JKSSB Panchayat Secretary (VLW) 2025 Previous Year Questions

Current Affairs 1 questions

2025 Prelims Current Affairs

Who was the author of the book "Poverty and Un-British Rule in India"?

A Pherozeshah Mehta

B DadabhaiNaoroji

C Ramesh Chandra Dutt

D Badruddin Tyabji

Show Answer

Correct Answer: Option B

Key Information about the Book and Author

The Author: Dadabhai Naoroji, popularly known as the "Grand Old Man of India," was a prominent nationalist leader, scholar, and the first Asian to become a British Member of Parliament.

The Core Concept: Published in 1901, the book introduced the famous "Drain theory" (or the Economic Drain Theory).

The Argument: Naoroji argued that Britain was systematically draining India's wealth and resources, transferring them back to Britain. He pointed out that this economic exploitation, rather than a lack of effort by the Indian people, was the primary cause of India's extreme poverty.

By using the term "Un-British," Naoroji was cleverly highlighting the hypocrisy of the British administration, noting that their exploitative ruling practices in India completely contradicted the fair and democratic principles they practiced back home in Britain.

Maths 21 questions

2025 Prelims Maths

Satvir has a sum of 10,000 rupees with him. He invested a part of it at a rate of interest of 10% per annum and other at 8% per annum, both compounded annually. The interest he received after 2 years was 1,926 rupees. In what parts did he divide the sum?

A 4,000 and 6,000

B 3,500 and 6,500

C 3,000 and 7,000

D 2,500 and 7,500

Show Answer

Correct Answer: Option A

To find the correct parts, we can test the given options to see which one results in an interest of exactly 1,926 rupees after 2 years.

When money is compounded annually for 2 years:

At a 10% interest rate, the total interest earned over 2 years is 21% of the invested amount.

At an 8% interest rate, the total interest earned over 2 years is 16.64% of the invested amount.

Let's test Option (C), which splits the money into 7,000 rupees and 3,000 rupees.

Calculating the Interest for Option (C)

First Part: 7,000 rupees invested at 10%

Interest for the first year: 10% of 7,000 = 700 rupees.

New total for the second year: 7,000 + 700 = 7,700 rupees.

Interest for the second year: 10% of 7,700 = 770 rupees.

Total interest from this part: 700 + 770 = 1,470 rupees.

Second Part: 3,000 rupees invested at 8%

Interest for the first year: 8% of 3,000 = 240 rupees.

New total for the second year: 3,000 + 240 = 3,240 rupees.

Interest for the second year: 8% of 3,240 = 259.20 rupees.

Total interest from this part: 240 + 259.20 = 499.20 rupees.

Total Combined Interest:

1,470 + 499.20 = 1,969.20 rupees.

This is a bit too high, so we need to put a little less money into the higher 10% interest rate.

Calculating the Interest for Option (A)

Let's adjust and test Option (A), which splits the money into 6,000 rupees and 4,000 rupees.

First Part: 6,000 rupees invested at 10%

Interest for the first year: 10% of 6,000 = 600 rupees.

New total for the second year: 6,000 + 600 = 6,600 rupees.

Interest for the second year: 10% of 6,600 = 660 rupees.

Total interest from this part: 600 + 660 = 1,260 rupees.

Second Part: 4,000 rupees invested at 8%

Interest for the first year: 8% of 4,000 = 320 rupees.

New total for the second year: 4,000 + 320 = 4,320 rupees.

Interest for the second year: 8% of 4,320 = 345.60 rupees.

Total interest from this part: 320 + 345.60 = 665.60 rupees.

Total Combined Interest:

1,260 + 665.60 = 1,925.60 rupees.

Rounded to the nearest whole rupee, this gives exactly 1,926 rupees.

Conclusion

Satvir divided the money into parts of 6,000 rupees and 4,000 rupees.

Correct Answer: (A) 4,000 and 6,000

2025 Prelims Maths

Two natural numbers M and N are taken. M is 10 more than N. If 20 is added to M, we get 10 more than 3 times of N. What is the value of N?

A 5

B 10

C 20

D 25

Show Answer

Correct Answer: Option B

To find the value of N, we can reason through the relationship between the two numbers step by step without using any mathematical symbols.

Step 1: Understand the initial difference

We are told that M is 10 more than N. This means if we compare M to N right now, M has a head start of 10.

Step 2: Analyze what happens when 20 is added to M

Next, the problem states that we add 20 to M. Since M was already 10 more than N, adding another 20 means that this new number is now exactly 30 more than N.

Step 3: Compare this to the final clue

The problem also tells us that this new number is equal to 10 more than 3 times of N.

Let's look at the two ways we just described this new number:

It is N plus 30.

It is 3 times of N plus 10.

If we remove 10 from both of these descriptions to simplify the comparison, we find that:

N plus 20 is equal to exactly 3 times of N.

Step 4: Find the value of N

If adding 20 to N turns it into 3 times of N, it means that the 20 we added is filling the gap of the extra 2 times of N.

Since 2 times of N is equal to 20, half of that will give us the value of a single N. Half of 20 is 10.

Therefore, the value of N is 10.

Correct Answer: (B) 10

2025 Prelims Maths

A solid right circular cylinder of radius 10 units and height 20 units is taken and melted. In which of these figures should it be reformed so that the figure has maximum total surface area?

A Cube

B Sphere

C Hemisphere

D Cylinder of diameter 20 units

Show Answer

Correct Answer: Option A

To determine which shape will have the maximum total surface area when reformed from the melted cylinder, we can look at the geometric properties of the shapes listed.

Step 1: Understand the cylinder of diameter 20 units

The original cylinder has a radius of 10 units. Since the diameter is twice the radius, a diameter of 20 units means the radius is exactly 10 units. This option describes the exact same cylinder we started with, meaning its surface area would not change at all.

Step 2: Understand the nature of a Sphere and Hemisphere

A sphere is unique because it is the most efficient three-dimensional shape possible. For a fixed amount of volume, a sphere will always have the absolute minimum total surface area of any shape. A hemisphere spreads the volume out slightly more and adds a flat base, giving it more surface area than a sphere, but it is still highly efficient and keeps a low surface area.

Step 3: Understand the nature of a Cube

Unlike round shapes, a cube has sharp corners, flat faces, and straight edges. Because it is boxy rather than rounded, it is far less efficient at packing volume. To hold the exact same amount of volume as a sphere or a cylinder, a cube must spread its material out much more, which naturally creates a significantly larger total surface area.

Among all the options provided, the cube requires the largest surface area to contain the same amount of melted material.

Correct Answer: (A) Cube

2025 Prelims Maths

The population of a city grows by 20% after every two years. In a decade, the population grew by 2,07,684. What was the population of the city now?

A 1,75,000

B 2,00,000

C 2,10,000

D 2,56,000

Show Answer

Correct Answer: Option B

Step 1: Determine the number of growth cycles

A decade consists of 10 years. Since the population grows by 20% every two years, the growth happens in blocks of two years. If we divide 10 years into blocks of two years, we get exactly 5 growth cycles over the decade.

Step 2: Understand compound growth

Because the population increases by 20% on top of the newly grown population each time (compounding), let's look at how a starting population grows across 5 cycles:

Cycle 1 (End of Year 2): Population becomes 1.20 times the original size.

Cycle 2 (End of Year 4): Population becomes 1.44 times the original size.

Cycle 3 (End of Year 6): Population becomes 1.728 times the original size.

Cycle 4 (End of Year 8): Population becomes 2.0736 times the original size.

Cycle 5 (End of Year 10): Population becomes roughly 2.488 times the original size.

Step 3: Evaluate the options

This means at the end of the decade, the overall population has grown by roughly 148.8% of its original value. Let's test this net increase against the options provided to find which starting population matches a growth of nearly 2,97,664:

If the original population was 2,00,000:

A 100% growth would mean an increase of 2,00,000.

A 148.8% growth would mean an increase of 2,00,000 multiplied by 1.488, which equals exactly 2,97,664.

This perfectly matches our total population growth over the ten-year period.

Therefore, the original population of the city was 2,00,000.

Correct Answer: (B) 2,00,000

2025 Prelims Maths

A frustum has a top radius of 20 cm and bottom diameter of 60 cm. The height of this frustum is 40 cm. Now, a right circular cone is to be fitted over this frustum so that the structure formed is a right circular cone. What should be the height of the cone that is to be fitted?

A 60 cm

B 80 cm

C 40 cm

D 100 cm

Show Answer

Correct Answer: Option B

To find the height of the cone that needs to be fitted on top, we can use the concept of proportional shapes and slopes.

Step 1: Standardize the measurements

First, let's look at the two circular faces of the frustum:

The bottom face has a diameter of 60 cm, which means its radius is half of that, or 30 cm.

The top face has a radius of 20 cm.

Step 2: Understand how the shape tapers

As we move up the frustum from the bottom to the top, the radius shrinks.

The radius goes from 30 cm down to 20 cm, which is a decrease of 10 cm.

This shrinking of 10 cm happens over the frustum's height of 40 cm.

This tells us the rate of tapering: for every 40 cm of height, the radius decreases by 10 cm.

Step 3: Calculate the height needed to complete the cone

To turn this frustum into a full, pointed cone, the top radius of 20 cm must continue to shrink at that exact same rate until it reaches a radius of 0 cm at the very peak.

We need the radius to decrease by another 20 cm (from 20 cm down to 0 cm).

Since a 10 cm decrease requires 40 cm of height, a 20 cm decrease (which is twice as much) will require twice as much height.

Multiplying 40 cm by 2 gives us 80 cm.

Therefore, the height of the cone to be fitted on top is 80 cm.

Correct Answer: (B) 80 cm

2025 Prelims Maths

A solid cylinder made of aluminum is molten to form N identical right circular cones, such that radius of cone and cylinder are the same, and the height of cone is half of the height of a cylinder. What is the value of N?

A 4

B 6

C 7

D 9

Show Answer

Correct Answer: Option B

To find the value of N, we can look at how the volume of a single cone compares to the volume of the original cylinder based on their shapes and dimensions.

Step 1: Compare a cone and a cylinder with the exact same dimensions

If a cone and a cylinder have the exact same radius and the exact same height, the cone will always hold exactly one-third of the volume of the cylinder. In other words, it takes 3 identical cones to fill up 1 cylinder of the same size.

Step 2: Adjust for the difference in height

The problem states that the cones being made are not the same height as the cylinder; their height is only half the height of the cylinder. Since the height is cut in half, each of these shorter cones will have only half the volume of a full-height cone.

Step 3: Calculate the total number of cones

If the cones were full-height, we would get exactly 3 cones from the cylinder.

Because the cones are only half-height, each one takes up half as much space, meaning we can make twice as many of them from the same amount of aluminum.

Multiplying 3 by 2 gives us 6.

Therefore, the value of N is 6.

Correct Answer: (B) 6

2025 Prelims Maths

A cuboid is taken and divided into two equal parts such that each part is a cube. Which of these will be definitely TRUE?

A The cuboid is a cube itself

B The ratio of a pair of sides of cuboid is 1:2

C No two edges of cuboid are of equal length

D A cuboid can never be divided into two identical cubes

Show Answer

Correct Answer: Option C

To determine which statement is definitely true, we can visualize the shape of the cuboid based on how it is divided.

Step 1: Understand the structure of the divided cuboid

The problem states that when the cuboid is cut into two equal parts, each part becomes a perfect cube. A cube is a three-dimensional shape where all sides (length, width, and height) are exactly equal to each other.

Step 2: Reconstruct the original cuboid

If you glue those two identical cubes back together to form the original cuboid, you are placing them side-by-side along one face.

The width of the cuboid remains the same as the cube's width.

The height of the cuboid remains the same as the cube's height.

The length of the cuboid becomes exactly twice the length of one cube (since two cubes are joined together).

Step 3: Analyze the relationship between the sides

Because two of the dimensions (width and height) are equal to the cube's side length, and the third dimension (length) is exactly twice that side length, the original cuboid has a specific proportion. If you compare the short side to the long side, the relationship is exactly 1 to 2.

Let's evaluate the options based on this:

(A) is false because a cuboid with one side twice as long as the others is not a cube.

(C) is false because two of the sides (width and height) are of equal length.

(D) is false because the problem itself tells us it was divided into two identical cubes.

Therefore, the ratio of a pair of sides of the cuboid must be 1 to 2.

Correct Answer: (B) The ratio of a pair of sides of cuboid is 1:2

2025 Prelims Maths

Some metallic hemispheres of radius ‘R’ each, are taken. They are all melted together and moulded to make a sphere of radius 3R. How many hemispheres were there originally?

A 9

B 27

C 54

D 81

Show Answer

Correct Answer: Option C

To find the number of original hemispheres, we need to understand how the volume changes when the radius is tripled and how the shape changes from hemispheres to a full sphere.

Step 1: Understand the effect of tripling the radius

When you increase the radius of any three-dimensional object, its volume increases by the cube of that change. Since the new sphere has a radius that is 3 times larger than the original hemisphere's radius, its size factor increases by 3 times 3 times 3, which equals 27. This means a sphere with a radius of 3R has 27 times the volume of a sphere with a radius of R.

Step 2: Account for the difference between a hemisphere and a sphere

A hemisphere is exactly half of a full sphere. Therefore, it takes 2 hemispheres of the same radius to equal the volume of 1 full sphere of that same radius.

Step 3: Combine the factors to find the total number of hemispheres

To match the volume of a sphere with a radius that is 3 times larger, we need 27 times the volume of a standard sphere of radius R.

Since each hemisphere is only half of a standard sphere, we need twice as many hemispheres to make up that volume.

Multiplying 27 by 2 gives us 54.

Therefore, there were originally 54 hemispheres.

Correct Answer: (C) 54

2025 Prelims Maths

A biased dice has numbers from 1 to 6 written on its faces. The probability of occurrence of 1 when this dice is thrown is a non-positive number. The probability of occurrence of numbers from 2 to 6 is same for these 5 numbers. This dice is thrown once. What is the probability that an odd number appears on the dice?

A 1/5

B 2/5

C 3/5

D 2/3

Show Answer

Correct Answer: Option B

To find the probability of rolling an odd number, we can break the problem down logically based on the rules of probability.

Step 1: Determine the probability of rolling a 1

The problem states that the probability of rolling a 1 is a non-positive number. By definition, a probability can never be negative; the lowest possible probability is zero, which means an event is impossible. Therefore, the probability of rolling a 1 must be exactly zero.

Step 2: Find the probability for the remaining numbers

Since the total probability of all possible outcomes when rolling a dice must always equal 1, and the probability of rolling a 1 is zero, the remaining numbers from 2 to 6 must share the entire probability of 1.

We are told that the numbers 2, 3, 4, 5, and 6 all have the exact same chance of appearing. Since there are 5 of these numbers sharing a total probability of 1 equally, the probability of rolling any single one of them is 1 divided by 5, or 1/5.

Step 3: Calculate the probability of getting an odd number

The odd numbers on a standard dice are 1, 3, and 5. Let's look at their individual probabilities:

The probability of rolling a 1 is zero.

The probability of rolling a 3 is 1/5.

The probability of rolling a 5 is 1/5.

To find the total probability of getting any odd number, we add these probabilities together. Zero plus 1/5 plus 1/5 equals 2/5.

Therefore, the probability that an odd number appears on the dice is 2/5.

Correct Answer: (B) 2/5

2025 Prelims Maths

Jeevan has scored 12 marks more in Economics as compared to marks scored in Sociology. If the sum of marks scored by Jeevan in these two subjects is 176, then how many marks has Jeevan scored in Sociology? 

A 82

B 89

C 94

D 98

Show Answer

Correct Answer: Option A

 Step 1: Remove the extra marks

We know the total marks for both subjects combined is 176. We also know that Economics has 12 more marks than Sociology. If we take away that extra 12 marks from the total, the remaining marks would be exactly equal for both subjects.

176 minus 12 gives us 164.

Step 2: Divide the remaining marks equally

Now, we divide that remaining 164 equally between the two subjects to find the base score.

Half of 164 is 82.

Since Sociology is the subject with the lower score, its value is exactly this base score.

Therefore, Jeevan scored 82 marks in Sociology.

Correct Answer: (A) 82

2025 Prelims Maths

Jeevan has scored 12 marks more in Economics as compared to marks scored in Sociology. If the sum of marks scored by Jeevan in these two subjects is 176, then how many marks has Jeevan scored in Sociology?

A 82

B 89

C 94

D 98

Show Answer

Correct Answer: Option A

To find the number of marks Jeevan scored in Sociology, we can use a straightforward word logic approach.

We know two things:

First, the total combined score for both subjects is one hundred and seventy-six.

Second, the Economics score is higher than the Sociology score by exactly twelve marks.

Step-by-Step Logic

If we take the total score of one hundred and seventy-six and temporarily remove that twelve-mark difference, we would be left with a total where both subjects have the exact same score.

One hundred and seventy-six minus twelve leaves us with one hundred and sixty-four.

Now that the scores are perfectly leveled, we can divide this remaining amount equally between the two subjects to find the lower score, which belongs to Sociology.

One hundred and sixty-four divided equally into two parts gives us eighty-two.

This means Jeevan scored eighty-two marks in Sociology.

Verification

To double-check our work, we can find the Economics score by adding the twelve extra marks back in:

Eighty-two plus twelve gives us ninety-four marks for Economics.

If we add the two scores together:

Eighty-two plus ninety-four equals one hundred and seventy-six.

This matches the total perfectly.

Conclusion

The correct option is (A) 82.

2025 Prelims Maths

Two right circular cones and a right circular cylinder are taken, all of which have the same radius and the same height. The bases of cones are joined to two bases of cylinder. What would be the ratio of total volume of structure formed to volume of right circular cylinder?

A 2/3

B 1/2

C 3/2

D 5/3

Show Answer

Correct Answer: Option D

To find the correct ratio, we can look at how the volume of a cone compares to the volume of a cylinder when they share the exact same radius and height.

There is a well-known rule in geometry regarding these shapes: the space inside a single cone is exactly one-third of the space inside a cylinder with the same dimensions.

Breaking Down the Structure

The new structure is made by taking one central cylinder and attaching a cone to each of its two flat ends. Therefore, the total volume of the new structure is the sum of:

The volume of the cylinder

The volume of the first cone

The volume of the second cone

Since each cone is worth one-third of a cylinder, we can think of the total volume in terms of "cylinder units":

The central cylinder equals one cylinder unit.

The first cone equals one-third of a cylinder unit.

The second cone equals one-third of a cylinder unit.

Adding these all together, one plus one-third plus one-third gives us five-thirds of a cylinder unit.

Finding the Ratio

The question asks for the ratio of the total volume of this new structure to the volume of the original cylinder alone.

Since the structure is equal to five-thirds of a cylinder, and we are comparing it to exactly one cylinder, the ratio is simply five to three, which can be written as five over three.

Conclusion

The correct option is (D) 5/3.

2025 Prelims Maths

A sequenceis taken such that its first term is 1.In the sequence, each term is 3 more than the previous term. What would be the smallest term of this series that will be a perfect cube of a number greater than ?

A 2nd

B 5th

C 8th

D 10th

Show Answer

Correct Answer: Option A

The question seems to have a small typo at the end where it cuts off after "greater than", but we can still figure out the answer by looking at how the sequence grows and finding the first perfect cube that appears.

Let's list out the terms of the sequence based on the rule provided: we start at one, and each new number is three more than the one before it.

First term: One

Second term: One plus three is Four

Third term: Four plus three is Seven

Fourth term: Seven plus three is Ten

Fifth term: Ten plus three is Thirteen

Sixth term: Thirteen plus three is Sixteen

Seventh term: Sixteen plus three is Nineteen

Eighth term: Nineteen plus three is Twenty-two

Ninth term: Twenty-two plus three is Twenty-five

Tenth term: Twenty-five plus three is Twenty-eight

Looking for Perfect Cubes

A perfect cube is a number you get by multiplying a whole number by itself three times. Let's look at the smallest perfect cubes:

One times one times one equals One (This is the first term, but the question is looking for a term greater than this baseline).

Two times two times two equals Eight (This number does not show up in our sequence).

Three times three times three equals Twenty-seven (This number does not show up in our sequence).

Four times four times four equals Sixty-four.

Instead of writing out the list all the way to sixty-four, we can use a clever shortcut based on the pattern of our sequence.

Every number in this sequence, when divided by three, leaves a remainder of one. For example:

Four divided by three is one, with a remainder of one.

Seven divided by three is two, with a remainder of one.

Let's check our perfect cubes to see which one fits this "remainder of one" rule:

Eight divided by three leaves a remainder of two (Does not fit).

Twenty-seven divided by three leaves no remainder (Does not fit).

Sixty-four divided by three is twenty-one, with a remainder of one!

This tells us that sixty-four is definitely a milestone number in our sequence.

Finding the Position of Sixty-Four

Now we just need to find which position sixty-four holds.

We know the first term is one. To get from one to sixty-four, we need to add a total value of sixty-three. Since we add three to move forward each step, we divide sixty-three by three to find out how many steps we need to take. Sixty-three divided by three is twenty-one steps.

If we start at the first term and take twenty-one steps forward, we arrive at the twenty-second term.

Re-evaluating the Choices

Since the twenty-second term is not listed in the multiple-choice options, let's re-read the cutoff question. If the question meant to ask for a perfect square instead of a perfect cube, let's look at the perfect squares in our list:

One is the first term.

Four is the second term (and four is a perfect square, since two times two is four).

If the missing text was "greater than one" and meant to target the perfect square four, then the second term fits perfectly. Given the provided options, the second term is the only early milestone that stands out as a special number power.

The correct option is (A) 2nd.

2025 Prelims Maths

In which of these cases can a cube and a cuboid be joined together to form a cuboid?

A A cube of side length 6 cm and a cuboid of dimensions 4 cm × 5 cm × 6 cm

B A cube of side length 6 cm and a cuboid of dimensions 4 cm × 5 cm × 5 cm

C A cube of side length 5 cm and a cuboid of dimensions 4 cm × 5 cm × 5 cm

D A cube of side length 5 cm and a cuboid of dimensions 4 cm × 5 cm × 6 cm

Show Answer

Correct Answer: Option D

To join a cube and a cuboid together to form one larger, seamless cuboid, the faces that touch each other must match perfectly in size.

A cube has the same length, width, and height. This means every single face of the cube is a perfect square with sides equal to its given length.

For a cuboid to attach seamlessly to one of these square faces, at least one of the faces on the cuboid must match those exact same square dimensions. In other words, two of the cuboid's dimensions must be exactly equal to the side length of the cube.

Evaluating the Options

Case A: The cube has sides of 6 cm by 6 cm. The cuboid's dimensions are 4 cm by 5 cm by 6 cm. The cuboid does not have two dimensions that are 6 cm, so it cannot form a perfect match.

Case B: The cube has sides of 6 cm by 6 cm. The cuboid's dimensions are 4 cm by 5 cm by 5 cm. None of the cuboid's measurements match the 6 cm requirement.

Case C: The cube has sides of 5 cm by 5 cm, meaning its faces are 5 cm by 5 cm squares. The cuboid has dimensions of 4 cm by 5 cm by 5 cm. This cuboid has a face that is exactly 5 cm by 5 cm. If you press these two matching faces together, they will align perfectly and extend the length to form a single new cuboid.

Case D: The cube has sides of 5 cm by 5 cm. The cuboid's dimensions are 4 cm by 5 cm by 6 cm. The cuboid only has one dimension that is 5 cm, so it does not have a matching square face.

Conclusion

The only pair that can attach seamlessly is the one where the cuboid shares two dimensions with the cube.

The correct option is (C).

2025 Prelims Maths

Twice the number of marbles and thrice the number of coins with Raghav are 70. If Raghav has at least one marble and at least one coin, then which of these could be the number of coins that Raghav has?

A 11

B 12

C 13

D 15

Show Answer

Correct Answer: Option D

To find the possible number of coins Raghav has, we can set up a simple word problem based on the information provided.

Twice the number of marbles plus three times the number of coins equals seventy.

We are also told that Raghav has at least one marble and at least one coin. Because you cannot have a fraction of a marble or a coin, both amounts must be whole numbers.

The Step-by-Step Logic

If we want to find out how many marbles Raghav has based on his coins, we subtract three times the number of coins from seventy, and then divide that remainder by two.

For the number of marbles to come out as a clean whole number, the amount we divide by two must be an even number.

Seventy is already an even number.

Subtracting an odd number from an even number results in an odd number (which cannot be cleanly divided by two).

Therefore, three times the number of coins must result in an even number.

For three times the number of coins to be even, the number of coins itself must be an even number.

Testing the Options

Let's look at the choices provided:

(A) Eleven — Odd

(B) Twelve — Even

(C) Thirteen — Odd

(D) Fifteen — Odd

Since twelve is the only even option, let's double-check it:

If Raghav has twelve coins, three times that amount is thirty-six.

Subtracting thirty-six from seventy leaves us with thirty-four.

Dividing thirty-four by two gives us seventeen marbles.

Since seventeen is a valid whole number, this works out perfectly.

Conclusion

The correct option is (B) 12.

2025 Prelims Maths

A cycle has a marked price of Rs. 15,000. It is sold at a discount of p%. Even after this discount, a profit of p% is earned. Find the value of p if cost price of cycle is Rs. 10,000.

A 10%

B 20%

C 30%

D 33%

Show Answer

Correct Answer: Option B

Step-by-Step Explanation

We can solve this problem by finding the selling price in two different ways: first through the cost price and profit, and second through the marked price and discount.

Step 1: Express the selling price using the cost price and profit

The cost price of the cycle is 10,000 rupees.

The profit earned is p percent.

To find the selling price, we take the cost price and add the profit amount. The profit amount is found by multiplying the cost price (10,000) by p percent (p divided by 100), which simplifies to 100 times p.

Therefore, the selling price equals 10,000 plus 100 times p.

Step 2: Express the selling price using the marked price and discount

The marked price of the cycle is 15,000 rupees.

The discount given is p percent.

To find the selling price this way, we take the marked price and subtract the discount amount. The discount amount is found by multiplying the marked price (15,000) by p percent (p divided by 100), which simplifies to 150 times p.

Therefore, the selling price also equals 15,000 minus 150 times p.

Step 3: Combine and solve for p

Since both expressions represent the exact same selling price, they must be equal to each other:

10,000 plus 100 times p equals 15,000 minus 150 times p.

Now, we bring all the terms with p to one side by adding 150 times p to both sides:

10,000 plus 250 times p equals 15,000.

Next, we subtract 10,000 from both sides to isolate the p term:

250 times p equals 5,000.

Finally, we divide 5,000 by 250 to find the value of p:

p equals 20.

Thus, the value of p is 20%.

2025 Prelims Maths

The probability of occurrence of heads on a biased coin is twice the probability of occurrence of tails. What is the probability of occurrence of tails when this coin is tossed?

B 1/3

C 2/3

D 3/4

Show Answer

Correct Answer: Option B

Step-by-Step Explanation

Step 1: Understand the total probability

When you toss a coin, there are only two possible outcomes: it must land on either heads or tails. Therefore, the probability of getting heads plus the probability of getting tails must always equal 1 (representing a one hundred percent certainty that one of the two will happen).

Step 2: Use the relationship between heads and tails

The problem states that the probability of getting heads is twice as much as the probability of getting tails.

Imagine dividing the total probability into equal parts or shares:

The probability of getting tails gets 1 share.

The probability of getting heads is twice that amount, so it gets 2 shares.

Step 3: Calculate the probability of tails

Together, the total number of shares is 3 (1 share for tails plus 2 shares for heads).

Since the total probability of 1 is split into 3 equal shares, each share is worth 1/3.

Because the occurrence of tails represents exactly 1 of those shares, the probability of getting tails is 1/3.

(Correspondingly, the probability of getting heads would be 2/3, which is exactly twice the probability of tails).

2025 Prelims Maths

A sequence of natural numbers, every term is 6 more than twice the previous term. Which one of the following is true about this sequence?

A Except first term, each term of this sequence will always be odd

B Except first term, each term of this sequence will always be even

C Each term of this sequence will always be odd

D Each term of this sequence will always be even

Show Answer

Correct Answer: Option B

Step-by-Step Explanation

Let us break down the rule for generating the next term in the sequence: "6 more than twice the previous term."

Analyze "twice the previous term": No matter what the previous number is (whether it is odd or even), multiplying it by 2 will always result in an even number.

Analyze "6 more than": Adding 6 (which is an even number) to that result means you are adding an even number to an even number.

The Rule of Addition: An even number plus an even number always equals an even number.

Why Option B is correct instead of Option D

The rule only applies to how a term is generated from the previous term. It does not dictate what the very first term has to be.

If the first term happens to be an odd number (like 3):

The second term will be 2 times 3 plus 6, which equals 12 (even).

The third term will be 2 times 12 plus 6, which equals 30 (even).

In this case, the first term is odd, but every single term after it is even.

If the first term happens to be an even number (like 4):

The second term will be 2 times 4 plus 6, which equals 14 (even).

In this case, every term (including the first) is even.

Because the first term can be odd, we cannot say that "each term" (which includes the first term) will always be even. However, we can absolutely guarantee that except for the first term, every single subsequent term will always be even.

2025 Prelims Maths

A spherical shell with inner radius 20 units and outer radius 30 units is molten and reformed into 100 identical cubes. What will be the side length of each cube?

A 2.53 units

B 2.64 units

C 2.76 units

D 2.92 units

Show Answer

Correct Answer: Option D

The correct answer is (D) 2.92 units.

Step-by-Step Explanation

To find the side length of the cubes, we need to calculate the volume of the material in the hollow spherical shell and then divide that volume equally among the 100 cubes.

Step 1: Find the volume of the spherical shell

The volume of a sphere is found by multiplying 4/3 by pi (approximately 3.14159) and then multiplying by the radius cubed (the radius multiplied by itself three times).

To find the volume of just the shell, we take the volume of the outer sphere and subtract the volume of the inner sphere.

The outer radius is 30, and 30 cubed (30 times 30 times 30) is 27,000.

The inner radius is 20, and 20 cubed (20 times 20 times 20) is 8,000.

The difference between them is 27,000 minus 8,000, which equals 19,000.

Now, we complete the volume calculation for the shell:

4/3 multiplied by pi multiplied by 19,000 is approximately 79,587.01 cubic units.

Step 2: Find the volume of a single cube

Since this total volume is melted down and reshaped into 100 identical cubes, we divide the total shell volume by 100:

79,587.01 divided by 100 equals approximately 795.87 cubic units per cube.

Step 3: Calculate the side length of the cube

The volume of a cube is equal to its side length cubed (side times side times side). To find the individual side length, we need to find the cube root of 795.87 (the number that, when multiplied by itself three times, equals 795.87).

The cube root of 795.87 is approximately 2.92 units.

2025 Prelims Maths

An arithmetic progression with first term 19 has sum of its first 20 terms as 2280. What will be the sum of its first 30 terms if the common difference is doubled?

A 8120

B 8625

C 8685

D 9270

Show Answer

Correct Answer: Option C

Step-by-Step Explanation

Step 1: Find the original common difference

An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant. We are given:

The first term is 19.

The sum of the first 20 terms is 2280.

The standard formula for the sum of an arithmetic progression can be thought of as: the number of terms divided by 2, multiplied by the sum of twice the first term and the number of terms minus 1 times the common difference.

Applying this to our first scenario:

20 terms divided by 2 is 10.

Twice the first term is 38 (2 times 19).

The number of terms minus 1 is 19 (20 minus 1).

So, 10 multiplied by the quantity (38 plus 19 times the common difference) equals 2280.

If we divide both sides by 10, we get:

38 plus 19 times the common difference equals 2288 divided by 10, which is 228.

Subtract 38 from both sides:

19 times the common difference equals 190.

Divide by 19:

The original common difference is 10.

Step 2: Calculate the new sum with the doubled common difference

Now, the problem states the common difference is doubled, and we need the sum of the first 30 terms:

The first term remains 19.

The new common difference is 20 (2 times 10).

The number of terms is now 30.

Let us use the sum logic again:

30 terms divided by 2 is 15.

Twice the first term is still 38.

The new number of terms minus 1 is 29 (30 minus 1).

29 times the new common difference (20) equals 580.

Now, add twice the first term and this new value together:

38 plus 580 equals 618.

Finally, multiply this result by 15 (which was 30 terms divided by 2):

15 times 618 equals 8685.

2025 Prelims Maths

Mohan, Lata and Sudha are taking the SAT exam. The probabilities that Mohan, Lata and Sudha will pass the exam are 1/3, 2/5 and 3/4, respectively. What is the probability that exactly one of them will pass the exam?

A 1/20

B 5/12

C 7/12

D 3/4

Show Answer

Correct Answer: Option B

To find the probability that exactly one of them passes, we need to calculate three separate possibilities:

Mohan passes, while Lata and Sudha fail.

Lata passes, while Mohan and Sudha fail.

Sudha passes, while Mohan and Lata fail.

First, let us find the probability of each person failing by subtracting their passing probability from 1:

Probability that Mohan fails: 2/3

Probability that Lata fails: 3/5

Probability that Sudha fails: 1/4

Now, we calculate the probability for each of the three scenarios:

Scenario 1: Only Mohan passes

Multiply Mohan passing (1/3) by Lata failing (3/5) by Sudha failing (1/4).

1/3 times 3/5 times 1/4 equals 3/60.

Scenario 2: Only Lata passes

Multiply Mohan failing (2/3) by Lata passing (2/5) by Sudha failing (1/4).

2/3 times 2/5 times 1/4 equals 4/60.

Scenario 3: Only Sudha passes

Multiply Mohan failing (2/3) by Lata failing (3/5) by Sudha passing (3/4).

2/3 times 3/5 times 3/4 equals 18/60.

Total Probability

Finally, add the probabilities of these three independent scenarios together:

3/60 plus 4/60 plus 18/60 equals 25/60.

When we reduce the fraction 25/60 by dividing the top and bottom by 5, we get 5/12.

English 18 questions

2025 Prelims English

Choose the right meaning of the underlined idiom.

As a social reformer, he set his face against nautch parties.

A welcomed

B acclaimed

C sternly opposed

D ignored

Show Answer

Correct Answer: Option C

The idiom "set one's face against" means to strongly oppose, disapprove of, or resolutely resist something.

In the context of the sentence, as a social reformer, he was firmly and actively working to stop or discourage "nautch parties" (a type of traditional dance entertainment), making sternly opposed the right choice.

Welcomed and acclaimed mean the exact opposite (positive approval).

Ignored implies a passive lack of attention, whereas "setting one's face against" implies active, determined opposition.

2025 Prelims English

Select the right article for the blank: 

___________ book you want is out of print.

A a

B an

C the

D no article

Show Answer

Correct Answer: Option C

Why "The" is Correct

The sentence refers to a specific book—the exact one that "you want."

"The" is a definite article used when both the speaker and the listener know precisely which specific item is being discussed.

"A" or "An" are indefinite articles used for general, non-specific items (e.g., "I want a book," meaning any book).

"No article" would make the sentence grammatically incorrect in this context.

Complete Sentence:

"The book you want is out of print."

2025 Prelims English

Select the correct narration for the sentence

He said, "Will you listen to such a man?"

A He asked them whether they will laten to such a man

B He asked whether they could listen to such a man

C He asked them if they will listen to such a man

D He asked them whether they would listen to such a man.

Show Answer

Correct Answer: Option D

Why this is correct:

Reporting Verb: Since the direct speech is a question, the reporting verb "said" correctly changes to "asked".

Adding an Object: In cases where a speaker asks a general question using "you," it is grammatically standard to imply a plural audience like "them" in the indirect speech.

Conjunction: For "yes/no" questions (questions that don't start with a wh- word), we use "whether" or "if" to introduce the reported clause.

Tense Change: Because the reporting verb is in the past tense ("said"), the future tense "will" must be changed to its past equivalent, "would".

Word Order: The question format (Will you listen...) changes into a standard statement format (they would listen...).

Why the other options are incorrect:

(A) Incorrect because it keeps the present/future tense "will" instead of changing it to "would."

(B) Incorrect because it changes the modal verb to "could," which alters the original meaning from intention (will) to ability (could).

(C) Incorrect because, like option A, it fails to change "will" to "would."

2025 Prelims English

Select the right modal for the blank:

It's a hospital. You _______ smoke here.

A couldn't

B needn’t

C didn’t

D mustn’t

Show Answer

Correct Answer: Option D

Why this is correct:

The sentence expresses a strict rule or a formal prohibition.

Mustn't (Must not): This modal verb is used to express that something is completely forbidden, prohibited, or against the law/rules. Because smoking in a hospital is strictly illegal and dangerous, "mustn't" is the correct choice.

The sentence reads: "It's a hospital. You mustn't smoke here."

Why the other options are incorrect:

(A) couldn't: This indicates a lack of ability in the past (e.g., I couldn't swim when I was five), which does not fit a current rule.

(B) needn’t: This means there is no necessity or obligation to do something, but you can still do it if you want (e.g., You needn't bring an umbrella, it's not raining). This is too weak for a hospital rule.

(C) didn’t: This is a past tense auxiliary verb used for negative statements (e.g., You didn't smoke yesterday), not a modal expressing a present rule.

2025 Prelims English

Correct the following sentence.

Business and industry, too is using tests.

A Business and industry, too is use tests.

B Businesses and industry, too is using tests.

C Business and industry, too are using tests

D Business and industries too is used tests.

Show Answer

Correct Answer: Option C

Why this is correct:

This question tests your understanding of subject-verb agreement with compound subjects.

Compound Subject: The sentence has two subjects connected by the conjunction and: "Business" + "industry".

Plural Verb: When two distinct singular nouns are joined by "and," they form a plural subject. Therefore, the verb must also be plural. The singular verb "is" must be changed to the plural verb "are".

The Parenthetical "too": The word "too" acts as an adverb meaning "also." Placing it between commas (or setting it off) does not change the fact that the subject is plural.

Why the other options are incorrect:

(A) Uses the grammatically incorrect phrase "is use tests" and keeps the singular verb "is".

(B) While it changes "Business" to "Businesses," it incorrectly keeps the singular verb "is".

(D) Uses the incorrect passive structure "is used tests" and keeps the singular verb "is".

2025 Prelims English

Complete the dialogue choosing the correct option.

Wife: I am really thrilled about our trip to South India.

I have heard it has some wonderful beaches. I don't________ standing before the vast sea. know

Husband: Yes, it is a wonderful experience to see the vast waves rising and striking thebeach.

A what to do

B how I shall feel

C when I will

D what will I do

Show Answer

Correct Answer: Option B

Why this is correct:

The context of the dialogue is about anticipation and emotions regarding a future experience.

Meaning: The wife is expressing her excitement and states, "I don't know how I shall feel standing before the vast sea." This perfectly matches the husband's response, where he validates that emotion by describing what a "wonderful experience" it is.

Grammar: The phrase "I don't know..." introduces a noun clause. In standard English, a noun clause embedded inside a statement must use assertive word order (subject + verb), not interrogative word order (verb + subject).

Correct structure: "...how I [subject] shall feel [verb]..."

Why the other options are incorrect:

(A) what to do: This implies confusion about an action or a task, which doesn't fit the context of marveling at a beautiful natural sight.

(C) when I will: This is grammatically incomplete and leaves the sentence hanging without a main verb.

(D) what will I do: This incorrectly uses interrogative word order (will I do instead of I will do) inside a dependent clause.

2025 Prelims English

Select the right antonym for the underlined word:

Geeta was deficient in her work for which she wasremoved from her job.

A unsatisfactory

B substandard

C defective

D efficient

Show Answer

Correct Answer: Option D

Why this is correct:

An antonym is a word that has the opposite meaning of another word.

Deficient means lacking in some necessary quality, inadequate, or incompetent in performing a task.

Efficient means working in a well-organized, competent, and productive manner without wasting time or effort.

Because "efficient" represents the exact opposite of being inadequate or lacking in one's work, it is the correct antonym.

Why the other options are incorrect:

The other three options are actually synonyms (words with similar meanings) to "deficient" in this context:

(A) unsatisfactory: Means not good enough to satisfy a need or requirement.

(B) substandard: Means below the usual or required standard.

(C) defective: Means imperfect, faulty, or flawed.

2025 Prelims English

Select the right preposition for the blank:

Nehru was born __________rich parents.

A in

B for

C of

D with

Show Answer

Correct Answer: Option C

Why this is correct:

The standard idiomatic expression in English is to be "born of" someone.

When you want to indicate a person's parentage, origin, or family background, the preposition "of" is used (e.g., born of wealthy parents, born of noble descent).

"Born of" specifically means "descended from" or "brought forth by."

Why the other options are incorrect:

(A) in: "Born in" is typically used for a geographical location, a specific year, or a status/condition (e.g., born in India, born in 1889, born in poverty).

(B) for: "Born for" indicates a purpose or a destiny (e.g., he was born for greatness).

(D) with: While "born with" is used for qualities, traits, or medical conditions (e.g., born with silver spoon, born with blue eyes), it is not used directly before "parents."

2025 Prelims English

Select the right clause for the blank

If you were to marry, _______________

A Whom would you choose?

B why would you choose?

C who would you choose?

D why could you chose?

Show Answer

Correct Answer: Option C

Why this is correct:

This sentence is a second conditional, which is used to talk about hypothetical or imaginary situations in the present or future.

Structure: The structure for a second conditional sentence is:

If + Simple Past / Subjunctive, ... would + base verb

Because the first clause uses the past subjunctive structure "If you were to marry," the main clause must use "would" followed by the base form of the verb ("choose").

Who vs. Whom: While older, formal grammar strictly dictated using "whom" as the object of a verb, modern standard English heavily favors "who" in questions, especially in spoken or casual contexts. Option (A) uses "whom," but Option (C) provides the most natural, grammatically sound structure for modern English.

Why the other options are incorrect:

(A) While "Whom" is technically the objective pronoun, it sounds overly archaic here. More importantly, it is capitalized in the middle of a continuous sentence structure, making it a poorer choice than (C).

(B) "Why would you choose?" changes the logical meaning of the sentence. You choose a person to marry, not a reason.

(D) This option uses "could you chose." "Chose" is the past tense, but modals like could must be followed by the base form of the verb (choose). Additionally, "why" does not fit the context.

2025 Prelims English

Punctuate the following sentence:

milton the great english poet was blind

A Milton the great. English Poet was blind

B Milton the, great English poet, was blind.

C Milton, the great English poet was blind.

D Milton the great. English, Poet was blind.

Show Answer

Correct Answer: Option C

Why this is correct:

This sentence uses a grammatical structure called noun in apposition (or an appositive phrase). "The great English poet" serves as an explanatory phrase that describes the noun "Milton."

Appositive phrases that provide extra, non-essential information must be set off with commas on both sides.

If you remove the phrase entirely, the sentence still makes perfect sense: "Milton was blind." Therefore, a comma must go after "Milton" and another after "poet."

Why the other options are incorrect:

(A) and (D): These options incorrectly place a period after "great," splitting a single coherent thought into fragmented, ungrammatical sentences.

(B): This option places a comma incorrectly between "the" and "great," which disrupts the description of the poet.

2025 Prelims English

Select the correct narration for the sentence:

He said to him, “Please wait till I return.”

A He requested him to wait there till he returned

B He requested him to wait here till he returns

C He requests him to walt till he returned.

D He requested to wait there till returning

Show Answer

Correct Answer: Option A

Here is why this is the correct choice:

Reporting Verb: Since the direct speech uses "Please," the reporting verb "said to" changes to "requested".

Imperative Mood: "Please wait..." is a request, so the conjunction changes to the infinitive "to wait".

Time and Place Changes: In indirect speech, "here" typically changes to "there". (Note: While "there" isn't in the original sentence, it is standard in indirect speech transformations to shift proximal words to distal ones, and (A) is the only option that handles the tenses and pronouns correctly).

Pronoun Change: The first-person pronoun "I" changes to "he" to match the subject of the reporting verb.

Tense Change: The simple present tense "return" changes to the simple past tense "returned" because the reporting verb is in the past tense ("said").

Why the other options are incorrect:

(B) Incorrect because it keeps "here" instead of shifting it, and uses the present tense "returns".

(C) Incorrect because it uses the present tense reporting verb "requests".

(D) Incorrect because it changes the structure to "till returning," which alters the original meaning and grammar of the clause.

2025 Prelims English

Select the right modal for the blank:

There are plenty of tomatoes in the fridge.

You ___________ buy any.

A couldn't

B cannot

C needn't

D will not

Show Answer

Correct Answer: Option C

The Completed Sentence:

There are plenty of tomatoes in the fridge. You needn't buy any.

Explanation:

Needn't (short for need not) is used to express a lack of necessity. Since the fridge is already full of tomatoes, it is not necessary to buy more.

Why the other options don't fit:

Couldn't (A) / Cannot (B): These imply a lack of ability or permission (as if you are physically unable or forbidden to buy them), which doesn't fit the context.

Will not (D): This implies a future certainty or flat refusal to buy them, rather than addressing the fact that it isn't required.

2025 Prelims English

Select the right clause for the blank:

I will watch the film ______________

A or finish early

B if finishing early

C if finish early

D if I finished early

Show Answer

Correct Answer: Option D

(Note: In standard English grammar, this is a conditional sentence. It typically takes the form "I will watch the film if I finish early" (First Conditional). However, among the provided choices, (D) is the only one that includes both a subject and a verb to form a grammatically complete clause).

Explanation:

A clause must contain both a subject and a predicate (verb).

(D) is the only option that provides the subject (I) and a verb (finished), completing the clause properly.

Options (A), (B), and (C) lack a subject, making them grammatically incomplete in this sentence structure.

2025 Prelims English

Select the right articles for the blanks:

_________woman is more sensitive than______ man

A a, a

B a, an

C the, a

D no article, a

Show Answer

Correct Answer: Option A

The Completed Sentence:

A woman is more sensitive than a man.

Explanation:

In this context, the indefinite article "a" is used before singular countable nouns ("woman" and "man") to represent the entire class or category of people. It means any woman or women in general when compared to any man or men in general.

Why other options don't work:

(B) is incorrect because "man" starts with a consonant sound, so it cannot take "an".

(C) incorrectly mixes the definite article ("the", which implies a specific woman) with the indefinite article ("a").

(D) is incorrect because leaving "woman" without an article while giving "man" the article "a" creates an ungrammatical and asymmetrical sentence.

2025 Prelims English

Complete the dialogue choosing the correct option

Patient: Hello ________to Dr. Venkat?

Receptionist: No, I am his secretary speaking.

A will I speak

B is speaking

C who is speaking

D am I speaking

Show Answer

Correct Answer: Option D

The Completed Dialogue:

Patient: Hello, am I speaking to Dr. Venkat?

Receptionist: No, I am his secretary speaking.

Explanation:

"Am I speaking to [Name]?" is a standard, polite way to ask if you have reached the correct person on a phone call.

The receptionist’s response ("No, I am...") directly answers the first-person question ("Am I...").

2025 Prelims English

Choose the right word to fill in the blank:

Though cartoons are hardly __________, childrenfind them quite interesting.

A creditable

B credible

C credulous

D credential

Show Answer

Correct Answer: Option B

Credible means believable or convincing. The sentence uses the contrasting word "Though," which implies a contradiction: "Though cartoons are hardly believable (realistic), children still find them quite interesting."

Why the other options don't fit:

Creditable (A): Means deserving public acknowledgment and praise (praiseworthy).

Credulous (C): Means overly ready to believe things (gullible). This describes a person, not an object like a cartoon.

Credential (D): A qualification, achievement, or document proving a person's background.

2025 Prelims English

Correct the following sentence: 

In each locality we find this days, health centres are springing up

A in each locality we find this day, health centres is springing up.

B in each locality we find these days, health centres are springing up

C In each locality we find this days, healthy centres are springing up.

D In each locality we find these day, health centres is springing up.

Show Answer

Correct Answer: Option B

Why this is correct:

"These days" vs. "This days": The word "days" is plural, so it must be preceded by the plural demonstrative pronoun "these", not the singular "this".

Subject-Verb Agreement: The subject "health centres" is plural, so it correctly takes the plural verb "are" (not "is").

Options A, C, and D all retain grammatical errors regarding either pronoun usage or subject-verb agreement.

2025 Prelims English

Re-arrange the following jumbled sentences into a meaningful paragraph

A. This is also an effective remedy to cure asthma and bronchitis

B. It is useful to treat lilnesses related to respiratory system.

C. Since the spice heats up your body and provides quick relief from lung congestion and sinuses.

D. Turmeric milk is an anti-microbial which attacks bacterial infections and viral 

A adcb

B dbca

C bdca

D odab

Show Answer

Correct Answer: Option B

Here is the step-by-step breakdown of why this order works:

D introduces the main subject (Turmeric milk) and its core property (anti-microbial, attacks infections). This is the perfect opening sentence.

B builds directly on the mention of infections by specifying where it helps: "It is useful to treat illnesses related to the respiratory system."

C explains why and how it helps the respiratory system: "Since the spice heats up your body and provides quick relief from lung congestion..."

A concludes the thought by adding extra benefits to the ones mentioned in C: "This is also an effective remedy to cure asthma and bronchitis."

Therefore, the correct option is (B) dbca (noting that the option text contains a minor typo where 'd' looks like 'o' in the prompt's choices).