What is the remainder when 65^99 is divided by 11?

Consider the following numbers :

1. 437

2. 797

3. 1073

How many of the above numbers are prime ?

The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number ?

When every even power of every odd integer (greater than 1) is divided by 8, what is the remainder ?

It is given that 5 does not divide n - 1, n and n + 1, where n is a positive integer. Which one of the following is correct?

What is the largest 5-digit number, which leaves remainder 7, when divided by 18 as well as by 1 ?

Average marks in Mathematics of Section A comprising 30 students is 65 and that of Section B comprising 35 students is 70. What are the average marks (approximately) of both the sections if it was detected later that an entry of 47 marks was wrongly made as 74?

Consider the following statements in respect of all factors of 360 :

1. The number of factors is 24.

2. The sum of all factors is 1170.

Which of the above statements is/are correct?

Consider a 6-digit number of the form XYXYXY. The number is divisible by :

Let m and n be natural numbers. What is the minimum value of (m + n) such that 33m + 22n is divisible by 121?

The number 97^30 - 14^30 is divisible by:

Consider the following statements :

1. n³ - n is divisible by 6

2. n⁵ - n is divisible by 5

3. n⁵ - 5n³ + 4n is divisible by 120

Which of the statements given above are correct ?

What is the last digit of the sum S = 9²⁷ + 27⁹ ?

If three times the greater of two numbers is divided by the smaller number, the quotient will be 6 and the remainder will be 6. If five times the smaller number is divided by the greater number, the quotient will be 2 and the remainder will be 3. What is the difference between the numbers ?

There are two natural numbers x and y, where x >.y When x is divided by 6, it leaves the remainder 2 and; when y is divided by 6, it 22. leaves the remainder 3. What is the remainder when (x - y) is divided by 6?

The value of a 2-digit number is 5 times the sum of the digits. What is the product of the digits ?

Consider the number N= 12⁶ × 3⁸ x 5³. Which of the following statements is/are correct ?

1. The number of odd factors of N is 60.

2. The number of even factors of N is 720.

Select the correct answer using the code given below:

If p is the difference between a number and its reciprocal and q is the difference between the square of the same number and the square of its reciprocal, then what is p⁴ + 4p² equal to ?

What is the median of all possible factors of 120 ?

Select the missing number from the given alternatives :

How many numbers between 200 and 600 are divisible by 4, 5 and 6?

The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The number are

If sign +, represents multiplication, x addition; - division, ÷ difference, > equal and = represents greater than, then which of the following relation is true?

How many times the digit 9 occurs in the numbers from 100 to 999?

Which one of the following cannot be the square of a natural number?

How many prime numbers are there between 1 and 50?

A number when divided by 342 gives a remainder 47. When the same number is divided by 19, what would be the remainder?

How many numbers between 11 and 90 are divisible by 7?

How many numbers between 100 and 500 are divisible by 4, 5 and 6?

What are the two natural numbers whose product is 2400 and the sum of whose squares is 5200?

If the median of observations

12, 1, 8, 54, 61, 28, 45, 35, 21, 17

is M, then what is the value of 2M + 5?

A 2-digit number is such that the sum of the number and the number obtained by reversing the order of the digits of the number is 55. Further, the difference of the given number and the number obtained by reversing the order of the digits of the number is 45. What is the product of the digits?

What is the digit at the 100th place of number (225)⁴⁰ ?

When the number 12345678910111213 . . . 99100 is divided by 16, what will be the remainder?

What is the smallest natural number n such that (n + 1) x n x (n - 1) x (n - 2) x . . . 3 x 2 x 1 is divisible by 910 ? (where x is multiplication symbol)