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Remainders - 2 || Quantitative Aptitude || CAT 2021 || 14 April

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Question 1

What is the remainder when 675n is divisible by (n – 9125) , where n is the the lowest number which when increased by 6 is divisible by 35, 63 and 87 .

Question 2

If n is not a prime and greater than 4 , then find the remainder when 7n − 6n(3n − 2) − 7 is divided by 18 .

Question 3

A set P comprises 303 squares of natural numbers, selected at random. What is the maximum number of elements of P that one can always find such that each of them leaves the same remainder when divided by 9?

Question 4

A natural number x when divided by k gives a remainder of 5 . When the square of another number y is divided by k, the remainder is 1. If x and y are consecutive natural numbers, then the value of k cannot be

Question 5

The number 37371 - 26371 is divisible by:

Question 6

What is the remainder when 4500! – 6161 is divided by 7 ?

Question 7

How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

Question 8

If N is a 50 digit number where each digit is a prime number. If N is to be maximized and maximum possible value of N gives x + 1  as remainder when divided by 74, then what should be the value of x.

Question 9

Let n! = 1×2×3×…….×n for integer n3 1. If p =1! + (2×2!) + (3×3!) + ……..+ (10×10!) then p + 2 when divided by 11! Leaves a remainder of

Question 10

The integers 34041 and 32506 when divided by a three-digit integer n,  leave the same remainder. What is n?
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