Number System T...

If n is any integer, which of the following statements is true?

Find the number of pairs of natural numbers with LCM equal to 56.

There are 5 consecutive natural numbers with L.C.M. 60. The product of the first two numbers is equal to the 5^th number. What is the sum of the numbers?

The numbers a and b have prime factors as 2 and 3 and their ratio is 36. Which of the following statements is true?

Find the remainder when 9³⁶ is divided by 730.

In a division, the remainder was 71. With the same divisor, but twice the dividend, the remainder is 43. Which of the following numbers is the divisor?

If n is a natural number, n⁴ + n² + 1 is

The sum of all odd numbers of four digits which are divisible by 9 is _______.

How many zeroes are left in the end when we solve 75!?

Two out of six papers for an examination are of physics. What are the number of ways in which the papers can be arranged so that two physics papers are not together?

If t_{n + 1} = 2t_n + 1(n = 0, 1, 2, 3…) and t₀ = 0, which of the following numbers is nearest to t₁₀?

Given odd positive integers x, y and z, which of the following options is not necessarily true?

If n is a natural number, which of the following options must always be odd?

The number 2.525252…. can be written as a fraction when reduced to its lowest form. The sum of the denominator and numerator is ______.

The sum of a 2 digit number and a number obtained by reversing the digits is a perfect square. How many such numbers exist?

Let x + y = 1. Find the minimum value of (x + )² + (y + )².

If a and b are real numbers such that |a| + |b| > |a + b|, which of the following options is true?

Find the maximum power of 3 in 20!.

The remainder obtained when 7⁸⁴ is divided by 342 is

If x is negative, y is greater than 0 and less than 1, and z is greater than 1, then which of the following statements is false?

Find the number of positive integers which are not greater than 100 and are not divisible by 2, 3 or 5.

If x, y > 0, where x is a prime number and y is a composite number, which of the following statements is true?

Find the sum of two digit numbers which gives remainder 3 when divided by 7.

What is the remainder when 4⁹⁶ is divided by 6?

The sum of the quotient and the remainder when a number is divided by 4 is 8 and the sum of their squares is 34. Find the number.