1
###
While writing all the numbers from 700 to 1000, how many numbers occur

While writing all the numbers from 700 to 1000, how many numbers occur in which the digit at hundred's place is greater than the digit at ten's place, and the digit at ten's place is greater than the digit at unit's place?

- 61
- 64
- 85
- 91

2
###
Let p be a prime number greater than 5. Then (p^2 - 1) is

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p^{2} - 1) is

- always divisible by 6, and may or may not be divisible by 12
- always divisible by 24
- never divisible by 6
- always divisible by 12, and may or may not be divisible by 24

3
###
If n is a positive integer, then (√3+1)^2n - (√3-1)^2n is

If n is a positive integer, then (√3+1)^{2n} - (√3−1)^{2n} is

- An even positive integer
- A rational number other than positive integers
- An odd positive integer
- An irrational number

5
###
When we multiply a certain two-digit number

When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits, we get 486. Find the number?

- 81
- 45
- 36
- 54

6
###
Consider four-digit numbers for which the first two digits are equal

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

- 1
- 2
- 3
- 4

7
###
The number of integers n satisfying -n+2 ≥ 0 and 2n ≥ 4 is

The number of integers n satisfying -n+2 ≥ 0 and 2n ≥ 4 is

- 0
- 1
- 2
- 3

8
###
What is the right most non-zero digit of the number 30^2720

What is the right most non-zero digit of the number 30^{2720}?

- 1
- 3
- 7
- 9

9
###
The product of all integers from 1 to 100 will have the following numbers

The product of all integers from 1 to 100 will have the following numbers of zeros at the end?

- 19
- 20
- 22
- 24

10
###
The sum of four consecutive two-digit odd numbers, when divided by 10

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

- 21
- 25
- 41
- 67

11
###
The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

- 55
- 57
- 58
- 59

13
###
What is the digit in the unit’s place of 2^51

What is the digit in the unit’s place of 2^{51}?

- 1
- 2
- 4
- 8

14
###
When you reverse the digits of the number 13, the number increases by 18

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?

- 5
- 6
- 7
- 8

15
###
How many times will the digit 5 come in counting from 1 to 99

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

- 16
- 15
- 14
- 13

16
###
What is the number of all possible positive integer values of n for which n^2 + 96 is a perfect square

What is the number of all possible positive integer values of n for which n^{2} + 96 is a perfect square?

- 2
- 4
- 5
- Infinite

17
###
If N = (11^(p+7)) (7^(q-2)) (5^(r+1)) (3^s) is a perfect cube

If N = (11^{p + 7})(7^{q – 2})(5^{r + 1})(3^{s}) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

- 5
- 6
- 7
- 8
- 9

18
###
If the product of three consecutive positive integers is 15600

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

- 1777
- 1785
- 1875
- 1877

19
###
Let f(x) = x^2 and g(x) = 2x, for all real x

Let f(x) = x^{2} and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

- 16
- 18
- 36
- 40

- Production and legitimation of scientific knowledge can be approached
- The woodland’s canopy receives most of the sunlight
- Impartiality and objectivity are fiendishly difficult concepts
- The beginning of the universe had, of course, been discussed for a long time
- I was so eager not to disappoint my parents that I ran errands for anyone
- The celebrations of economic recovery in Washington may be as premature
- Experts such as Larry Burns, head of research at GM, reckon
- This is now orthodoxy to which I subscribe - up to a point