Number System T...

How many numbers are there between 500 and 600 in which 9 occurs only once?

2! + 4! + 6! + 8! + 10! +.......100! when divided by 3, would leave remainder

For any natural number n, n⁴ + n² + 1 is always

Solve for x: .

Let D be a rational number of the form D = 0. abcd abcd abcd ......, where digits a, b, c and d are integers lying between 0 to 9. At most three of these digits are zero. By which number should D be multiplied so that the result will be a natural number?

What is the greatest positive power of 5 that exactly divides 30!?

The largest number that always divides the product of 3 consecutive multiples of 2 is

The sum of two natural numbers is 85 and their LCM is 102. Find the numbers.

By which smallest number must 21,600 be multiplied or divided in order to make it a perfect square?

If we write all the natural numbers from 259 to 492 side by side, we shall get a very large natural number 259260261262…490491492. How many 8s will be used to write this large natural number?

When the sum of two natural numbers is multiplied by each number separately, the products obtained are 2418 and 3666. What is the difference between the two numbers?

If 'p' be a number between 0 and 1, which one of the following is true?

Dividing by 3/8 and then multiplying by 5/6 is equivalent to dividing by which number?

A number when divided by 238, leaves a remainder 79. What will be the remainder when that number is divided by 17?

What is the remainder when 17 to the power 23 is divided by 16?

The product of two numbers is 16,200. If their LCM is 216, find their HCF.

The LCM of two numbers is 72 and their HCF is 12. If one of the numbers is 24, what is the other number?

4a56 is a four digit number divisible by 33. What is the value of a?

A number when divided by 5 leaves a remainder 3. What is the remainder when the square of this number is divided by 5?

A two digit number is such that cube of its 24^th part is same as the number obtained by interchanging the digits of the number. What is the number?

What are the unit digits of 3⁶⁹, 6⁸⁶⁴ and 4⁷²⁵, respectively?

If the last two digits of a four-digit number are interchanged, the new number obtained is greater than the original number by 54. What is the difference between the last two digits of the number?

A number formed by writing any digit 6 times (say as 444444 or 999999) is always divisible by

A positive interger which is nearest to 1000 and divisible by 2, 3, 4, 5 and 6 is

There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and that of the last three is 1001. Find the first number.