Number System Questions with Solutions

The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's place is 3 more than the digit in the ten's place, then the number is

How many numbers from 1 to 100 are divisible by 8 and have at least one digit equal to 8?

How many numbers between 1 and 1000 (both excluded) are both squares and cubes?

Find the remainder when $X=1!+2!+3!+\cdots +100!$ is divided by $240$.

Find the unit digit of ${\left(13647\right)}^{3265}$.

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

Let $x,y,z$ be distinct integers, where $x$ and $y$ are odd positive integers and $z$ is an even positive integer. Which of the following cannot be true?

Choose the correct option for the remainder when $X=1!+2!+3!+\dots +100!$ is divided by 24.

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is

The remainder when $2^{31}$ is divided by 5 is

The last digit of the number obtained by multiplying the numbers 81 x 82 x 83 x 84 x 85 x 86 x 87 x 88 x 89 is

How many numbers between 1 and 1000 are divisible by all the numbers 2, 3, 4, 5 and 6?

Among the given numbers below, the smallest number which, when divided by 9, 10, 15 and 20, leaves the remainders 4, 5, 10 and 15 respectively, is

Ramu visits Delhi every 15 days and Samu goes to Delhi every 20 days. They met at Delhi 5 days back. After how many days, from today, will they meet at Delhi next time?

A two-digit number is such that the product of its digits is 12. If 36 is added to the number, the digits interchange their places. What is the number?