IAS 2025 — Maths

If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?

How many possible values of (p + q + r) are there satisfying [Image: image] where p, q, and r are natural numbers (not necessarily distinct)?

A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the train?

Three prime numbers p, q, and r, each less than 20, are such that p – q = q – r. How many distinct possible values can we get for (p + q + r)?

The 5-digit number PQRST (all distinct digits) is such that T is not equal to 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to the ratio of number of runs scored by Y to number of runs scored by Z. Value-I = Runs scored by X Value-II = Runs scored by Y Value-III = Runs scored by Z Which one of the following is correct?

A natural number N is such that it can be expressed as N = p + q + r, where p, q, and r are distinct factors of N. How many numbers below 50 have this property?

A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills [Image: image] th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?

The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹ 90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?

X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in [Image: image] days. What is n equal to?

There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?

A 4-digit number N is such that when divided by 3, 5, 6, 9 it leaves a remainder of 1, 3, 4, 7 respectively. What is the smallest value of N?

If N2 = 12345678987654321, then how many digits does the number N have?

Consider a set of 11 numbers: Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ –5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct?

If n is a natural number, then what is the number of distinct remainders of [Image: image] when divided by 4?

Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR − PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?

P and Q walk along a circular track. They start at 5:00 am. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999?

Let x be a real number between 0 and 1. Which of the following statements is/are correct? 1. [Image: image] 2. [Image: image] Select the correct answer using the code given below:

The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?

What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35n?

Let both p and k be prime numbers such that (p2 + k) is also a prime number less than 30. What is the number of possible values of k?

Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers. Value-II = Maximum value of p × q when p ≥ 6, q ≥ 4. Which one of the following is correct?

Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

What is the 489th digit in the number 123456789101112...?

What is the remainder when [Image: image] is divided by 6?

Let [Image: image] be a 3-digit number. What is the HCF of P and 481?

The price (p) of a commodity is first increased by k%, then decreased by k%; again increased by k%, and again decreased by k%. If the new price is q, then what is the relation between p and q?

Consider the following statements: 1. There exists a natural number which when increased by 50% can have its number of factors unchanged. 2. There exists a natural number which when increased by 150% can have its number of factors unchanged. Which of the statements given above is/are correct?

Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had Team Y's average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by Team X?