IAS 2024 — Maths

A can X contains 399 liters of petrol and a can Y contains 532 liters of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of liters is an integer. How many different bottle sizes are possible?

Two persons P and Q enter into a business. P puts ₹14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹400 more than Q’s share out of the total profit of ₹2,000, what is the capital contributed by P?

Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements: 1. (p – r)2 (qs) is even. 2. (q – s) q2 s is even. 3. (q + r)² (p + s) is odd. Which of the statements given above are correct?

Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?

What is the number of fives used in numbering a 260-page book?

A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?

325 + 227 is divisible by

What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?

Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10: 1. The unit digit of S can be 0. 2. The unit digit of S can be 9. 3. The unit digit of S can be 5. Which of the statements given above are correct?

421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?

On January 1st, 2023, a person saved ₹1. On January 2nd, 2003, he save ₹2 more than that on the previous day. On January 3rd, 2023, he saved ₹2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube?

Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?

Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X+Y) is the greatest two-digit number, then what is the number of possible values of X?

What is the sum of the first 28 terms in the following sequence? 1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,..

What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?

A number is mistakenly divided by 4 instead of multiplying by 4. What the percentage change in the result due to this mistake?

In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, –, × each at most two times. What is the smallest non-negative value of the expression?

Consider the following: Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women If the average weight of the women is 63 kg, then what is the average weight of the boys?

X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?

A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?

How many consecutive zeros are there at the end of the integer obtained in the product \(1^{2} \times 2^{4} \times 3^{6} \times 4^{8} \times ... \times 25^{50}\)?

If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

222333 + 333222 is divisible by which of the following numbers?

P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary?

Consider the following: 1. 1000 litres = 1 m³ 2. 1 metric ton = 1000 kg 3. 1 hectare \( = 10000\text{ }\text{m}^{2} \) Which of the above are correct?

The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements: 1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples. 2. The total cost of one orange and one mango is equal to the cost of one apple. Which of the statements given above is/are correct?

What is the rightmost digit preceding the zeros in the value of 3030?