are interchanged, which of the following will be the second highest number?
534
283
395
768
Correct answer
283
Why this answer is correct
As per the given information:
Given: 283 395 768 534 187
The positions of the first and second digits in each number are interchanged, then we have:
Clearly, 823 is the second highest number after the interchange.
Hence, the correct answer is "283".
Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option which is different from the others.
Silver
Iodine
Nickel
Copper
Correct answer
Iodine
Why this answer is correct
The logic follows here is:
Silver, Nickle, and Copper are all metals.
Whereas,
Iodine is not a metal.
Thus, Iodine is the odd one.
Hence, the correct answer is "Iodine".
In the question a statement is given, followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at odds with commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements.
Statement:
A ≤ B ≥ C > D; A ≥ E = F < G
Conclusion:
I. B > F
II. B = F
Both conclusions I and II follow
Only conclusion I follows
Either conclusion I or II follows
Only conclusion II follows
Correct answer
Either conclusion I or II follows
Why this answer is correct
Given statement : A ≤ B ≥ C > D; A ≥ E = F < G
On combining: G > F = E ≤ A ≤ B ≥ C > D
Conclusions :
I. B > F → FALSE (as G > F = E ≤ A ≤ B ≥ C > D → F ≤ B, thus it is false)
II. B = F → FALSE (as G > F = E ≤ A ≤ B ≥ C > D → F ≤ B, thus it is false)
Conclusion I and II form a complementary pair and both of them are false. Thus, this is the case of either and or.
Hence, the correct answer is "Either conclusion I or II follows".
Additional InformationConditions of "Either and or" Case
Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option that is different from the others.
X
N
R
K
Correct answer
K
Why this answer is correct
The logic follows here is:
The positional values of X, N, and R are even numbers while the positional value of K is an odd number.
Thus, 'K' is different from the others.
Hence, the correct answer is "K".
Six friends Anil, Babita, Chaman, Dhoni, Ellen, and Farukh are going to college. Ellen is older than only Anil and Babita but shorter than only Farukh. Dhoni is younger than only Farukh and taller than only Anil and Babita. Neither Anil is the shortest nor Babita is the shortest one. How many friends are there who occupy the same position in both the orders?
4
2
1
3
Correct answer
2
Why this answer is correct
Given: Six friends Anil, Babita, Chaman, Dhoni, Ellen, and Farukh are going to college.
Farukh > Ellen > Anil/Babita > Anil/Babita. ____ (1)
Farukh > Dhoni > Anil/Babita > Anil/Babita. ____ (2)
After combining both the conditions, we get:
Farukh > Dhoni/Ellen > Anil/Babita > Anil/Babita > ___
Here, Dhoni and Ellen occupy the same position in both sequences.
Hence, the correct answer is '2 friends' who occupy the same position in both sequences.
Complete the following alphabet series:
AZOM, CXQK, EVSI, ___
FTTJ
GTUJ
GTUG
GUTG
Correct answer
GTUG
Why this answer is correct
The logic follows here is:
Hence, the correct answer is "GTUG".
Read all the information and answer the question.
A + B means 'A is the mother of B';
A – B means 'A is the brother of B';
A × B means 'A is the father of B';
A ÷ B means 'A is the daughter of B';
How is C related to E in the expression A - B + C × D ÷ E?
Wife
Father
Husband
Brother
Correct answer
Husband
Why this answer is correct
Given:
A + B means 'A is the mother of B';
A – B means 'A is the brother of B';
A × B means 'A is the father of B';
A ÷ B means 'A is the daughter of B';
Let us first decode the given symbols and then draw a family tree:
| A is | ||||
|---|---|---|---|---|
| Symbol | + | – | × | ÷ |
| Meaning | Mother | Brother | Father | Daughter |
| of B |
On checking: A - B + C × D ÷ E
1) A - B
Here, A is the brother of B.
2) B + C
Here, B is the mother of C.
Here, C is the father of D.
4) D ÷ E
Here, D is the daughter of E.
Thus, the following family tree can be drawn:
Clearly, C is 'husband' of E.
Hence, the correct answer is "Husband".
Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option which is different from the others.




Correct answer
Why this answer is correct
The logic follows here is:
The arrows inside the circles are in the clockwise direction in all the options except option(1).
option (1)
Here. the arrow is in the anti-clockwise direction. Thus, it is different from the others.
Hence, the correct answer is "option (1)".
The given sheet has been folded to form a cube. In the cube thus formed, which of the following pairs of symbols will be in opposite directions?





Correct answer
Why this answer is correct
The logic follows here is:
There is a pattern in which unfolded dice occur opposite to each other.
Two opposite faces are never together or adjacent to each other.
| Face | Opposite |
|---|---|
option(1) →
Clearly, pairs of symbols in option (1) will be in opposite directions.
Hence, the correct answer is "option (2)".
Select the option that is related to the third term in the same way as the second term is related to the first term.
65 : 74 :: 40 : ?
49
50
51
48
Correct answer
49
Why this answer is correct
The logic follows here is,
(First number) + 9 = (Second number)
→ 65 + 9 = 74 = second number.
Similarly,
→ 40 + 9 = 49 = second number.
Hence, the correct answer is "49".
From the given answer figures, select the figure in which the question figure is hidden/embedded.





Correct answer
D, C, B and A are sitting around a table facing each other. They like different colors yellow, blue, black, and red.
(1) D sits opposite the one who likes black color.
(2) C sits to the immediate right of the one who likes the blue color.
(3) The person who likes yellow color is to the left of the person who likes red color.
(4) A sits opposite B who does not like the yellow colour.
Who likes red?
A
B
D
C
Correct answer
D
Why this answer is correct
As per the given information:
D, C, B and A are sitting around a table facing each other. They like different colors yellow, blue, black, and red.
There are two possibilities:
Case I will be eliminated as it contradicts the above condition.
Clearly, 'D' likes red color.
Hence, the correct answer is "D".
Find the missing number in the given series:
53, 55, 113, 343, ___
1387
1377
1367
1357
Correct answer
1377
Why this answer is correct
Given: 53, 55, 113, 343, ___
The logic follows here is:
Hence, the correct answer is "1377.
Train A crosses a man in 12 seconds and train B running in the opposite direction crosses it in 24 seconds. If the length of train B is twice the length of train A and the speed of train B is 54 km/h, then find the speed of train A.
90 km/hr
108 km/hr
100 km/hr
75 km/hr
Correct answer
108 km/hr
Why this answer is correct
Given:
Formula:
Distance = Speed × Time
Calculation:
Let the length of train A be x and the length of train B be 2x.
According to the question,
Train A crosses a man in 12 seconds.
Therefore, the speed of Train A is = x/12 m/s
Train B running in the opposite direction crosses it in 24 seconds.
The relative speed = speed of train A + speed of Train B
Relative speed = (x/12) + 15
Now, by using the formula,
where distance is equal to the sum of the lengths of both trains i.e. 3x
⇒ distance = relative speed × Time
⇒ 3x = { (x/12 + 15)} × 24
⇒ x = { (x/12 + 15)} × 8
⇒ 12x = (x + 180) × 8
⇒ 3x = (x + 180) × 2
⇒ 3x = 2x + 360
⇒ x = 360
Thus, the length of train A is 360 m.
Speed of Train A = x/12 m/s
⇒ 360 / 12
⇒ 30 m/s = 30 × (18/5) = 108 km/hr
Hence, the correct answer is "108 km/hr".
Select the name of the peninsular country:
Brazil
Austria
India
Philippines
Correct answer
India
Why this answer is correct
The correct answer is India.
Key Points
Additional Information
The name of the anti-covid drug developed by DRDO is:
2-deoxy-D-glucose (2-DG)
2-deoxy (2-D)
1-deoxy-D-glucose (2-DG)
3-deoxy-d-glucose
Correct answer
2-deoxy-D-glucose (2-DG)
Why this answer is correct
The correct answer is 2-deoxy-D-glucose (2-DG).
Key PointsAnti-COVID-19 drug 2-deoxy-D-glucose (2-DG) has been developed by the Institute of Nuclear Medicine and Allied Sciences (INMAS), a lab of the Defence Research and Development Organisation (DRDO), in collaboration with Dr Reddy’s Laboratories (DRL), Hyderabad.
Additional Information
Which of the following is not a vector borne disease?
Dengue fever
Ebola virus
Malaria
lymphatic filariasis
Correct answer
Ebola virus
Why this answer is correct
The correct answer is the Ebola virus.
Key Points
Additional Information
The severity of the disease depends on the species of Plasmodium.
What are Mahayana and Hinayana?
Two major sects of Hinduism
Mahayana means 'the great vehicle'. 'Hinayana' means 'small vehicle' or 'lesser vehicle
Names of books written by the students of Mahatma Buddha
None of the Above
Correct answer
Mahayana means 'the great vehicle'. 'Hinayana' means 'small vehicle' or 'lesser vehicle
Why this answer is correct
The correct answer is Mahayana means 'the great vehicle'. 'Hinayana' means 'small vehicle' or 'lesser vehicle.
<br>Key Points
Additional Information
Milkha Singh was an Indian track and field sprinter who was also known as:
The Flym Man
The Fighter Sikh
The Fighter Flying Sikh
The Flying Sikh
Correct answer
The Flying Sikh
Why this answer is correct
The correct answer is The Flying Sikh.
Key Points
Milkha Singh.
Enzymes are required to:
Sharpen the eye sight
Make antibodies
Increasing oxygen level in body
Digest the food in the stomach
Correct answer
Digest the food in the stomach
Why this answer is correct
The correct answer is Digest the food in the stomach.
Key Points
Enzymes
Additional Information
Select dance styles that are popular in Maharashtra:
Bihu
Kathak
Satriya
Lavani
Correct answer
Lavani
Why this answer is correct
The correct answer is Lavani.
Key Points
Additional InformationKathak:
Satriya
Bihu
A very alkaline solution (high pH) will change the color of beetroot or beetroot juice to ______.
Purple to Yellow
Purple to diamond
Pink to black
Red to purple
Correct answer
Purple to Yellow
Why this answer is correct
The correct answer is Purple to Yellow.
Key Points
Important Points
Dadasaheb Phalke Award is given in which field?
Cinema
Sport
Peace
literature
Correct answer
Cinema
Why this answer is correct
The correct answer is Cinema.
Dada Saheb Phalke Award
What is the theme of the Economic Survey 2020-21?
Market Enablement, Promote 'Pro-Business'
Saving lives and Livelihood
"Shifting Gear"
Rural Development and Agricultural Education
Correct answer
Saving lives and Livelihood
Why this answer is correct
The correct answer is Saving lives and Livelihoods.
Key Points
At present (as of 2021), who is the Speaker of the Lok Sabha?
Om Birla
Om Puri
Meera Kumar
Sumitra Mahajani
Correct answer
Om Birla
Why this answer is correct
The correct answer is Om Birla.
Key Points
Additional Information
Speaker and Deputy Speaker -
Kabaddi is the national game of which country?
Bangladesh
Pakistan
India
Russia
Correct answer
Bangladesh
Why this answer is correct
The correct answer is Bangladesh.
Key Points
Additional Information
| Sports | National ;game | Famous Players |
|---|---|---|
| Cricket | England and Australia | Matthew Hayden (Aus), Virat Kohli, Sachin Tendulkar, M.S. Dhoni, etc. |
| Football | France, Italy, Italy, Poland, Mauritius, etc | Lionel Messi (Argentina), Christiano Ronaldo (Portugal), Neymar (Brazil), Nene (Brazil), Maradona (Argentina) |
| Badminton | Indonesia | Saina Nehwal, P.V. Sindhu, Lee Chong Wei (Malaysia), Chen Long (China), etc |
At present (as of 2021), who is the chairman of the Union Public Service Commission?
Sujata Mehta
Vinay Mittal
Arvind Saxena
Pro. (Dr.) Pradeep Kumar Joshi
Correct answer
Pro. (Dr.) Pradeep Kumar Joshi
Why this answer is correct
The correct answer is Pro. (Dr.) Pradeep Kumar Joshi.
Key Points
Additional Information
Article 71A deals with:
It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the Supreme Court.
It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the District Court
It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the High Court.
None of the Above
Correct answer
It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the Supreme Court.
Why this answer is correct
The correct answer is It provides that disputes arising out of the election of the President or the Vice-President shall be decided by the Supreme Court.
Key PointsArticles 71.
Important Points
| Article | Information |
|---|---|
| Article 63 | There shall be a Vice-President of India. |
| Article 64 | The Vice-President shall be ex-officio Chairman of the Council of States and shall not hold any other office of profit |
| Article 65 | The Vice-President to act as President or to discharge his functions during casual vacancies in the office, or during the absence, of President. |
| Article 66 | The Vice President shall be elected by the members of an electoral college consisting of the members of both Houses of Parliament. |
| Article 67 | A Vice-President may, by writing under his hand addressed to the President, resign his office |
Which cyclone hit Gujarat recently (in May 2021)?
Kyar
Tauktae
Pawan
Pabuk
Correct answer
Tauktae
Why this answer is correct
The correct answer is Tauktae.
Key Points
Important Points
Which is not a dwarf planet?
Venus
Pluto
Aris
Makemake
Correct answer
Venus
Why this answer is correct
The correct answer is Venus.
Key Points
Important Points
Milindapanha is a Buddhist text which may have been written initially in which language?
Hindi
English
Sanskrit
Urdu
Correct answer
Sanskrit
Why this answer is correct
The correct answer is Sanskrit.
Key Points
Additional InformationSanskrit
Which is the hottest planet in the solar system?
Mars
Uranus
Neptune
Venus
Correct answer
Venus
Why this answer is correct
The correct answer is Venus.
<br>Key Points
Important PointsMars
Neptune:
Uranus
At present (as of August 2021), who is the Governor of the Reserve Bank of India?
Raghuram Rajan
Urjit Patel
Mr. Shaktikanta Das
T Ravi Shankar
Correct answer
Mr. Shaktikanta Das
Why this answer is correct
The correct answer is Mr. Shaktikanta Das.
Key Points
Additional Information
Between 2003 and 2006, he was Chief Economist and director of research at the International Monetary Fund.
How many parts are there in the United Nations?
Eight
Six
Three
Seven
Correct answer
Six
Why this answer is correct
The correct answer is Six.
Key Points
Important Points
The police saw the thief from a distance of 200m. The speed at which the thief ran is 9 km/h and the police ran at the speed of 11 km/h. How far will the thief have to go before the police catch him?
990 m
800 m
900 m
890 m
Correct answer
900 m
Why this answer is correct
Given:
The police saw the thief from a distance of 200m or 0.2 km,
The speed at which the thief ran is 9 km/h and the police ran at the speed of 11 km/h.
Formula used:
Case 1: When two bodies 'a' and 'b' moves in the same direction.
Relative speed between a and b = a - b km/hr
Case 2: When two bodies 'a' and 'b' moves in the apposite direction.
Relative speed between a and b = a + b km/hr
Calculation:
According to the question,
Relative speed between thief and police = 11 - 9 = 2 km/hr
Time required by thief to be captured by police = 0.2/2 = 0.1 hour
Distance travelled by thief in 0.1 hour = 9 × 0.1 = 0.9 km = 900 m
Therefore, "900 m" is the required answer.
What is the average of the first 47 natural numbers?
42
2
24
4
Correct answer
24
Why this answer is correct
Formula used:
Average of n natural numbers =
In this formula:
"n" is the number of natural numbers you want to sum.
Calculation:
First natural number = 1
Last natural number = 47
Average = (1 + 47)/2 = 48/2 = 24
Therefore, "24" is the required answer.
The interest rate is 14% per annum which is being compounded half yearly. The amount is Rs. 965000 and the tenure is 3 years. What is compound interest?
Rs. 483420.79
Rs. 483402.79
Rs. 483200.79
Rs. 483204.79
Correct answer
Rs. 483204.79
Why this answer is correct
Given:
The interest rate is 14% per annum which is being compounded half yearly.
The amount is Rs 965000 and the tenure is 3 years.
Formula used:
The formula for compound interest is:
A = P
Where:
A = Final Amount
P = Principal amount
r = Annual interest rate
n = Number of times that interest is compounded per year.
t = the number of years the money is invested or borrowed
Calculation:
According to the question,
⇒ A = 965000 ×
⇒ A = 965000 ×
⇒ A = 965000 × 1.5 = 14,48,204.78
Now,
Compound Interest = 1448204.79 - 965000 ≈ Rs. 483204.79
Therefore, "Rs. 483204.79" is the required answer.
The percentage of alcohol in 8L solution of alcohol and water is 13%. If 2L of water is added to the solution, what will be the new percentage of alcohol in the solution?
11.0%
10.4%
10.0%
9.0%
Correct answer
10.4%
Why this answer is correct
Given:
The percentage of alcohol in 8L solution of alcohol and water is 13%.
Calculation:
According to the question,
Case 1:
Quantity of alcohol in 8L solution = 13% of 8 = 1.04L
Quantity of water in 8L solution = 8 - 1.04 = 6.96L
Case 2: If 2L of water is added to the solution
New quantity of water = 6.96 + 2 = 8.96L
Quantity of alcohol (remain unchanged) = 1.04L
Total quantity = 10L
Required % = 1.04/10 × 100 = 10.4%
Therefore, "10.4%" is the required answer.
A wall is 5.5 m high and 6.5 m wide. What is the maximum number of squares required to cover the wall with square shaped papers?
143
134
133
144
Correct answer
143
Why this answer is correct
Given:
A wall is 5.5 m high and 6.5 m wide.
Calculation:
The maximum size of squares required to cover the wall with square-shaped papers = H.C.F of (5.5 and 6.5) = 0.5 m
The number of number of squares required to cover the wall horizontally = 5.5/0.5 = 11
The number of number of squares required to cover the wall vertically = 6.5/0.5 = 13
The maximum number of squares required = 11 × 13 = 143
Therefore, "143" is the required answer.
P and Q can do the work of laying carpet in 6 days. Q and R can do the same carpet laying work in 8 days while R and P can do the same carpet laying work in 10 days. How much time will it take if they all work together?
241/47 days
240/49 days
240/47 days
241/49 days
Correct answer
240/47 days
Why this answer is correct
Given:
P and Q can do the work of laying carpet in 6 days.
Q and R can do the same carpet laying work in 8 days.
R and P can do the same carpet laying work in 10 days.
Formula used:
Where,
Time taken by A to do the work = a
Time taken by B to do the work = b
Time taken by C to do the work = c
Calculation:
Amount of work (in units) = L.C.M of (6, 8, 10) = 120 units
According to the question,
Efficiency of P and Q = 120/6 = 20 units per day
Efficiency of Q and R = 120/8 = 15 units per day
Efficiency of R and P = 120/10 = 12 units per day
Now, Combined Efficiency = 2(P + Q + R) = 47
Combined efficiency of P, Q and R = 47/2 units per day
Time taken to complete the work = 120 ÷ 47/2 = 240/47 days
Therefore, "240/47 days" is the required answer.
A person's salary is deducted by 8% for house rent. Then 15% of the remaining is spent on household utilities and 20% of the remaining is spent on miscellaneous and children's education. After these, his savings is Rs. 988448. What is the basic salary of the person?
Rs. 1850000
Rs. 185000
Rs. 1580000
Rs. 158000
Correct answer
Rs. 1580000
Why this answer is correct
Given:
A person's salary is deducted by 8% on house rent.
Then 15% of the remaining is spent on household utilities.
20% of the remaining is spent on miscellaneous and children's education.
After these, his savings are Rs 988448.
Calculation:
Let x be the salary of the person.
Remaining salary after house rent = (100% - 8%) of x
Remaining salary after household utilities = (100% - 15%) × (100% - 8%) of x
Remaining salary after miscellaneous and children's education = (100% - 20%) × (100% - 15%) × (100% - 8%) of x
According to the question,
⇒ (100% - 20%) × (100% - 15%) × (100% - 8%) of x = 988448
⇒ (80%) × (85%) × (92%) of x = 988448
⇒ × x = 988448
⇒ x = Rs. 15,80,000
Therefore, "Rs. 15,80,000" is the required answer.
What is the difference between the discount of 18% and two successive discounts of 12% and 6% on a bill of Rs. 48900?
Rs. 351
Rs. 352.08
Rs. 353
Rs. 350
Correct answer
Rs. 352.08
Why this answer is correct
Given:
Bill = Rs. 48900
Case 1: Discount of 18%.
Case 2: two successive discounts of 12% and 6%.
Formula used:
Calculations:
Case 1: Discount of 18%.
Case 2: two successive discounts of 12% and 6%.
Overall discount = 12 + 6 - = 18 - 0.72 = 17.28%
According to the question,
The required difference between two discounts = 18% - 17.28% = 0.72%
The overall discount in Rs. = × 48900 = Rs. 352.08
Therefore, "Rs. 352.08" is the required answer.
Ram, Shyam and Dheeraj are in a partnership. They made a profit of Rs. 531000 for the year. Their capital is in the ratio 1/2 : 1/5 : 1/7. What is Shyam's share?
Rs. 126000
Rs. 315000
Rs. 90000
Rs. 125000
Correct answer
Rs. 126000
Why this answer is correct
Given:
Ram, Shyam and Dheeraj are in a partnership. He made a profit of Rs 531000 for the year.
Their capital is in the ratio 1/2 : 1/5 : 1/7.
Concept:
Ratio in which Profit is distributed among the partners = Ratio in which investment are made among the partners
Calculation:
Ram, Shyam and Dheeraj capital is in the ratio = 1/2 : 1/5 : 1/7
Now multiply each term by 70.
Ram, Shyam and Dheeraj capital is in the ratio = 1/2 × 70 : 1/5 × 70 : 1/7 × 70 = 35 : 14 : 10
The share of profit made by Shyam = × 531000 = Rs. 126000
Therefore, "Rs. 126000" is the required answer.
A shopkeeper has a number of products worth Rs. 20000. 1/4 of them are sold at 14% profit. At what percentage profit should the remaining be sold so that the total profit is 16.5%?
16.0%
17.33%
15.0%
170%
Correct answer
17.33%
Why this answer is correct
Given:
A shopkeeper has a number of products worth Rs 20000.
1/4 of them are sold at 14% profit
The total profit is 16.5%
Concept:
Profit on 1 item = Profit on n items
Calculation:
Let the total number of product = 100
The number of product sold at 14% profit = 1/4 × 100 = 25
Remaining of the product at x% profit = 100 - 25 = 75
According to the question,
⇒ (25 × 14) + (75 × x) = 100 × 16.5
⇒ 350 + (75 × x) = 1650
⇒ 75x = 1300
⇒ x = 17.33%
Therefore, "17.33%" is the required answer.
Two numbers are in the ratio 3 : 7. When 12 is added to both the numbers the ratio becomes 9 : 17. What are the numbers?
42, 65
24, 56
24, 65
56, 24
Correct answer
24, 56
Why this answer is correct
Given:
Case 1:
Two numbers are in the ratio 3 : 7.
Case 2:
When 12 is added to both the numbers the ratio becomes 9 : 17.
Calculation:
Let the numbers are 3x and 7x.
According to the question,
⇒
⇒ 51x + 204 = 63x + 108
⇒ 204 - 108 = 63x - 51x
⇒ 96 = 12x
⇒ x = 8
First number = 3x = 24
Second number = 7x = 56
Therefore, "24, 56" are the required answer.
A person gives a discount of 16% on the list price. After the discount he makes a 12% profit at Rs. 9408. What is cost price?
Rs. 4800
Rs. 8000
Rs. 4000
Rs. 8400
Correct answer
Rs. 8400
Why this answer is correct
Given:
A person gives a discount of 16% on the list price.
After discount, he earns a profit of 12% on Rs 9408.
Formula used:
Selling price = (100% + Profit%) of Cost Price
Calculation:
Let cost price = x
Selling price = Rs. 9408
According to the question,
⇒ x × (100% + 12%) = 9408
⇒ x × 112% = 9408
⇒ × x = 9408
⇒ x = Rs. 8400
The cost price of the article = Rs. 8400
Therefore, "Rs. 8400" is the required answer.
What is the average of prime numbers between 15 to 49?
31.89
30.89
31.98
31
Correct answer
31.89
Why this answer is correct
Formula:
Average =
Calculation:
Prime numbers between 15 and 49 are: 17, 19, 23, 29, 31, 37, 41, 43 and 47
The sum of all prime numbers between 15 and 49 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 = 287
Number of Prime numbers between 15 and 49 = 9
Average = 287/9 ≈ 31.89
Therefore, "31.89" is the required answer.
The graph shows the passing percentage of different schools. Which school performs the worst?
P and Q
P
Q and R
Q
Correct answer
P
Why this answer is correct
Given:
The graph shows the passing percentage of different schools.
Calculation:
According to the question,
The passing percentage of school P of class VI, VII, VIII, IX, and X are 39%, 34%, 31%, 37% and 32% respectively.
The passing percentage of school Q of class VI, VII, VIII, IX, and X are 45%, 41%, 44%, 43% and 41% respectively.
The passing percentage of school R of class VI, VII, VIII, IX, and X are 56%, 58%, 60%, 52% and 57% respectively.
On comparing the above data it can be inferred that school P performs the worst in compare to other schools in every class.
Therefore, "P" is the required answer.
Simplify:
(0.023 × 0.023 × 0.023 + 0.017 × 0.017 × 0.017) / (0.023 × 0.023 - 0.023 × 0.017 + 0.017 × 0.017)
0.004
0.044
0.4
0.04
Correct answer
0.04
Why this answer is correct
Concept Used:-
Formula for the sum of cube of two values a and b can be given as,
Explanation:-
Given expression is,
Let the result of this expression is x. Thus,
In the exponential form terms can be written as,
In the numerator, there is cube of two values. Use the above mentioned formula and expand it to get,
Hence,
So, the correct option is 4.
The table shows the students who applied and qualified from different states. What is the median of qualified students?
| Year | 2010 | 2011 | 2012 | |||
|---|---|---|---|---|---|---|
| State | Application | Qualified | Application | Qualified | Application | Qualified |
| A | 3147 | 196 | 1554 | 208 | 2875 | 231 |
| B | 1618 | 153 | 4558 | 180 | 4109 | 256 |
| C | 3992 | 167 | 4410 | 183 | 3837 | 255 |
| D | 3730 | 190 | 3278 | 210 | 3762 | 238 |
| E | 2403 | 179 | 3261 | 171 | 2550 | 260 |
196
190
208
183
Correct answer
196
Why this answer is correct
Given:
The number of qualified students: 196, 153, 167, 190, 179, 208, 180, 183, 210, 171, 231, 256, 255, 238, 260
Formula used:
To find the median of raw discrete data, you can use the following steps:
Organize the data: Arrange the discrete data in ascending or descending order, which means listing the data values from smallest to largest.
Determine the number of data points (n): Count how many data points you have in your dataset.
Calculate the median:
Case 1: If n is odd, the median (M) is the middle value:
M = value
Case 2: If n is even, the median (M) is the average of the two middle values:
Md = Average of
Calculation:
Arrange the data in the ascending order:
153, 167, 171, 179, 180, 183, 190, 196, 208, 210, 231, 238, 255, 256, 260
The number of variables = 15
Median = (15 + 1)/2 = 8
Median = the value of 8th position = 196
Therefore, "196" is the required answer.
What is the least number which should be multiplied by 1536 to make a perfect cube?
7
10
9
8
Correct answer
9
Why this answer is correct
Given:
The given number is 1536.
Calculation:
According to the question,
Prime factorisation of 1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Make the number in group of three to find the cube root.
⇒ 1536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3
⇒ 1536 = 23 × 23 × 23 × 3
Now, we are required to multiply the number by 32.
⇒ 1536 × 32 = 23 × 23 × 23 × 3 × 32
⇒ 1536 × 32 = 23 × 23 × 23 × 33
∴ 9 should be multiplied by 1536 to make a perfect cube.
Therefore, "9" is the required answer.
If = 2 then what is the value of x?
5
5/4
4
4/5
Correct answer
4/5
Why this answer is correct
Given:
= 2
Calculation:
According to the question,
⇒ = 2
⇒ = 2
⇒ = 2
⇒ 7x = 2(2 + x)
⇒ 7x = 4 + 2x
⇒ x = 4/5
Therefore, "4/5" is the required answer.
What is the length of the largest ruler that can accurately measure three equilateral triangles with sides measuring 68 cm, 102 cm and 136 cm?
34 cm
2 cm
43 cm
44 cm
Correct answer
34 cm
Why this answer is correct
Given:
What is the length of the largest ruler that can accurately measure three equilateral triangles with sides measuring 68 cm, 102 cm and 136 cm?
Three equilateral triangles with sides 68, 102 and 136.
Calculation:
According to the question,
The length of the largest ruler that can accurately measure three equilateral triangles = H.C.F of (68, 102 and 136)
Now,
Prime factorisation of 68 = 2 × 2 × 17
Prime factorisation of 102 = 2 × 3 × 17
Prime factorisation of 136 = 2 × 2 × 2 × 17
The highest common factor for 68, 102 and 136 = 2 × 17 = 34
Therefore, The length of the largest ruler that can accurately measure three equilateral triangles is 34 cm.
Therefore, "34 cm" is the required answer.
A room is 17 m long, 12 m wide and 10 m tall. What will be the length of the pillar that can be kept in that room?
24 m
23 m
23.09 m
23.9 m
Correct answer
23.09 m
Why this answer is correct
Given:
A room is 17 m long, 12 m wide and 10 m tall.
Formula used:
Diagonal =
Where,
l = length of the cuboid
b = breadth of the cuboid
h = height of the cuboid
Calculation:
According to the question,
The length of the longest pole that can be inserted = ≈ 23.09 m
Therefore, "23.09" is the required answer.
Select the word segment that substitutes (replaces) the bracketed word segment correctly and completes the sentence meaningfully. Select the option 'no correction required' if the sentence is correct as given.
Even though (he do not realize it, he) was responsible for his own problems.
he didn’t realize it, he
he don't realize it, he
No correction required.
he don't realizes it, he
Correct answer
he didn’t realize it, he
Why this answer is correct
The correct solution is 'he didn't realize it'.
Key Points
The question below consist of a set of labelled sentences. Out of four options given, select the most logical order of the sentences which form a paragraph.
Pangaea or Pangea is derived from Ancient Greek pan meaning "all, entire, whole" and Gaia "Mother Earth, land").
P. It was a supercontinent that existed during the late Palaeozoic and early Mesozoic eras.
Q. Pangaea is the most recent supercontinent to have existed and the first to be reconstructed by geologists.
R. It assembled from earlier continental units approximately 335 million years ago, and began to break apart about 175 million years ago.
S. In contrast to the present Earth and its distribution of continental mass, Pangaea was centred on the Equator and surrounded by the superocean Panthalassa.
The forming of supercontinents and their breaking up appears to have been cyclical through Earth's history.
PRSQ
RSPQ
QPSR
SPRQ
Correct answer
PRSQ
Why this answer is correct
The correct solution is 'PRSQ'
Key Points
Select the most appropriate meaning for the word given below.
Axiom
A position requiring little or no work but giving the holder status or financial benefit.
The action or offence of speaking sacrilegiously about God or sacred things
Denoting a sin that is not regarded as depriving the soul of divine grace
A statement or proposition on which an abstractly defined structure is based
Correct answer
A statement or proposition on which an abstractly defined structure is based
Why this answer is correct
The correct solution is 'Axiom'.
Key Points
Select the word segment that substitutes (replaces) the bracketed word segment correctly and completes the sentence meaningfully. Select the option 'no correction required' if the sentence is correct as given.
She settles into the cockpit, (surrounding with dozen of complicating switches and sophisticated gauges,) sitting atop a massive $84 million piece of machinery.
surrounding with dozens of complicating switch and sophisticating gauges
No correction required
surrounded around dozens of complicated switches and sophisticated gauges,
surrounded by dozens of complicated switches and sophisticated gauges
Correct answer
surrounded by dozens of complicated switches and sophisticated gauges
Why this answer is correct
The correct solution is 'surrounded by dozens of complicated switches and sophisticated gauges'
Key Points
The sentences below are not complete. There are four options for each question.
Choose the best word to complete the sentence.
In the _______, completing a marathon makes us happier than eating a chocolate pie.
fastest run
long run
fast running
long duration
Correct answer
long run
Why this answer is correct
The correct solution is 'long run'.
Key Points
Some parts of a sentence have been jumbled up, and labelled P, Q, R and S. Select the option that gives the correct sequence in which these parts can be rearranged to form a meaningful and grammatically correct sentence.
Photosynthesis is a process
P. convert light energy into chemical energy that,
Q. can later be released to fuel the
R. used by plants and other organisms to
S. through cellular respiration,
organism's metabolic activities.
PQRS
QSRP
SRQP
RPSQ
Correct answer
RPSQ
Why this answer is correct
The correct solution is 'RPSQ'.
Key Points
Select the word that is similar in meaning (SYNONYM) to the word given below.
RAPACIOUSNESS
PROFUSION
MUNIFICENCE
VORACIOUSNESS
BENEFICENCE
Correct answer
VORACIOUSNESS
Why this answer is correct
The correct solution is 'VORACIOUSNESS'.
Key Points
Four words are given, out of which only one word is spelt correctly. Choose the correctly spelt word.
LAISON
LAISCION
LIASION
LIAISON
Correct answer
LIAISON
Why this answer is correct
The correct solution is 'Liaison'.
Key Points
Select the word that is similar in meaning (SYNONYM) to the word given below.
GRUDGE
RAPPORT
CONCORD
MALICE
COMMUNION
Correct answer
MALICE
Why this answer is correct
The correct solution is 'MALICE'.
Key Points
Fill in the blank with the most appropriate choice.
Still another _________ symptom has to be considered.
overwhelming
critical
violent
tuberous
Correct answer
critical
Why this answer is correct
The correct solution is 'critical'.
Key Points
The sentence below has been divided into three parts. Select the part of the sentence that has an error. If the sentence has no error, select the option 'No Error'.
But intellectual madness would have / resulted from a development that followed / the acceptance of it's own kind of art
But intellectual madness would have
the acceptance of it's own kind of art
resulted from a development that followed
No Error
Correct answer
the acceptance of it's own kind of art
Why this answer is correct
The correct solution is 'the acceptance of it's own kind of art'
Key Points
Select the most appropriate meaning of the given proverb.
The rats are leaving the sinking ship
In an emergency you do things that you would not otherwise do
Don’t expect a good event to happen before it has actually happened.
Turning away from failing or fleeing from an unpleasant situation
You shouldn’t be too sure of something, even if the prospect is good.
Correct answer
Turning away from failing or fleeing from an unpleasant situation
Why this answer is correct
The correct solution is 'Turning away from failing or fleeing from an unpleasant situation'.
Key Points
Select the most appropriate meaning of the given idiom.
Burn your bridges
To destroy a bridge or path behind oneself.
Overcome your emotions and move on in life
To destroy your enemies
To destroy confidential information
Correct answer
To destroy a bridge or path behind oneself.
Why this answer is correct
The correct solution is 'To destroy a bridge or path behind oneself'.
Key Points
The sentence below has been divided into three parts. Select the part of the sentence that has an error. If the sentence has no error, select the option 'No Error'.
This phenomena made its appearance / even during the short lived period of / the Soviet republic in Bavaria.
No Error
even during the short lived period of
the Soviet republic in Bavaria
This phenomena made its appearance
Correct answer
This phenomena made its appearance
Why this answer is correct
The correct solution is 'This phenomena made its appearance'.
Key Points
Select the most appropriate antonym of the given word.
Gratifying
Dreary
Eventful
Pleasant
Delightful
Correct answer
Dreary
Why this answer is correct
The correct solution is 'Dreary'.
Key Points
Read the passage carefully and choose the best answer to each question out of the four alternatives.
Bohemianism is the practice of an unconventional lifestyle, often in the company of like-minded people and with few permanent ties. It involves musical, artistic, literary, or spiritual pursuits. In this context, bohemians may be wanderers, adventurers, or vagabonds. This use of the word in the English language was imported from French in the mid 19th century and was used to describe the non-traditional lifestyles of artists, writers, journalists, musicians, and actors in major European cities. Bohemians were associated with unorthodox or anti-establishment political or social viewpoints, which often were expressed through free love, frugality, and—in some cases—simple living, van-dwelling or voluntary poverty. A more economically privileged, wealthy, or even aristocratic bohemian circle is sometimes referred to as haute boheme (literally "high Bohemia").
The term bohemianism emerged in France in the early 19th century, when artists and creators began to concentrate in the lower-rent, lower class, Romani neighbourhoods. Bohemian was a common term for the Romani people of France, who were mistakenly thought to have reached France in the 15th century via Bohemia (the western part of modern Czech Republic). Bohemianism and its adjective bohemian in this specific context are not connected to the native inhabitants of this region.
Three assertions are given below (A, B & C) on the basis of your understanding of the passage, which one of the options is incorrect?
A. Bohemians were unorthodox but had strongly supported political and social viewpoints.
B. Bohemian was a common term for the Romani people of France.
C. Some of the Bohemian people choose to live a life of poverty despite being wealthy.
A is correct
C is correct
B is correct
B & C are correct
Correct answer
A is correct
Why this answer is correct
The correct solution is '. Bohemians were unorthodox but had strongly supported political and social viewpoints.'
Key Points
On the basis of your reading of the above passage, what is the meaning of 'vandwelling'?
People who are not stationed at one location
Nomadic lifestyle
Van converted to home, people live in the van and travel around
Rich people travelling in caravan
Correct answer
Van converted to home, people live in the van and travel around
Why this answer is correct
The correct solution is 'Van converted to home, people live in the van and travel around'.
Key Points
Three assertions are given below (A, B & C) on the basis of your understanding of the passage, which one of the options is correct?
A. The use of the word bohemians as wanderers was imported in the English language from French in the mid 19th century.
B. Haute bohème means rich Bohemian people.
C. Bohemianism was started in the 15th century by the native inhabitants of Bohemia in France
Only C is correct.
Only A is correct
C is incorrect.
Only B is correct
Correct answer
C is incorrect.
Why this answer is correct
The correct solution is 'C is incorrect'.
Key Points
According to the passage, what would mean the opposite of 'economically privileged' from the given options?
Sceptical
Superior
Destitute
Affluent
Correct answer
Destitute
Why this answer is correct
The correct solution is 'destitute'.
Key Points
According to the passage, which of the following options define bohemianism aptly?
Journeying
Gratification
Leisure
Extravagant
Correct answer
Journeying
Why this answer is correct
The correct solution is 'Journeying'
Key Points
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए वाक्य के वृत्ति के भेद का सही विकल्प है।
क्या पता, मेरा मकान तुम्हे पसंद भी आए।
संदेहार्थ
निश्चयार्थ
संभावनार्थ
संकेतार्थ
Correct answer
संभावनार्थ
Why this answer is correct
दिए गए वाक्य के वृत्ति के भेद का सही विकल्प "संभवनार्थ" है।
Key Points
Important Points
Additional Information
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए मुहावरे का सही अर्थ हो।
छाती पर मूँग या कोदो दलना
अनुचित शब्द कहना
ईर्ष्या से हृदय जलना
किसी को कष्ट देना
साहसिक कार्य
Correct answer
किसी को कष्ट देना
Why this answer is correct
दिए गए विकल्पों में से 'छाती पर मूँग या कोदो दलना' मुहावरे का सही अर्थ "किसी को कष्ट देना" है।
Key Pointsअन्य विकल्प -
| मुहावरे | अर्थ | वाक्य प्रयोग |
|---|---|---|
| जबान चलाना | अनुचित शब्द कहना | सीमा बहुत जबान चलाती है, उससे कौन बात करेगा? |
| जान पर खेलना | साहसिक कार्य | भारतीय सेना आतंकवादी से नहीं डरती और सदा जान पर खेलने लिए तैयार रहती है |
| छाती पर साँप लोटना | ईर्ष्या से हृदय जलना | जब पड़ोसी ने नई कार ली तो शेखर की छाती पर साँप लोट गया। |
Additional Information
कुछ मुहावरे -
| मुहावरे | अर्थ | वाक्य प्रयोग |
|---|---|---|
| गाजर-मूली समझना | तुच्छ समझना | मोहन ने कहा कि उसे कोई गाजर-मूली न समझे, वह बहुत कुछ कर सकता है। |
| चादर से बाहर पैर पसारना | आमदनी से अधिक खर्च करना | चादर से बाहर पैर पसारोगे तो कष्ट पाओगे। |
| छक्के छुड़ाना | हराना | भारत ने युद्ध में पाक के छक्के छुड़ा दिए। |
| गुड़ गोबर करना | बनाया काम बिगाड़ना | वीरू ने जरा-सा बोलकर सब गुड़-गोबर कर दिया। |
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो विराम चिह्न युक्त वाक्य का सही विकल्प है।
'व्याकरण पल्लव " पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है
'व्याकरण पल्लव पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।
'व्याकरण पल्लव " पुस्तक आई सी .एस. ई बोर्ड में पढ़ाया जाता है।
'व्याकरण पल्लव' पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।
Correct answer
'व्याकरण पल्लव' पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।
Why this answer is correct
दिए गए विकल्पों में से विराम चिह्न युक्त वाक्य का सही विकल्प है-
'व्याकरण पल्लव " पुस्तक आई. सी .एस. ई बोर्ड में पढ़ाया जाता है।
Key Points
Important Points
| पूर्ण विराम-(।)- लिखते वक़्त वाक्य ख़त्म होने के बाद पूर्ण विराम लगाते है। ( विस्मायवाचक वाक्यों और प्रश्नवाचक वाक्यों को छोड़ कर ) |
|---|
| सूचक चिन्ह( . ) - किसी बड़े अंश का संक्षिप्त रूप लिखने के लिए लाघव चिन्ह/ संक्षेपसूचक का प्रयोग किया जाता है। |
| अवतरण या उदाहरण चिन्ह-( “…” )- किसी वाक्य के खास शब्द पर जोर देने के लिए, अवतरण चिह्न (”…”) का प्रयोग किया जाता है। |
Additional Information
हिंदी में प्रचलित प्रमुख विराम चिह्न -
| विराम चिन्ह का नाम | विराम- चिन्ह |
|---|---|
| पूर्ण विराम | (।) |
| अर्द्ध विराम | (;) |
| अल्प विराम | (,) |
| उप विराम | (:) |
| प्रश्नवाचक चिन्ह | (?) |
| योजक चिन्ह | (–) |
| कोष्ठक चिन्ह | () |
| अवतरण या उदहारणचिन्ह | ( “…” ) |
| विस्मयादिबोदक चिह्न | [ ! ] |
| लाघव चिन्ह/ संक्षेपसूचक | (०) |
| निर्देशक चिह्न | [ — ] |
| विवरण चिन्ह | ( :- ) |
| विस्मरण चिन्ह या त्रुटिपूरक चिन्ह/हंसपद | (^) |
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो विराम चिह्न युक्त वाक्य का सही विकल्प है।
अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ "
अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।
अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।''
अपाहिज ने हाथ जोड़कर कहा बाबा, मैं दुखिया हूँ।''
Correct answer
अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।''
Why this answer is correct
दिए गए विकल्पों में से विराम चिह्न युक्त वाक्य का सही विकल्प है-
अपाहिज ने हाथ जोड़कर कहा-" बाबा, मैं दुखिया हूँ।''
Key Points
Important Points
| पूर्ण विराम-(।)- लिखते वक़्त वाक्य ख़त्म होने के बाद पूर्ण विराम लगाते है। (विस्मयवाचक वाक्यों और प्रश्नवाचक वाक्यों को छोड़ कर) |
|---|
| अल्प विराम-(,)- वाक्य के बीच में विराम उत्पन्न करने वाले विराम चिन्ह को अल्प विराम कहते हैं। किसी वाक्य में दो या दो से ज़्यादा समान पद वाले शब्दों में अल्प विराम का प्रयोग किया जाता है। |
| अवतरण या उद्धरण चिन्ह-( “…” )- किसी वाक्य के खास शब्द पर जोर देने के लिए अवतरण चिह्न (”…”) का प्रयोग किया जाता है। |
| निर्देशक चिह्न (–) - किसी व्यक्ति के द्वारा कहे गए कथन को अधिकृत करने से पहले निर्देशक चिह्न का प्रयोग किया जाता है। |
Additional Information
हिंदी में प्रचलित प्रमुख विराम चिह्न -
| विराम चिन्ह का नाम | विराम-चिन्ह |
|---|---|
| पूर्ण विराम | (।) |
| अर्द्ध विराम | (;) |
| अल्प विराम | (,) |
| उप विराम | (:) |
| प्रश्नवाचक चिन्ह | (?) |
| योजक चिन्ह | (–) |
| कोष्ठक चिन्ह | () |
| अवतरण या उद्धरण चिन्ह | ( “…” ) |
| विस्मयादिबोदक चिह्न | [ ! ] |
| लाघव चिन्ह/ संक्षेपसूचक | (०) |
| निर्देशक चिह्न | [ — ] |
| विवरण चिन्ह | ( :- ) |
| विस्मरण चिन्ह या त्रुटिपूरक चिन्ह/हंसपद | (^) |
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए वाक्य के काल भेद का सही विकल्प है।
महिमा चली गई होगी।
अपूर्ण वर्तमान काल
हेतुहेतुमद भविष्य काल
संदिग्ध भूतकाल
सामान्य भूतकाल
Correct answer
संदिग्ध भूतकाल
Why this answer is correct
दिए गए वाक्य के काल भेद का सही विकल्प "संदिग्ध भूतकाल" है।
Key Points
Additional Information
काल के तीन भेद होते है-
| काल | परिभाषा | उदाहरण |
|---|---|---|
| वर्तमान काल | क्रिया के जिस रूप से वर्तमान में चल रहे समय का बोध होता है, उसे वर्तमान काल कहते है। | पिता जी समाचार सुन रहे हैं। |
| भूतकाल | क्रिया के जिस रूप से बीते हुए समय का बोध होता है, उसे भूतकाल कहते है। | वह खा चुका था। |
| भविष्यत काल | भविष्य में होनेवाली क्रिया को भविष्यतकाल की क्रिया कहते है। | वह कल घर जाएगा। |
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए शब्द -युग्म का सही अर्थ वाला विकल्प हो।
अजर - अजिर
देवता ,आँगन
हृदय, दूसरा
ऋण, चिंता
सेना, काँटा
Correct answer
देवता ,आँगन
Why this answer is correct
दिए गए शब्द -युग्म का सही अर्थ वाला विकल्प " देवता ,आँगन" है ।
Key Points
Additional Information
जैसे -
| शब्द अर्थ | शब्द अर्थ |
|---|---|
| अन्न-अनाज | अन्य – दूसरा |
| कटक - सेना | कंटक - काँटा |
| ओर - तरफ | और - दूसरा |
| उर - हृदय | ऊरू - जाँघ |
| उद्वेक - वृद्धि | उद्वेग - चिन्ता |
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए शब्द का सही तत्सम शब्द है।
खोपड़ी
लोक
व्याघ्र
लवंग
खर्पर
Correct answer
खर्पर
Why this answer is correct
दिए गए विकल्पों में से "खोपड़ी" शब्द का सही तत्सम शब्द "खर्पर" है।
Key Points"खोपड़ी" तद्भव शब्द है इसका तत्सम रूप "खर्पर" है।
अन्य विकल्प -
| तत्सम शब्द | तद्भव शब्द |
|---|---|
| लोक | लोग |
| व्याघ्र | बाघ |
| लवंग | लौंग |
Additional Information
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए शब्द का सही समानार्थी नहीं है।
कुसुमाकर
ऋतुराज
मधु
माधव
इन्द्रलोक
Correct answer
इन्द्रलोक
Why this answer is correct
दिए गए विकल्पों में से "इन्द्रलोक" शब्द कुसुमाकर का समानार्थी शब्द नहीं है।
Key Points
Additional Informationकुछ समानार्थी शब्द -
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो शुद्ध वाक्य का सही विकल्प हो।
लक्ष्मीबाई वीर थी।
मीरा विलाप करके रो रही थी।
मैं आगामी रविवार मुंबई जाऊंगा।
उसने ऐसा कार्य किया कि सब विस्मय हो गए।
Correct answer
मैं आगामी रविवार मुंबई जाऊंगा।
Why this answer is correct
दिए गए विकल्पों में से शुद्ध वाक्य का सही विकल्प है - मैं आगामी रविवार मुंबई जाऊंगा।
Key Pointsअन्य विकल्प -
| अशुद्ध वाक्य | शुद्ध वाक्य |
|---|---|
| - लक्ष्मीबाई वीर थी। | वाक्य में लिंग संबंधी अशुद्धि है। अतः वीर के स्थान पर वीरांगना होगा। - लक्ष्मीबाई वीरांगना थी। |
| - मीरा विलाप करके रो रही थी। | वाक्य में पुनरावृत्ति की अशुद्धि है। - मीरा विलाप कर रही थी। - मीरा रो रही थी। |
| - उसने ऐसा कार्य किया कि सब विस्मय हो गए। | वाक्य में विस्मय के स्थान पर विस्मित होगा।( क्रिया संबंधी अशुद्धि) - उसने ऐसा कार्य किया कि सब विस्मित हो गए। |
Additional Information
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए लोकोक्ति का सही अर्थ हो।
कबहुँ निरामिष होय न कागा
बहुत कठिन परिश्रम का थोड़ा लाभ
दुष्ट अपनी दुष्टता नहीं छोड़ता
कोई अपने माल को खराब नहीं कहता
ऊपरी वेशभूषा से किसी के अवगुण नहीं छिप जाते
Correct answer
दुष्ट अपनी दुष्टता नहीं छोड़ता
Why this answer is correct
दिए गए विकल्पों में से "कबहुँ निरामिष होय न कागा" लोकोक्ति का सही अर्थ है - "दुष्ट अपनी दुष्टता नहीं छोड़ता"
Key Pointsअन्य विकल्प -
| लोकोक्ति | अर्थ | वाक्य प्रयोग |
|---|---|---|
| खोदा पहाड़ निकली चुहिया | बहुत कठिन परिश्रम का थोड़ा लाभ। | बच्चा बेचारा दिन भर लाल बत्ती पर अख़बार बेचता रहा, परंतु उसे कमाई मात्र बीस रुपये की हुई। यह वही बात है- खोदा पहाड़ निकली चुहिया। |
| कुंजड़ा अपने बेरों को खट्टा नहीं बताता | कोई अपने माल को खराब नहीं कहता। | सब्जी वाले बासी सब्जी को भी ताजी बताकर बेचते हैं। कहावत सच है कुंजड़ा अपने बेरों को खट्टा नहीं बताता। |
| कमली ओढ़ने से फकीर नहीं होता | ऊपरी वेशभूषा से किसी के अवगुण नहीं छिप जाते। | विवेक साइकिल चोर है लेकिन सूट-बूट में रहता है। लोग उसे जानते है इसलिए उससे कतराते हैं। सच है कमली ओढ़ने से फकीर नहीं होता। |
Additional Information
कुछ लोकोक्तियाँ-
| लोकोक्तियाँ | अर्थ | वाक्य प्रयोग |
|---|---|---|
| अंधों के आगे रोना, अपना दीदा खोना | मूर्खों को सदुपदेश दे���ा या अच्छी बात बताना व्यर्थ है। | मुन्ना को समझाना तो अंधे के आगे रोना, अपना दीदा खोना वाली बात है। |
| खरी मजूरी चोखा काम | मजदूरी के तुरन्त बाद नकद पैसे मिलना। | रवि ने मालिक से कहा कि उसे अपनी मजदूरी के पैसे तुरन्त चाहिए- 'खरी मजूरी चोखा काम'। |
| कोठी वाला रोवे छप्पर वाला सोवै | अधिक धन चिन्ता का कारण होता है। | सेठ रामलाल सारी रात जागते रहते हैं, चोरों के भय से उन्हें नींद नहीं आती। सच है कोठी वाला रोवे छप्पर वाला सोवे। |
| चिराग में बत्ती और आँख में पट्टी | शाम होते ही सोने लगना। | अब राज के घर जाना बेकार है वह तो चिराग में बत्ती और आँख में पट्टी वालों में है। |
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए संधि शब्द का सही संधि - विच्छेद का विकल्प हो।
उद्धाटन =
ऊत + घाटन
उद + घटन
उत् + घाटन
उद + घाटन
Correct answer
उत् + घाटन
Why this answer is correct
दिए गए विकल्पों में से 'उद्धाटन' शब्द का सही संधि - विच्छेद "उत् + घाटन" होगा।
Key Points
Additional Information
संधि के तीन प्रकार होते हैं-
| संधि | परिभाषा | उदाहरण |
|---|---|---|
| स्वर संधि | जब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है। | - विद्या+आलय -विद्यालय |
| व्यंजन संधि | व्यंजन वर्ण के साथ स्वर वर्ण या व्यंजन वर्ण अथवा स्वर वर्ण के साथ व्यंजन वर्ण के मेल से जो विकार उत्पन हो, उसे ‘व्यंजन संधि’ कहते हैं। | - दिक+अंबर-दिगंबर - अभी+सेक- अभिषेक |
| विसर्ग संधि | जब विसर्ग के साथ स्वर या व्यंजन आ जाए तब जो परिवर्तन होता है ,वह विसर्ग संधि कहलाता है। | - मन: + अनुकूल = मनोनुकूल - नि: + पाप =निष्पाप |
निम्नलिखित प्रश्न में 'चार विकल्पों में से उस विकल्प का चयन करें जो दिए गए वाक्य के भेद का सही विकल्प है।
उसे जूते खरीदने थे, इसलिए वह बाज़ार गया।
सरल वाक्य
संयुक्त वाक्य
मिश्रित वाक्य
विधान वाचक वाक्य
Correct answer
संयुक्त वाक्य
Why this answer is correct
दिए गए वाक्य के भेद का सही विकल्प "संयुक्त वाक्य" है।
Key Points
Additional Information
रचना की दृष्टि से वाक्य तीन प्रकार के होते हैं-
| वाक्य | परिभाषा | उदाहरण |
|---|---|---|
| सरल वाक्य | सरल वाक्य वह जिसमें एक ही क्रिया होती है और एक उद्देश्य होता है और एक विधेय। इनमें एक-एक उद्देश्य अर्थात् कर्ता और विधेय अर्थात् क्रिया होती है। इसीलिए इन्हें सरल वाक्य कहा जाता है। | बादल बरसता है। |
| मिश्र वाक्य | जिस वाक्य में एक से अधिक वाक्य मिले हों किन्तु एक प्रधान उपवाक्य तथा शेष आश्रित उपवाक्य हों, मिश्रित वाक्य कहलाता है। | मेरा दृढ़ विश्वास है कि भारत जीतेगा। |
| संयुक्त वाक्य | जिस वाक्य में साधारण अथवा मिश्र वाक्यों का मेल संयोजक अवयवों द्वारा होता है, उसे संयुक्त वाक्य कहते हैं। | वह सुबह गया और शाम को लौट आया। |
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो वाक्यांश के लिए प्रयुक्त एक शब्द का सही विकल्प हो।
जिसका उल्लेख किया जा सके -
अनन्य
अकथनीय
अतुलनीय
उल्लेखनीय
Correct answer
उल्लेखनीय
Why this answer is correct
दिए गए विकल्पों में से "जिसका उल्लेख किया जा सके" वाक्यांश के लिए प्रयुक्त एक शब्द होगा - "उल्लेखनीय"
Key Pointsअन्य विकल्प -
Additional Information
वाक्यांश के लिए एक शब्द के उदाहरण-
निम्नलिखित प्रश्न में चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए संधि - विच्छेद शब्द का सही संधि का विकल्प हो।
अच् + अन्त =
अचंत
अचिन्त्य
अंत
अजन्त
Correct answer
अजन्त
Why this answer is correct
दिये गए संधि - विच्छेद शब्द का सही संधि का विकल्प "अजन्त" होगा।
Key Points
Additional Information
संधि के तीन प्रकार होते हैं-
| संधि | परिभाषा | उदाहरण |
|---|---|---|
| स्वर संधि | जब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है। | - विद्या+आलय -विद्यालय |
| व्यंजन संधि | व्यंजन वर्ण के साथ स्वर वर्ण या व्यंजन वर्ण अथवा स्वर वर्ण के साथ व्यंजन वर्ण के मेल से जो विकार उत्पन हो, उसे ‘व्यंजन संधि’ कहते हैं। | - दिक+अंबर-दिगंबर - अभी+सेक- अभिषेक |
| विसर्ग संधि | जब विसर्ग के साथ स्वर या व्यंजन आ जाए तब जो परिवर्तन होता है ,वह विसर्ग संधि कहलाता है। | - मन: + अनुकूल = मनोनुकूल - नि: + पाप =निष्पाप |
निम्नलिखित प्रश्न में ,चार विकल्पों में से उस विकल्प का चयन करें जो दिये गए शब्द का सही तद्भव शब्द है।
कोटर
खोखल
शत
कोटक
नित्य
Correct answer
खोखल
Why this answer is correct
दिए गए विकल्पों में से 'कोटर' शब्द का सही तद्भव शब्द "खोखल" है।
Key Points
Important Points
Additional Information
नीचे दिए गए गद्यांश को ध्यानपूर्वक पढ़ें और पूछे गए प्रश्नों का सर्वोत्तम उत्तर चुनें।
अपने कार्य को आप ही करना स्वावलंबन कहलाता है। बालक जब से होश संभालता है, अपने निजी कार्य स्वयं करने लगता है। इसी प्रकार यदि मनुष्य जीवन की किसी भी स्थिति में अपना कार्य स्वयं करे, तो वह स्वावलंबी कहलाता है। स्वावलंबी होना नागरिकता का महान गुण है। स्वावलंबन बड़प्पन का गुण है। कहते हैं कि एक दिन प्रसिद्ध विद्वान् ईश्वरचंद्र विद्यासागर रेलवे स्टेशन के बाहर खड़े थे। तभी भीतर से एक व्यक्ति हाथ में एक छोटा सा बक्सा लिए उनके पास आया। उन्हें साधारण वेश में देखकर भूल से कुली समझ बैठा और बोला, “मेरा सामान ले चलोगे? ” ईश्वरचंद्र बिना कुछ बोले उसका सामान उठाकर चल दिए। लक्ष्य पर पहुंचकर जब वह उन्हें मजदूरी देने लगा तो वे बोले, “ मजदूरी नहीं चाहिए। तुम अपना काम स्वयं नहीं कर सकते, इसलिए मैंने तुम्हारी सहायता कर दी है।” व्यक्ति लज्जित हुआ। जब उसे यह पता चला कि उनका कुली बंगाल का प्रसिद्ध विद्वान् है तो वह उनके पाँव में गिर पड़ा। उसने अपना कार्य आप करने की सौगंध ली
रेलवे स्टेशन के बाहर ईश्वरचंद्र विद्यासागर किस वेशभूषा में खड़े थे?
देखरेख करने वाले के रूप में
सभ्य एवं शिक्षित व्यक्ति की वेशभूषा में
कुली की वेशभूषा में
अत्यंत साधारण से दिखने वाले व्यक्ति की वेशभूषा में
Correct answer
अत्यंत साधारण से दिखने वाले व्यक्ति की वेशभूषा में
Why this answer is correct
रेलवे स्टेशन के बाहर ईश्वरचंद्र विद्यासागर अत्यंत साधारण से दिखने वाले व्यक्ति की वेशभूषा में खड़े थे।
Key Points
Additional Informationसभ्य:-
कुली:-
शिक्षित:-
नीचे दिए गए गद्यांश को ध्यानपूर्वक पढ़ें और पूछे गए प्रश्नों का सर्वोत्तम उत्त��� चुनें।
अपने कार्य को आप ही करना स्वावलंबन कहलाता है। बालक जब से होश संभालता है, अपने निजी कार्य स्वयं करने लगता है। इसी प्रकार यदि मनुष्य जीवन की किसी भी स्थिति में अपना कार्य स्वयं करे, तो वह स्वावलंबी कहलाता है। स्वावलंबी होना नागरिकता का महान गुण है। स्वावलंबन बड़प्पन का गुण है। कहते हैं कि एक दिन प्रसिद्ध विद्वान् ईश्वरचंद्र विद्यासागर रेलवे स्टेशन के बाहर खड़े थे। तभी भीतर से एक व्यक्ति हाथ में एक छोटा सा बक्सा लिए उनके पास आया। उन्हें साधारण वेश में देखकर भूल से कुली समझ बैठा और बोला, “मेरा सामान ले चलोगे? ” ईश्वरचंद्र बिना कुछ बोले उसका सामान उठाकर चल दिए। लक्ष्य पर पहुंचकर जब वह उन्हें मजदूरी देने लगा तो वे बोले, “ मजदूरी नहीं चाहिए। तुम अपना काम स्वयं नहीं कर सकते, इसलिए मैंने तुम्हारी सहायता कर दी है।” व्यक्ति लज्जित हुआ। जब उसे यह पता चला कि उनका कुली बंगाल का प्रसिद्ध विद्वान् है तो वह उनके पाँव में गिर पड़ा। उसने अपना कार्य आप करने की सौगंध ली
अनुछेद के अनुसार 'स्वावलंबन' का क्या अर्थ है?
दूसरों पर अवलंबित रहना
दूसरों की सहायता से अपना काम करना
दूसरों को अपने पर अवलंबित रखना
अपने कार्य को अपने आप करना
Correct answer
अपने कार्य को अपने आप करना
Why this answer is correct
अनुछेद के अनुसार 'स्वावलंबन' का अर्थ है- अपने कार्य को अपने आप करना
Key Pointsअवलंबित:-
परावलम्बी:-
इनमे से कौन-सा 'स्वावलंबी' का विलोम शब्द है ?
आत्मनिर्भरता
स्वयं
स्वाश्रय
परावलम्बी
Correct answer
परावलम्बी
Why this answer is correct
'स्वावलंबी' का विलोम शब्द है- परावलम्बी
Key Pointsस्वयं**-**
Additional Informationकुछ अन्य महत्वपूर्ण विलोम शब्द:-
ईश्वरचंद्र विद्यासागर के सम्मुख वह व्यक्ति बहुत लज्जित क्यों हुआ ?
क्योंकि उसका काम किसी और ने किया
क्योंकि उसने अपना काम स्वयं किया था
ईश्वरचंद्र विद्यासागर को कुली समझ लिया था
उसकी मदद करने वाले ने पैसा लेने से मना कर दिया
Correct answer
ईश्वरचंद्र विद्यासागर को कुली समझ लिया था
Why this answer is correct
ईश्वरचंद्र विद्यासागर के सम्मुख वह व्यक्ति बहुत लज्जित हुआ क्योंकि वह ईश्वरचंद्र विद्यासागर को कुली समझ लिया था
Key Pointsईश्वर चन्द्र विद्यासागर:-
Additional Informationकुली:-
अनुच्छेद के लिए उचित शीर्षक दीजिये।
अवलंबन की आवश्यकता
परावलंबन एक श्रेष्ठ गुण
स्वावलंबन एक श्रेष्ठ गुण
अवलंबन एक श्रेष्ठ गुण
Correct answer
स्वावलंबन एक श्रेष्ठ गुण
Why this answer is correct
अनुच्छेद के लिए उचित शीर्षक है- स्वावलंबन एक श्रेष्ठ गुण
Key Pointsस्वावलंबन:-
Additional Informationअवलंब:-
श्रेष्ठ:-
What is the curved surface area of the cone in general form?
πr (r + l)
πrh
πrhl
πrl
Correct answer
πrl
Why this answer is correct
Explanation:
The Curved Surface Area of Cone is πrl
Where r is the radius and l is the slant height of the cone
Hence, The Correct Answer is option 4.
What will be the rank of every non singular matrix of order n?
2n + 1
n + 1
n
2n
Correct answer
n
Why this answer is correct
Concept use:
Rank of the Matrix : The Smallest Sub Matrix from the Given Marix having Determinant non zero then order of that matrix is rank.
Non Singular Matrix: The Matrix having determinant non zero.
Explanation:
Given that Matrix is Non Singular means Determinant non zero
means Rank of Matrix is n.
Since, The Non Singular Matrix is of order n.
Hence, The Correct Option is 3.
2587322568103 is a number, which will be divisible by which number?
2
7
6
11
Correct answer
7
Why this answer is correct
Concept -
(i) A number is divisible by 2 if its last digit is even.
(ii) A number is divisible by 6 if the number is divisible by 2 and 3 both.
(iii) A number is divisible by 3 if the sum of all the digits of the number is divisible by 3.
(iv) A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11 .
Explanation -
For Option (1) -
A number is divisible by 2 if its last digit is even.
The last digit of 2587322568103 is 3, which is odd.
Therefore, 2587322568103 is not divisible by 2.
For Option (2) -
There isn't a simple divisibility rule for 7, but you could use long division. In this case, 2587322568103 is divisible by 7.
For Option (3) -
A number is divisible by 6 if the number is divisible by 2 and 3 both.
The sum of the digits of 2587322568103 is 63, which is divisible by 3.
But this number is not divisible by 2.
Therefore, 2587322568103 is not divisible by 6.
For Option (4) -
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11 .
However, in this case, the difference is not divisible by 11.
So, the option(2) is correct.
The curve given by xy = 15 is symmetrical about what?
x axis
about the line x = y
about the origin
y axis
Correct answer
about the line x = y
Why this answer is correct
Concept use:
Symmetry defines that the shape is identical on both sides when it is divided by a line. The symmetry of different shapes, regular or irregular.
Explanation:
The curve given by xy = 15 is symmetrical about about the line x = y.
Option (2) is true.
A polynomial with real coefficients of n degree has ______ roots?
n imaginary roots
n real roots
n (may be real or imaginary)
n - 1 roots
Correct answer
n (may be real or imaginary)
Why this answer is correct
Concept use:
Fundamental Theorem of Algebra States that A polynomial with real coefficients of n degree has n roots
Explanation:
A polynomial with real coefficients of n degree has n roots may be real or imaginary
For example x2 - 1 having two roots (equal to its degree) and real
x2 + 1 having two roots (equal to its degree) and real and imaginary.
Hence, The Correct Option is 3.
Find total number of asymmetric relations on a set A = {e, f, g} ?
34
64
27
128
Correct answer
27
Why this answer is correct
Concept use:
The Total Number of asymetric relation is 3(n^2 - n)/2
Explanation:
total number of asymmetric relations on a set A = {e, f, g}
The Total Number of asymetric relation is 3(3^2 - 3)/2 = 3(9-3)/2 = 33 = 27
Hence, The Correct Answer is option 3.
Euler function tends to infinity if which condition follows?
n tends to zero
n tends to infinity
n tends to a positive limit
n tends to a negative limit
Correct answer
n tends to infinity
Why this answer is correct
Explanation:
Euler's totient function ϕ(n) counts the number of positive integers less than n that are coprime to n.
Euler function tends to infinity if n tends to infinity.
(2) is correct
Which of the following properties does not possess?
[x] = x if x is integer
[-x] = -[x] - 1 if x is integer
[x + y] > [x] + [y]
[- x] = [x] if x is integer
Correct answer
[- x] = [x] if x is integer
Why this answer is correct
Concept use:
The greatest integer function is a function that results in the integer nearer to the given real number. It is also called the step function. The greatest integer function rounds off the given number to the nearest integer.
Explanation:
The greatest integer function of x is given by
[x] = x if x is integer
[-x] = -[x] - 1 if x is integer
Also, [x + y] > [x] + [y].
So, options (1), (2), (3) are satisfied.
But option (4) is not true as
For x = 2
[-x] = [-2] = -2
and [2] = 2
Hence [- x] ≠ [x] if x is integer.
Find the middle term of an AP if it is given that the sum of three numbers in the AP is 15?
10
5
15
20
Correct answer
5
Why this answer is correct
Explanation:
Let's represent the three consecutive terms as a, a + d, and a + 2d, where a is the first term, and d is the common difference between the terms.
The sum of the three consecutive terms is 15.
We can write the equation:
a + (a + d) + (a + 2d) = 15
3a + 3d = 15
a = (15 - 3d) / 3
Let a = 5 because if we substitute d = 0, then a = 5, and the three terms become 5, 5, and 5, whose sum is 15.
While taking a + d = 15, 20, 10 then This will not form Arithmetic Progression.
Hence, the middle term (a + d) = 5 + 0 = 5
Hence, the correct option is: 2) 5
Find the gradient of the scalar field if f(x, y) = x + y at (1, 2)?
j + 2i
i + 2j
j - i
i + j
Correct answer
i + j
Why this answer is correct
Explanations:
The gradient of a scalar field f(x, y) is defined as the vector (df/dx, df/dy), and it gives the direction of the maximum rate of increase of the function.
Let's proceed by taking the required partial derivatives for f(x,y) = x + y:
df/dx = 1 df/dy = 1
So the gradient of the function at a give point, (∇f) is given by (∇f) = i*(df/dx) + j*(df/dy).
So, (∇f) = i1 + j1 = i + j.
The gradient of the function at any point is a constant vector i + j, and this also holds at the point (1,2).
How many subsets of the set A will there be if A = {1, 2, 3, 4)?
8
2
4
16
Correct answer
16
Why this answer is correct
Concept use:
The Number of Subset of Set A is 2n where, n is the Cardinality of the set.
Explanation:
Given Set A = {1, 2, 3, 4}
The Number of Subset of A is 24 = 16
Hence, The Correct Answer is Option 4.
If the inner product between the vectors vanishes then what will be the angle between them?
45
90
35
0
Correct answer
90
Why this answer is correct
Explanation:
Real and complex inner products are generalizations of the real and complex dot products, respectively.
■
An inner product space is a vector space that possesses three operations: vector addition, scalar multiplication, and inner product.
■
For vectors x, y and scalar k in a real inner product space, 〈x, y〉 = 〈y, x〉, and 〈x, ky〉 = k 〈x, y〉.
■
For vectors x, y and scalar k in a real or complex inner product space, 〈kx, y〉 = k 〈x, y〉.
■
For vectors x, y and scalar k in a complex inner product space,
〈 x, y 〉 = 〈 y, x 〉
〈 x, ky 〉 = k 〈 x, y 〉 and ||kx|| = | k|| x is = ∥kx∥=|k|∥x∥∥kx∥=|k|∥x∥∥kx∥=|k|∥x∥‖kx‖=|k|‖x‖ .
■
The length of a vector x in an inner product space is ||x|| = 〈 x, x 〉, and the distance between vectors x and y in an inner product space is ||x−y||||x−y||||x−y||||x−y|| .
■
The angle θ between two vectors in a real inner product space is defined as the angle between 0 and π such that θ = 〈 x, y 〉 / ||x|| ||y||).
■
Orthogonal and orthonormal sets of vectors, and orthogonal complements of subspaces, are defined for inner product spaces analogously as for real vector spaces.
Thus, If the inner product between the vectors vanishes then what will be the angle between them is zero.
because cosθ = 0 is possible only when θ = 90°.
The rank of a matrix in echleon form is equal to:
number of zero rows of the matrix
order of matrix
number of variables
Number of non zero rows of the matrix
Correct answer
Number of non zero rows of the matrix
Why this answer is correct
Explanation:
A matrix is in reduced row echelon form if it is in row echelon form, the first nonzero entry of each row is equal to 1
and the ones above it within the same column equal 0. The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it.
Rank of that matrix is equal to the Number of Non Zero rows of the matrix.
Hence, The Correct Option is 4.
In what range does sec(x) become invertible?
R
R - (-1,1)
R - {0}
Z
Correct answer
R - (-1,1)
Why this answer is correct
Explanation:
sec x will not be defined at the points where cos x is 0. Hence, the domain of sec x will be R-(2n+1)π/2, where n∈I. The range of sec x will be R- (-1,1).
The domain of sec inverse x is given by (-∞, -1] U [1, ∞) and its range is [0, π/2) U (π/2, π].
Hence, Sec(x) become invertible R - (-1, 1)
Hence, The Correct option is 2.
What is the volume of curve between the ordinate 0 to 4 around the curve x = y?
31.33
21 π
21.33 π
31 π
Correct answer
21.33 π
Why this answer is correct
Concept:
Suppose y = f(x) is non-negative and continuous on [a,b]. If the region bounded above by the graph of f, below by the x-axis, and on the sides by x = a and x = b is revolved around the x-axis, the volume V of the generated solid is
V =
Explanation:
Volume of the curve between the ordinate 0 to 4 around the curve x = y is
V = = π = 21.33π
Option (3) is true.
At what point are the tangents to the asymptotes curve?
Infinity
Three point
Two points
One point
Correct answer
Infinity
Why this answer is correct
Concept use:
An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
Explanation:
An asymptote of a curve is a line that is tangent to the curve at a point at infinity.
Option (1) is true.
For any matrix to be in row reduced form which of the following conditions is not satisfied?
Each leading one is to the right of one preceding row
Any row if has zero is at the bottom
zero row is at the top of the matrix
any leading entry is one
Correct answer
zero row is at the top of the matrix
Why this answer is correct
Explanation:
The conditions for a matrix to be in row echelon form are
(i) All non-zero rows should be above all zero rows.
(ii) 1st non-zero element of each row should be 1
(iii) Number of zeros before the 1st non-zero element in 1st, 2nd, 3rd …. rows should be increasing.
Therefore the incorrect option is option (3)
If the discriminant D > 0 then what can you say about the nature of the root?
No real root
Same root
Exclusive genuine root
Fictional root
Correct answer
Exclusive genuine root
Why this answer is correct
Explanation:
The general form of a quadratic equation is ax2 + bx +c = 0, a ≠ 0
whose discriminant (D) = b2 - 4ac.
If D > 0 then the roots are real and unequal i.e., roots are exclusive genuine roots.
If D < 0 then roots are complex conjugate.
If D = 0 then roots are equal.
Option (3) is true.
If A = 3i + j + k; B = 5i + j – k; C = i + j - k then find the volume of parallelogram if A, B, and C are the sides of the parallelepiped respectively.
16
32
0
8
Correct answer
8
Why this answer is correct
Explanation:
A = 3i + j + k; B = 5i + j – k; C = i + j - k
The volume of parallelogram if A, B, and C are the sides of the parallelepiped
= \(\begin{vmatrix}3&1&1\5&1&-1\1&1&-1\end{vmatrix}\)
= 3(-1 + 1) +1(-1 + 5) +1(5 - 1)
= 0 + 4 + 4 = 8
Option (4) is true.
What is the scope of the definition of exponential function?
Whole numbers
Integers
Rational Numbers
Real numbers
Correct answer
Real numbers
Why this answer is correct
Explanation -
The scope of the definition of an exponential function (f(x) = ex) encompasses real numbers.
Exponential functions can be defined for any real number base raised to any real number exponent.
Therefore, the correct answer is (4).
Which model is the one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables?
continuous model
discrete model
deterministic model
probability model
Correct answer
deterministic model
Why this answer is correct
Concept -
A deterministic model is a mathematical representation where the outcome is completely determined by the initial conditions and the parameters of the model.
In other words, there is no randomness involved, and given the same inputs, the model will always produce the same outputs.
This makes deterministic models predictable and suitable for situations where outcomes can be precisely calculated based on known factors.
Explanation -
The model described in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables is a "deterministic model."
Therefore, the correct option is (3)
Let f be a sequence of bounded functions and the series given by f is uniformly continuous to some function say g then ______.
g is bounded
g occurs virtually to follow 1
g is infinite
g is unbounded
Correct answer
g is bounded
Why this answer is correct
Concept -
If a sequence of bounded functions f converges uniformly to some function g, then the limit function g is also bounded. This property follows from the fact that uniform convergence preserves boundedness of functions.
Explanation:
Let f be a sequence of bounded functions and the series given by f is uniformly continuous to some function say g then bounded.
(1) is correct
The general solution of the equation y" (x) = 0 with the initial value problem s.t. at x = 0; y = 0 and y' = 0 is?
y(x) = x2/2
y(x) = 0
y(x) = x
y(x) = x/2
Correct answer
y(x) = 0
Why this answer is correct
The given differential equation is y''(x) = 0.
Integrate both sides y'(x) = c1'
again Integrate both sides y(x) = c1''x + c1
y(0) = 0 = c1'' × 0 + c1 ⇒ c1 = 0
y(x) = c1' x by y' = 0 we get c1' = 0
Hence, y(x) = 0
If a function f is from to and a be a point which is given convergent to us, then what can we say about the sequence which is generated by its image i.e. f(a)
it is divergent
it is convergent
it occurs finitely
it is bounded
Correct answer
it is convergent
Why this answer is correct
Concept -
If a function f is continuous at a point a and the sequence an converges to a, then the sequence of function values f(an) converges to f(a). This is a fundamental property of continuous functions, known as the continuity of limits.
Explanation:
If a function f is from to and a be a point which is given convergent to us, then the sequence is convergent which is generated by its image i.e. f(a)
(4) is correct
Which of the following is used in mathematical modelling in Boolean algebra?
mines geometry
constructive solid geometry
lines figure
complex analysis
Correct answer
constructive solid geometry
Why this answer is correct
Explanation -
Constructive solid geometry (CSG) is a technique used in computer graphics and mathematical modeling to represent complex shapes and objects by combining simple geometric primitives like cubes, spheres, and cylinders using Boolean operations such as union, intersection, and difference.
In the context of Boolean algebra, CSG is often employed to create models and representations of logical operations and relationships.
Hence Option (2) is correct.
The graph of the solution of the curve given y = f (x), where y is the function of x, also x and y are real numbers and is termed as
functional curve
bitsman curve
solution curve
polynomial curve
Correct answer
solution curve
Why this answer is correct
Explanation:
The graph of the solution of the curve given y = f (x), where y is the function of x, also x and y are real numbers and is termed as solution curve.
Option (3) is true.
How many singular solutions occur for nth order ordinary linear diffrential equation?
no singular solutions
three
two
one
Correct answer
no singular solutions
Why this answer is correct
Explanation -
The number of singular solutions for an ordinary differential equation depends on the nature of the equations. But usually, for an ordinary linear differential equation of order 'n', the total number of independent solutions (including both regular and singular) is 'n'.
Not all differential equations have singular solutions. Like ordinary linear differential equations with constant coefficients do not have singular solutions.
Hence option (i) is correct.
What type of curve is obtained in exponential growth?
S shaped curve
J shaped curve
T shaped curve
W shaped curve
Correct answer
J shaped curve
Why this answer is correct
Explanation:
Graph for exponential growth is
i.e., the curve obtained in exponential growth is J shaped curve.
Option (2) is true.
Which model accounts for time dependent change of a model?
dynamic model
bi-model
generalized model
static model
Correct answer
dynamic model
Why this answer is correct
The correct answer is the dynamic model.
Key Points
Here are some examples of dynamic models:
Dynamic models can be used to predict future outcomes, make informed decisions, and design systems that are more efficient and effective.
Every bounded sequence with a unique limit point is ______?
convergent
doesn't exist
divergent
oscillatory
Correct answer
convergent
Why this answer is correct
Concept -
Every bounded sequence with a unique limit point is Convergent.
Explanation:
Every bounded sequence with a unique limit point is convergent
(1) is correct
The sum of the series n(Sin(n)) is ______.
convergent
oscillates infinitely
divergent
oscillates finitely
Correct answer
divergent
Why this answer is correct
Concept:
A series ∑ an is convergent then = 0 i.e, if ≠ o then the series ∑ an divergent.
Explanation:
The sum of the series n(sin(n)) = is divergent.
≠ 0
Hence is diveregent.
Option (3) is true.
What condition is satisfied if sequence of functions f is said to be uniformly bounded?
f(x) converge to a finite point
f(x) converge to an infinite point
|f(x)| = M for some constant M
|f(x)| ≤ M for some constant M and for all values of x
Correct answer
|f(x)| ≤ M for some constant M and for all values of x
Why this answer is correct
Concept -
A sequence of functions fn(x) is said to be uniformly bounded if there exists a constant M such that the absolute value of each function fn(x) in the sequence is less than or equal to M for all n and for all x in the domain of the functions.
Explanation:
A sequence of functions f(x) is said to be uniformly bounded if there exist a constat M such that |f(x)| ≤ M for all values of x.
(4) is correct
The greatest limit point of a bounded sequence is called
minimum point of f
limit superior of f
limit inferior of f
maximum point of f
Correct answer
limit superior of f
Why this answer is correct
Concept -
If a be the term of the sequence and it repeats infinite times in the sequence then a is the limit point for the sequence. and limit superior ( lim sup ) is greatest limit point of the sequence.
Explanation:
The greatest limit point of a bounded sequence is called limit superior of f
(2) is correct
The limit of the function f (x, y) = x + y - 6 at x = 1; y = 2 is ?
-3
-4
4
3
Correct answer
-3
Why this answer is correct
Explanation -
We have the function f (x, y) = x + y - 6
The limit of the function f(x, y) = x + y - 6 as x → 1 and y → 2,
we simply substitute these values into the function:
f(1, 2) = 1 + 2 - 6 = -3
So, the limit of the function f(x, y) = x + y - 6 as x → 1 and y → 2 is -3.
Hence Option(1) is correct.
Change in number of individuals in population over time is called?
remainder rate
immigration rate
mortality rate
Population growth rate
Correct answer
Population growth rate
Why this answer is correct
Explanation:
Let N be the number of population then the changes in number of individuals in population over time i.e., is called population growth rate.
where as the mortality or death rate is the proportion of a population who die of a defined cause.
Option (4) is true.
Any non-empty set of R which is bounded from above has ______?
An infinite exists
Both exist finitely
l.u.b
g.l.b
Correct answer
l.u.b
Why this answer is correct
Explanation:
Any non-empty set of R which is bounded from above has least upper bound (l.u.b) and the non-empty set of R which is bounded from below has the greatest lower bound (g.l.b)
Let's consider the set �={�∈�:�<3} A = {x ∈ R : x < 3}. This set contains all real numbers that are strictly less than 3.
The set �����
A is bounded from above because 3 is an upper bound for �����[Math Processing Error]
A. Any number less than 3 is also an upper bound.
However, the least upper bound (supremum) of � A is 3, because it is the smallest real number greater than or equal to all elements of ����
A. No number less than 3 is an upper bound for �����[Math Processing Error]
A.
Option (3) is true.
When the per capita rate of increase (r) takes the same positive value regardless of the population size, then we get which growth?
transversal growth
exponential growth
both logistic and exponential
logistics growth
Correct answer
exponential growth
Why this answer is correct
Concept -
Exponential growth occurs when the per capita rate of increase (r) remains constant, leading to a growth rate that accelerates over time and results in a continuously increasing population size.
This growth pattern is characteristic of scenarios where resources are abundant and population growth is not limited by factors such as competition or resource depletion.
Explanation:
When the per capita rate of increase (r) takes the same positive value regardless of the population size, then we get exponential growth.
Option (2) is true.
Pick the wrong statement?
Any Cauchy sequence is bounded.
In real every bounded monotonic sequence is divergent
Any real Cauchy sequence is convergent
Any convergent sequence is Cauchy
Correct answer
In real every bounded monotonic sequence is divergent
Why this answer is correct
Explanation:
We know that
Any cauchy sequence is bounded.
In real every bounded monotonic sequence is convergent.
Any real Cauchy sequence is convergent
Any convergent sequence is cauchy
Hence (2) is the wrong statement.
If cardinality of a set A is 6 and that of set B is 7 then find the Cardinality of A Δ B?
7
35
5
can not be determined
Correct answer
can not be determined
Why this answer is correct
Concept use:
n(A Δ B) = n(A ∪ B) - n(A ∩ B)
Explanation:
Given cardinality of A, n(A) = 6, cardinality of B, n(B) = 7.
n(A Δ B) = n(A ∪ B) - n(A ∩ B) = n(A) + n(B) - n(A ∩ B) - n(A ∩ B)
Here cardinality of A ∩ B i.e., n(A ∩ B) is not given.
So, the cardinality of A Δ B can not be determined.
Option (4) is true
What is the limit point of the sequence < f > = 1?
2
infinity
0
1
Correct answer
1
Why this answer is correct
Concept -
If a be the term of the sequence and it repeats infinite times in the sequence then a is the limit point for the sequence.
Explanation:
<f> = 1
This implies that it is constant sequence.
Hence limit point is 1
(4) is correct
Let f and g be two uniformly continuous functions on interval I and also each function is bounded on I, then what can you not say about product f.g?
f.g is continous
f.g is bounded
f.g is integrable
f.g is uniformly continous on R
Correct answer
f.g is uniformly continous on R
Why this answer is correct
Concept -
Let f and g be two uniformly continuous functions on interval I and also each function is bounded on I then
(i) f.g is continous
(ii) f.g is bounded
(iii) f.g is integrable
Explanation:
Let f and g be two uniformly continuous functions on interval I and each function is bounded on I, then f.g may not be uniformly continous on .
Counter example -
If f(x) = x and g(x) = x and the interval I = [0,1]
Now f and g is uniformly continuous on R as well but f.g = x2 is not uniformly on .
(4) is correct
If f(x, y) = 0 then find the directional derivative at c = (0, 0) along the direction u = (a, b)?
1
2
0
3
Correct answer
0
Why this answer is correct
Concept:
Directional derivative at c = (x0, y0) along the direction of u = (a, b) is
Duf =
Explanation:
f(x, y) = 0
Hence directional derivative at c = (0, 0) along the direction u = (a, b)
Duf = = = 0
(3) is correct
Find the value of where F(x, y, z) = (y + z, z + x, x + y)
-1
2
0
1
Correct answer
0
Why this answer is correct
Concept -
The curl of a vector field is given by the vector cross product of the del operator with , i.e., . It is computed as:
=
Explanation -
The form f corresponds to a vector field .
Now P = y+z , Q = z+x , and R = x+y into the formula for the curl:
⇒ = 1 - 1 = 0
⇒ = 1 - 1 = 0
⇒ = 1 - 1 = 0
Put these values in the given formula we get -
Hence, the curl of is:
Now
Hence Option(3) is correct.
The function f(x) = x for every x in R which is continuous in R is called
Riemann function
Constant function
Identity function
Dirichlet function
Correct answer
Identity function
Why this answer is correct
Explanation:
The function f(x) = x for x ∈ R is called identity function which is continuous everywhere.
An example of the identity function would be �(�)=��(�)=��(�)=�
f(x) = x where ���
x belongs to the set of real numbers ���
R. For instance, if you plug in �=5�=5�=5
x = 5, the function would output �(5)=5�(5)=5�(5)=5
f(5) = 5.<br>
Similarly, for any other real number input, the output will be the same as the input due to the nature of the identity function.
Option (3) is true.
Which condition is not required in checking for Taylor's theorem?
It's (n -1)th derivative is derivable on (a, b)
It's (n - 1)th derivative is continuous on [a, b]
f is necessarily bounded
there exists a real number between a and b
Correct answer
f is necessarily bounded
Why this answer is correct
Concept -
Taylor's theorem -
Let f(x) be a function that is n times differentiable on an interval containing [a, b], and let x = c be a point within that interval. Then, there exists a real number ξ between a and b such that the Taylor polynomial of degree n for f(x) centered at c can be expressed as:
where:
is the Taylor polynomial of degree n for f(x) centered at c,
Rn(x) is the remainder term, given by .
The remainder term Rn(x) quantifies the difference between the actual function f(x) and its Taylor polynomial approximation Pn(x). The presence of ξ ensures that Taylor's theorem guarantees an exact equality at some point between a and b, assuming the function f(x) satisfies the conditions of the theorem.
Explanation:
According to Taylor's theorem, f is not necessarily to be bounded
Hence condition (3) is not required
When will be matrix of derivative of f given by f(x, y) = (x - y, xy) will be singular?
if x = y
if x = 0
if x = -y
if y = 0
Correct answer
if x = -y
Why this answer is correct
Explanation:
f(x, y) = (x - y, xy)
i.e., f1 = x - y and f2 = xy
= 1, = -1, = y, = x
matrix of derivative of f will be zero if
\(\begin{vmatrix}{\partial f_1\over \partial x}&{\partial f_1\over \partial y}\{\partial f_2\over \partial x}&{\partial f_2\over \partial y}\end{vmatrix}\) = 0
⇒ \(\begin{vmatrix}1&-1\y&x\end{vmatrix}\) = 0
⇒ x + y = 0
⇒ x = -y
Option (3) is true.
The oscillation of a bounded function f on an interval [a, b] is the ______ of the set {|f(x) - f(y)|} of the numbers.
supremum
infimum
maximum
minimum
Correct answer
supremum
Why this answer is correct
Concept -
The oscillation of a bounded function on an interval measures how much the function can vary within that interval. It is defined as the supremum (least upper bound) of the set of absolute differences between the function values at different points within the interval. In simpler terms, it represents the maximum distance between any two points on the graph of the function within the given interval.
Explanation:
The oscillation of a bounded function f on an interval [a, b] is the supremum of the set {|f(x) - f(y)|} of the numbers.
(1) is correct
What is the interval of Taylor series expansion of tan(x)?
(-π, π)
(0, 90)
(-90, 90)
Infinite field
Correct answer
(-90, 90)
Why this answer is correct
Concept -
Explanation -
The Taylor series expansion of tan(x) is centered around x = 0 and it is given by:
This Taylor series expansion is valid for all x such that |x| < , which means it converges within the interval .
Beyond this interval, the tangent function has singularities (vertical asymptotes) at where n is an integer,
so the Taylor series does not converge beyond .
Hence Option (3) is correct.
The functions which are present on one side of Green's theorem are of which kind?
Continuous partial derivative
only partial derivatives
discrete derivatives
complete derivatives
Correct answer
Continuous partial derivative
Why this answer is correct
Explanation:
Let C be the positively oriented, smooth, and simple closed curve in a plane, and D be the region bounded by the C. If P and Q are the functions of (x, y) defined on the open region, containing D and have continuous partial derivatives, then Green’s theorem is stated as
=
i.e., the functions which are present on one side of Green's theorem are Continuous partial derivative
Option (1) is true.
Which theorem is valid in calculating integral for a multiple connected domain R?
Green's theorem
Stokes theorem
Iterated integrals
Gauss divergence theorem
Correct answer
Green's theorem
Why this answer is correct
Explanation:
Let C be the positively oriented, smooth, and simple closed curve in a plane, and D be the region bounded by the C. If P and Q are the functions of (x, y) defined on the open region, containing D and have continuous partial derivatives, then Green’s theorem is stated as
=
Therefore, Green's theorem is valid in calculating integral for a multiple connected domain R.
Option (1) is true.
While finding maximum value of a function what will we get in the case if it's second derivative becomes zero?
we get maxima at that point
we get minima at that point
we get possible inflection point
we get both maxima and minima
Correct answer
we get possible inflection point
Why this answer is correct
Explanation:
Let f(x) be a function. Then we get the critical points from f'(x) = 0.
If f''(x) < 0 at the critical point then we get maxima at that point.
If f''(x) > 0 at the critical point then we get minima at that point.
If f''(x) = 0 at the critical point then we get possible inflection point.
Hence while finding maximum value of a function, if it's second derivative becomes zero we get possible inflection point.
Option (3) is true.
Let a lie in the domain of a function f such that for all x in the domain, f(x) < f(a)
f is said to have a minimum value at x = a.
f is said to have a maximum value at x = a.
f is unbounded
f has both a maximum and a minimum value at x = a.
Correct answer
f is said to have a maximum value at x = a.
Why this answer is correct
Explanation:
A function f(x) is said to have a maximum at a point x = a if f(x) < f(a) for all x and said to have a minimum at a point x = a if f(x) > f(a) for all x.
Hence option (2) is true.
The sequence given by interval [0,1] is ______.
Bounded
unbounded
connvergent
divergent
Correct answer
Bounded
Why this answer is correct
Explanation:
The sequence given by interval [0,1] is bounded with lower bound 0 and upper bound 1 because all the elements of the sequence belongs to [0,1].
Hence the sequence is bounded.
The sequence is need not be convergent if you take
(1) is correct
If y is expressed in terms of a variable x as y = f(x), then y is called what?
explicit function
convergent function
implicit function
divergent function
Correct answer
explicit function
Why this answer is correct
Explanation:
An explicit function is an algebraic function in which the output variable (dependent variable) can be written explicitly only in terms of the input variable (independent variable).
Hence, The Correct Option is 1.
How do we find the volume of a solid surface?
By finding its line integral
By double integrating it
By integrating over the surface
By integrating it threefold over the surface
Correct answer
By integrating it threefold over the surface
Why this answer is correct
Concept -
The volume of a solid surface, we integrate over the surface. This involves calculating the triple integral of the function representing the surface over the region it occupies in three-dimensional space.
The integration process considers the infinitesimal volume elements throughout the surface to determine the total volume enclosed by the surface.
Explanation:
To find the volume of a solid surface we integrate the threefold over the surface.
Option (4) is true.
The necessary and sufficient condition for a function f to be Riemann integrable is that for every partition P for every ε > 0; which of the following condition must occur?
Upper and lower sum vanishes
|U(f, P) - L(f, P)| > ε
|U(f, P) - L(f, P)| = ε
|U(f, P) - L(f, P)| < ε
Correct answer
|U(f, P) - L(f, P)| < ε
Why this answer is correct
Concept -
Theorem -
f(x) is integrable on [a,b] if and only if for every ϵ > 0 there exist a partition P such that U(P,f) - L(P,f) < ϵ
Explanation:
The necessary and sufficient condition for a function f to be Riemann integrable is that for every partition P for every ε > 0, |U(f, P) - L(f, P)| < ε where U(P, f) is upper Reimann sum and L(P. f) is Reimann sum.
(4) is correct
Pick the correct statement.
If function is increasing in interval it is not increasing in each of its subinterval
Every continous function is not Riemann integrable
Every monotonic increasing function f is not Riemann integrable
Every continuous function is Riemann integrable
Correct answer
Every continuous function is Riemann integrable
Why this answer is correct
Concept -
(i) Every continuous function is Riemann Integrable because it has 0 discontinuous points.
(ii) Every monotone function has at most countable discontinuity.
(iii) If the function has countable discontinuity then the function is Riemann Integrable.
Explanation:
For option (1) -
If function is increasing in interval then it is increasing in each of its subinterval.
So, it's a false option.
Hence by using above concept we get -
option(4) is correct.
Find the simultaneous limit of function y sin(1/x) ?
1
0
3
2
Correct answer
0
Why this answer is correct
Explanation:
Simultaneous limit of the function
=
=
=
= 0
Option (2) is true.
Which of the following is not the application of Taylor's series?
It is used in optimization techniques
It reduces mathematical proofs
It is used to find value of whole function
It fails to solve power flow analysis
Correct answer
It fails to solve power flow analysis
Why this answer is correct
Explanation:
It is used in optimization techniques: True. Taylor series expansions are often used in optimization algorithms, especially in numerical optimization methods, to approximate functions and iteratively find optimal solutions.
It reduces mathematical proofs: True. Taylor's series can be used to simplify mathematical proofs by providing accurate approximations of functions and enabling easier manipulation of expressions.
It is used to find the value of the whole function: True. Taylor series can be used to approximate the value of a function at a point based on its derivatives at that point, providing a way to estimate the behavior of the entire function.
It fails to solve power flow analysis: False. Taylor series expansions can be used in power flow analysis and related engineering applications to linearize complex nonlinear systems and make them more manageable for analysis and simulation.
Hence, The option that does not represent a typical application of Taylor's series is (4) It fails to solve power flow analysis.
If r = 2xyi + j + kl then the value of curl(r) is
-2yk
-2xk
0
-2zk
Correct answer
-2xk
Why this answer is correct
Concept -
The curl of a vector field
is given by:
Explanation -
We have, , so:
P(x, y, z) = 2xy
Q(x, y, z) = 1
R(x, y, z) = l
Now, let's compute the partial derivatives:
Now, plug these derivatives into the curl formula:
=
So, the value of is .
Every element of a group G when expressed as internal Direct product of a, b, c, ... z if and only of every element is uniquely expressed as ?
G = a. b. c ... z
G = a - b - c ... -z
G = a + b - c. .. z
G = a + b + c +.... + z
Correct answer
G = a. b. c ... z
Why this answer is correct
Explanation:
To express a group G as an internal direct product of subgroups a, b, c, ... z, you typically mean that each element of G can be represented uniquely as a product of elements from each of these subgroups.
This implies that every element g in G can be expressed uniquely as g = a . b . c . ... . z, where a is from subgroup a, b is from subgroup b, and so forth.
So the correct option is:
G = a . b . c ... z
This expression represents the unique product from each subgroup. Note that the operation here isn't necessarily numerical multiplication— it's the group operation, whatever that might be in the specific context of the group in question.
The expansion of power series having R as the radius of convergence and x, a be any two points in R, converges if ______.
|x - a| > R
|x - a❘ = R
nowhere convergent
|x - a| < R
Correct answer
|x - a| < R
Why this answer is correct
Explanation:
The expansion of power series having R as the radius of convergence and x, a be any two points in R, converges if |x - a| < R
(4) is correct
If we are given two overlapping sets A and B in metric space then what can we say about d(A, B)?
infinity
doesn't exist
zero
finite
Correct answer
zero
Why this answer is correct
Explanation -
In a metric space, the distance between two sets A and B, denoted as d(A, B), is defined as d(A, B) = inf{d(a, b) : a ∈ A, b ∈ B}
In other words, the distance between A and B is the infimum (greatest lower bound) of the distances between each element of A and each element of B.
However, when the sets A and B overlap, meaning they have at least one common element, the distance between them is 0. This is because there exists at least one pair (a,b) such that a = b and both are in A and B. And as per the properties of metric space, the distance between identical points is 0 (d(a, b) = d(a, a) = 0), hence d(A, B) = 0.
Hence option(iii) is correct.
Find the limit point of the sequence <1, 2, 1/2, 3, 1/3..... >
3
0
2
1
Correct answer
0
Why this answer is correct
Concept use:
The limit of a sequence is a point such that every neighborhood around it contains infinitely many terms of the sequence
Explanation:
<1, 2, 1/2, 3, 1/3..... >
The Sequence having even terms as 1/2, 1/3, 1/4, ..... which tends towards 0
Hence, Zero is the Limit point of the Sequence because it Contains infinitely many terms in the neighborhood.
The Sequence has odd terms such as 1, 2, 3, 4, ..... which goes to infinity
Hence, The Limit point of the Sequence is Zero
Hence, The correct Answer is option 2.
If f is a continuous function from X to Y, then this property is called?
completeness of metric space
distance variant
continuous invariant
continous variant
Correct answer
continuous invariant
Why this answer is correct
Explanation -
If f is a continuous function from one metric space X to another metric space Y, then the property being referred to is typically called the "Continuity of f". In more precise terms, a function f: X → Y is continuous if for any open set O in Y, the preimage is an open set in X. This use of open sets is a standard way to define continuity in topology and metric spaces then the property being referred the "Continuous invariant of f".
Hence option (iii) is correct.
A group is called abelian if it satisfies ______ property.
associative property
existence of identity
existence of inverse
commutative property
Correct answer
commutative property
Why this answer is correct
Concept -
An abelian group is a set, G, with an operation (commonly denoted as '+'), satisfying these properties:
Closure: If a and b are in G, then a+b is in G.
Associativity: For all a, b, c in G, (a+b)+c equals a+(b+c).
Identity: There's an element '0' in G, such that for all a in G, 0+a and a+0 equals a.
Inverse: For every a in G, there exists a '-a' in G, such that a + (-a) and (-a) + a equals 0.
Commutativity: For all a, b in G, a+b equals b+a.
Explanation-
A group satisfy all four property like closure, Associativity, Identity and Inverse. In question we have a group so if we add the commutative property then it will be Abelian group.
Hence option (iv) is correct.
Every absolutely convergent improper integral is ______.
infinite
oscillatory
divergent
convergent
Correct answer
convergent
Why this answer is correct
Concept -
Every absolutely convergent improper integral is always convergent but converse is not true in general.
Explanation:
Every absolutely convergent improper integral is convergent.
(4) is correct
Which statement states that "Every complete metric space is of second category"?
Baire category theorem
Cantor Theorem
Fundamental theorem
Baire sandwich theorem
Correct answer
Baire category theorem
Why this answer is correct
Explanation -
The statement given in the question is known as the Baire Category Theorem. In its simplest form, it states that:
"Every complete metric space is of second category."
In the context of topology, a space is said to be of second category (or a "Baire space") if it cannot be expressed as a countable union of nowhere dense sets (sets whose closure has empty interior). So, the Baire Category Theorem verifies that complete metric spaces are "large" in the sense that they are not the countable union of "small" sets, which are in this context the nowhere dense sets. This theorem is a fundamental result in topology and has significant implications in various fields of mathematics.
Hence option (i) is correct.
If f = <1/n>, then what can you say about monotonic nature of f?
monotonically decreasing
both increasing and decreasing
monotonically increasing
monotonic
Correct answer
monotonically decreasing
Why this answer is correct
Concept -
(i) A sequence is monotonically increasing if an ≤ an+1
(ii) A sequence is monotonically decreasing if an ≥ an+ 1
Explanation:
f = <1/n> = {1, , , , ...} and 1 > 1/2 > 1/3 ...
So we can see that sequence is monotonically decreasing
(1) is correct
Inner automorphism corresponding to every element of an abelian group is?
trivial
infinite
bounded
non trivial
Correct answer
trivial
Why this answer is correct
Explanation -
In an abelian group (also known as a commutative group), the operation of the group commutes. This means that for any two elements a and b in the group, the equation ab = ba holds true. Because of the commutative property, the inner automorphism corresponding to any element of an abelian group is the identity function.
let (G, *) be an abelian group, and let's denote by the inner automorphism of G defined by some element a, where 'x' is an element of G. Then
However, since the group operation is commutative, we can rearrange the terms to obtain: where 'e' is the identity element of the group.
Since for any element x in the group, the inner automorphism of an element of the Abelian group is the identity map for any element a in an abelian group G.
Hence option (i) is true.
Every uniformly continuous function on an interval is ______ on that interval.
continuous
convergent
divergent
oscillatory
Correct answer
continuous
Why this answer is correct
Concept -
Every uniformly continuous function is continuous on any domain.
Explanation:
Every uniformly continuous function on an interval is always continuous on that interval.
(1) is correct
If a group G is internal Direct product of its subgroups A, B, C, .... Z then G is isomorphic to ______.
A, B, C, ... Z
external direct product of A, B, C... Z
internal Direct product of A, B, C... Z
it is not isomorphic
Correct answer
external direct product of A, B, C... Z
Why this answer is correct
Concept -
If a group G is the internal direct product of its subgroups A, B, C, ..., Z then G is isomorphic to the external direct product of the groups A, B, C, ..., Z.
Explanation -
If a group G is the internal direct product of its subgroups A, B, C, ..., Z then G is isomorphic to the external direct product of the groups A, B, C, ..., Z.
Formally, if G = A x B x C x ... x Z for subgroups A, B, C, ..., Z of G, then G is isomorphic to the group A * B * C * ... * Z where * is the direct product operation.
In more precise terms, the fundamental theorem of finitely generated abelian groups states that every finitely generated abelian group G is isomorphic to a direct product of cyclic groups of prime power order.
Hence option(ii) is correct.
Let (X, d) be a metric space then what can you say about X and d?
d is called metric and X is called ground set
both are called ground sets
d is called metric but can't say about X
X is called metric and d is called ground set
Correct answer
d is called metric and X is called ground set
Why this answer is correct
Concept -
In a metric space (X, d):
( d ) is called the metric, which is a function that measures the distance between elements of the set ( X ).
( X ) is the set of elements, sometimes referred to as the ground set or the underlying set.
Explanation -
Let (X, d) be a metric space then d is called metric and X is called ground set
Hence option (1) is correct.
Which of the following metric space is not complete?
set of complex numbers
set of rationals
set of irrationals
set of real numbers
Correct answer
set of rationals
Why this answer is correct
Explanation:
An incomplete metric space is one where there exist Cauchy sequences that do not converge within the space. For instance, the set of rational numbers (ℚ, d), where d is the standard absolute difference, is an example of an incomplete metric space. This is because there are Cauchy sequences of rational numbers that converge to irrational numbers not in ℚ for example: sequence that approximates the square root of 2.
Hence option (2) is correct.
From the direct theorem we know that the set of real numbers is complete.
The set of complex numbers ℂ is complete, i.e., every Cauchy sequence in ℂ converges in ℂ.
(1) and (4) are complete
The set of irrational numbers is not complete when considered as a subspace of the real numbers with the standard Euclidean metric; this means that a Cauchy sequence of irrational numbers can converge to a rational number, which is not in the set of irrationals.
(3) is also correct.
But in official answer (2) is correct only.
Let (X, d) be a complete metric space and let B be a subset of X then if B is closed then B is also ______.
Unbounded
Complete
Dense
Bounded
Correct answer
Complete
Why this answer is correct
Explanation -
Let (X, d) be a complete metric space and let B be a subset of X, then if B is compact, then B is complete.
Every Cauchy sequence in B is also a Cauchy sequence in X (because the metrics agree). Since X is complete, the sequence converges to some limit in X. Because B is closed, that limit point lies in B. Hence the sequence converges in B, so B is complete.
The correct option is Complete.
Let (X, d) be a metric space and Pn be the Cauchy sequence defined then {Pn} is ______.
divergent
cauchy
bounded
convergent
Correct answer
convergent
Why this answer is correct
Explanation -
Let (X, d) be a metric space and Pn be a Cauchy sequence. Then, by definition, the sequence {Pn} is said to be Cauchy.
A sequence {Pn} in a metric space is called a Cauchy sequence if for every positive real number ε > 0, there is a positive integer N such that for all natural numbers m, n > N, the distance d(Pm, Pn) < ε.
Basically, a Cauchy sequence is one where the terms of the sequence become arbitrarily close to each other as the sequence progresses. If (X, d) is a complete metric space, then every Cauchy sequence converges to some limit in X. If the space is not complete, a Cauchy sequence may not have a limit within the space.
Hence option (iv) is true.
What powers of x does expansion of sin(x) contains?
all powers of x
even powers of x
any alternate powers of x
odd powers of x
Correct answer
odd powers of x
Why this answer is correct
Explanation:
The Maclaurin series expansion for Sin (x) is given by the summation from n=0 to infinity of (-1)n × x(2n+1)/(2n+1)!
The Expansion of Sinx = x -x3/3! + x5/5! -............
Hence, The Expansion of Sinx contains all the odd powers of x.
Hence, The Correct option is 4.
In metric space which function is always continuous?
bounded function
distance function
continuous function
discrete function
Correct answer
distance function
Why this answer is correct
Explanation -
Constant functions are always continuous in any space, including metric spaces. A constant function is a function for which the value of the function is the same for every input in the domain. Additionally, "identity function" is also always continuous in a metric space. Here, the output value is always equal to the input value, i.e., the function f: X -> X, where X is a metric space, defined by f(x) = x is always continuous.
the distance function in a metric space is also always continuous.
Formally, the distance function d: X × X -> R (where X is a metric space and R is the set of real numbers) is continuous. This is the definition of the distance function for a metric space X: for any two points a, b in X, the distance function d(a, b) gives the distance between a and b.
Hence option (ii) is correct.
If f is the derivative of some function on [a, b], then there exists a number c in (a, b) such that Integral of f with respect to x =
f(c)
f(c) . (b - a)
(b + a - c) f(c)
f(c) . (b + a)
Correct answer
f(c) . (b - a)
Why this answer is correct
Concept use:
The Mean Value Theorem for Integrals states that if f is continuous on the closed interval [a, b], then there exists at least one number c in the open interval (a, b) such that:
∫from a to b f(x) dx = f(c) · (b - a)
This theorem guarantees the existence of at least one point c in the interior of the interval [a, b] where the value of the function f(c) multiplied by the length of the interval (b - a) gives the integral of f(x) over that interval
Explanation:
In the given statement, if f is the derivative of some function on the interval [a, b], then the Mean Value Theorem for Integrals applies.
According to this theorem, there exists a number c in the open interval (a, b) such that the integral of f(x) over the interval [a, b] is equal to f(c) multiplied by the length of the interval (b - a).
Hence, the correct option is: f(c) · (b - a)
Hence, The Correct Option is 2.
Let (X, d) be a metric space and E is contained in X, E is called nowhere dense set if ______.
closure of E is empty
closure of E terminate after some steps
closure of E is not defined
closure of E is finite
Correct answer
closure of E is empty
Why this answer is correct
Explanation -
In a metric space (X, d), a subset E is called a "nowhere dense" set if its closure has empty interior.
This means that for any point in X and for any radius, no matter how small, the open ball centered at that point with that radius always contains a point not in the closure of E.
In simpler terms, a set is nowhere dense if it is not dense in any neighborhood - it doesn't "fill up" any portion of the space.
Hence option (i) is correct.
Which theorem states that "An integral function attains every finite value with atmost one possible exception"?
Picard's theorem
Jensen's inequality
Jensen's formula
Schwartz' lemma
Correct answer
Picard's theorem
Why this answer is correct
Concept -
Picard's theorem states that a complex function, if analytic near an essential singularity, will attain every complex value, except possibly one, in any
neighborhood of that singularity.
Explanation:
Picard's theorem states that An integral function attains every finite value with atmost one possible exception.
Option (1) is true.
What is order of convergence of cosh√z?
0
infinite
one
two
Correct answer
infinite
Why this answer is correct
Explanation:
We know that the order of convergence of cosh z is infinity
So order of convergence of cosh√z is infinite
(2) is correct
Which of the following group is not normal under usual ring operation?
3 ssg
2 ssg
7 ssg
5 ssg
Correct answer
2 ssg
Why this answer is correct
Explanation -
For Option (1) -
This subset consists of all integers that are multiples of 3.
we need to verify that for every element h ∈ and every element r in , the product rh is also in .
Since multiplying any integer by 3 yields a multiple of 3, is closed under multiplication and thus normal under the usual ring operation.
For Option (2) - (the multiples of 2):
is not normal under the usual ring operation because there exist elements h and r such that rh is not in .
For example, if we take h = 2 and r = 3, then rh = 3 x 2 = 6, which is not in .
For Option (3) - (the multiples of 7):
Similar to , is also normal under the usual ring operation because multiplying any integer by 7 yields a multiple of 7.
For Option (4) - (the multiples of 5):
Like and , is normal under the usual ring operation because multiplying any integer by 5 yields a multiple of 5.
Hence Option (2) is correct.
Name the smallest non cyclic group.
abelian group of p order
Matrix group
Correct answer
Why this answer is correct
Concept -
(i) every prime order group is always cyclic.
(ii) every cyclic group is always abelian.
Explanation -
(i) Abelian group of p order is cyclic. Hence option (i) is false
(ii) group is non abelian non cyclic but it is not smallest non cyclic group. Hence option (ii) is false.
(iii) Matrix group is non abelian non cyclic but it is not smallest non cyclic group. Hence option (iii) is false.
(iv) group is abelian non cyclic but it is smallest non cyclic group. Hence option (iv) is true.
Does C-R equations are necessary and sufficient for a function to be analytic?
FALSE
can't say about nature of equations
TRUE
depend on range of functions
Correct answer
FALSE
Why this answer is correct
Explanation:
,
CR equation states that
Here \(\begin{align*} u_x(0,0) &= \lim_{h\to 0} \frac{u(0+h,0) - u(0,0)}{h} = 0, \ u_y(0,0) &= \lim_{k\to 0} \frac{u(0,0+k) - u(0,0)}{k} = 0. \end{align*}\)
vx(0, 0) = 0 and vy(0, 0) = 0
Hence, CR Equation is satisfied but Function is not Analytic
Since, Limit of this function along y = mx not Exist
∴ CR equation is only Necessary Condition but Not Sufficient
Hence, Option 1 is Correct.
The external direct product of two cyclic groups is ______.
not abelian
always cyclic
never cyclic
need not cyclic
Correct answer
need not cyclic
Why this answer is correct
Concept -
if you have two cyclic groups of order m and n, the external direct product of these two groups will form a new group of order mn. If m and n are coprime, this group is cyclic. If m and n are not coprime , then the resulting group is not cyclic.
Explanation -
For example, let's consider two cyclic groups, one of order 2 and one of order 3. Their external direct product will be a cyclic group of order 6, because 2 and 3 are coprime. However, if you take two cyclic groups both of order 2, their external direct product will be a group of order 4, but it won't be cyclic, it will rather be isomorphic to the Klein four-group, which is not a cyclic group.
Hence option(iv) is correct.
Let k be the number of p-ssg of a finite group G. Then ______.
k does not divide O(G)
k divides O(G)
k does not exist
k bipolars
Correct answer
k divides O(G)
Why this answer is correct
Concept -
If k is the number of p - ssg (subgroups of order p) of a finite group G, then k necessarily divides the order of G.
This means that the number of p - ssg evenly divides the total number of elements in the group.
Explanation -
Consider the cyclic group , where p is a prime number.
In this group, every nontrivial subgroup has order p, so the number of p - ssg is p - 1.
However, p - 1 does divide the order of G, which is p.
Therefore, the correct Option is (2).
If f(z) is analytic function whose real part is constant then f(z) is ______.
constant
Function of x and y both
Function of y only
Function of x only
Correct answer
constant
Why this answer is correct
Concept:
If f(z) = u + iv is an analytic function, then it must satisfy the Cauchy-Riemann equations,
ux = vy , uy= -vx
Calculations:
Let the real part of f(z) be a, where a is a constant.
f(z) = a + iv
ux = 0 and uy = 0 implies vy = 0 and vx = 0 (Using Cauchy-reimann equation)
So, f'(z) = ux + ivx = 0
Integraing both sides we get,
f(z) = constant
Hence, option (1) is correct.
Multiply (1 2 3) and (5 6 4 1)?
(1 5 6 4 2 3)
(2 3 4 5 6 7)
(1 2 3 4 5 6)
(3 6 3 7 3 8)
Correct answer
(1 5 6 4 2 3)
Why this answer is correct
Explanation:
The symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group
defined over a finite set of
symbols consists of the permutations that can be performed on the
symbols. Since there are
such permutation operations, the order (number of elements) of the symmetric group
is
.
Multiplication of Symmetric Group :
(1 2 3)
Images of the first Permutation element
1 --> 2, 2 --> 3, 3 --> 1, 4 --> 4, 5 --> 5, 6 --> 6
(5 6 4 1)
Images of the Second Permutation element
1 --> 5, 2 --> 2, 3 --> 3, 4 --> 1, 5 --> 6, 6 --> 4
For Multiplying the Element of the Group
we have to process from backward to forward
1 --> 5, 5 --> 5 so, The Image of 1 under Permutation is 5
2 --> 2, 2 --> 3 so, The image of 2 under Permutation is 3
3 --> 3, 3 --> 1 so, The image of 3 under Permutation is 1
4 --> 1, 1 --> 2 so, The image of 4 under Permutation is 2
5 --> 6, 6 --> 6 so, The image of 5 under Permutation is 6
6 --> 4, 4 --> 4 so, The image of 6 under Permutation is 4
So, The multiplication of (1 2 3)(5 6 4 1) = (1 5 6 4 2 3)
What is the number of elements of order 100 in Z(200)?
40
120
80
160
Correct answer
40
Why this answer is correct
Concept -
Number of elements of order m in Zn is .
Explanation -
The number of elements of order 100 in Z(200) =
"What type of family allows a woman to marry more than one man?"
Extended family
Polygamous family
Monogamous family
Polyandry family
Correct answer
Polyandry family
Why this answer is correct
There are various types of family structures, and they can vary based on cultural, societal, and personal factors.
Key Points
Hint
Hence, polyandry family is correct.
Which of the following skill is a sociological term relating to a person's "EQ"?
Hard skills
People skills
Soft skills
Social skills
Correct answer
Soft skills
Why this answer is correct
Soft skills are a set of personal attributes that enable someone to interact effectively and harmoniously with other people.
Key Points
Hence, soft skills are a sociological term relating to a person's EQ.
The school should aim at developing ______.
Social, moral and spiritual values.
Political and spiritual values.
Economic, political and social values.
Emotional, Moral and political values.
Correct answer
Social, moral and spiritual values.
Why this answer is correct
A school is an educational institution designed to provide learning spaces and learning environments for the teaching of students under the direction of teachers.
Key Points
Hence, the school should aim at developing social, moral and spiritual values.
From the following strategies which strategy can not be employed to make students conscious of gender issues which would result in developing an attitude of gender equality?
Film analysis
Society analysis
Analysis of data collected from Interview
Analysis of Biographies
Correct answer
Analysis of Biographies
Why this answer is correct
Gender issues are the social, economic, and political challenges that people face due to their gender. Gender issues can impact both men and women, but they disproportionately impact women and girls.
Key Points
Effective strategies for making students conscious of gender issues and developing an attitude of gender equality:
Hint
Hence, Analysis of Biographies is correct.
Piaget's learning theory does not revolve around which pillars of schemas?
Equilibration
Assimilation
Assessment
Accommodation
Correct answer
Assessment
Why this answer is correct
Piaget's learning theory revolves around the four pillars of schemas: assimilation, accommodation, equilibration, and organization. Assessment is not a pillar of Piaget's learning theory.
Key PointsHere is a brief explanation of each of the four pillars of Piaget's learning theory:
Hint
Hence, Piaget's learning theory does not revolve around assessment.
Often referred to as the skin sense, the ______ involves touch, movement and body positions in space.
Sense of Hearing
Kinesthetic Sense
Sense of Smell
Tactual Sense
Correct answer
Kinesthetic Sense
Why this answer is correct
A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli.
Key Points
Hint
Hence, often referred to as the skin sense, the Kinesthetic Sense involves touch, movement and body positions in space.
Which one is correct Objective of teaching English?
Develop the ability of appreciation of ideas
Develop knowledge
Develop self-study habit
Literacy development
Correct answer
Literacy development
Why this answer is correct
Literacy development is the process of learning to read and write. It is an essential skill for success in school and in life. Teaching English should help students develop their literacy skills in both English speaking and writing.
Key Points
Here are some of the specific objectives of teaching English that are related to literacy development:
Hence, literacy development is the objective of teaching English.
Who decides textbook curriculum?
the government
the education minister
the State Board of Education
the principal of school
Correct answer
the State Board of Education
Why this answer is correct
The textbook curriculum is the set of topics and skills that are covered in a textbook. It is typically aligned with the state standards, which are the academic standards that all students in the state are expected to meet.
Key Points
Here are some of the factors that State Boards of Education consider when setting the textbook curriculum:
Hint
Hence, the correct answer is the State Board of Education.
Teachers comprehend the relationship between different concepts through ______ which visually illustrate the relationships between concepts and ideas.
Concept diagrams
Concept maps
Concept graph
Concept charts
Correct answer
Concept maps
Why this answer is correct
Concept maps are visual representations of concepts and the relationships between them.
Key Points
Hence, the correct answer is concept maps.
Hint
What is the importance of discussion method in teaching?
Initiate Talking
Stimulate critical thinking
Guided Conversation
Activate Learning
Correct answer
Stimulate critical thinking
Why this answer is correct
The discussion teaching method is a teaching strategy that involves a group of students and a teacher exchanging ideas and opinions on a particular topic. It is a collaborative learning process that encourages students to think critically, listen actively, and communicate effectively.
Key Points
Hint
Hence, stimulate critical thinking is correct.
200 questions in the full paper