Maths PYQ — Page 3

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?

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?