CAT Previous Year Questions| Number System

CAT 2019 Slot 2 Question 2

How many factors of 2⁴ × 3⁵ × 10⁴ are perfect squares which are greater than 1?

CAT 2018 Slot 2 Question 3

If N and x are positive integers such that N^N = 2¹⁶⁰ and N² + 2^N is an integral multiple of 2^x, then the largest possible x is

CAT 2018 Slot 1 Question 4

The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is

CAT 2021 Slot 3 Question 5

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

CAT 2021 Slot 2 Question 6

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

CAT 2021 Slot 1 Question 7

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the 15th group is equal to

CAT 2021 Slot 1 Question 8

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

CAT 2020 Slot 3 Question 9

Let N, x and y be positive integers such that N = x + y, 2 25, then how many distinct values are possible for N?

CAT 2020 Slot 2 Question 10

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

CAT 2019 Slot 1 Question 11

The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

CAT 2018 Slot 2 Question 12

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

CAT 2018 Slot 2 Question 13

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

CAT 2018 Slot 1 Question 14

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

CAT 2017 Slot 2 Question 15

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is