**Question 1:**

Let a, b, c be distinct digits. Consider a two-digit number ‘ab’ and a three-digit number ‘ccb’, both defined under the usual decimal number system, if (ab)

^{2}= ccb > 300, then the value of b is

Topic: Digits

[1] 1

[2] 0

[3] 5

[4] 6

**Question 2:**

The remainder when 7

^{84}is divided by 342 is

Topic: Remainders

[1] 0

[2] 1

[3] 49

[4] 341

**Question 3:**

If n = 1+ x where x is the product of four consecutive positive integers, then which of the following is/are true?

A. n is odd

B. n is prime

C. n is a perfect square

Topic: Basics

[1] A and C only

[2] A and B only

[3] A only

[4] None of these

**Question 4:**

For two positive integers a and b define the function h(a,b) as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the G.C.F of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is

Topic: HCF LCM

[1] \(\frac{1}{2}n\)

[2] \(\left( {n - 1} \right)\)

[3] N

[4] None of these

**Question 5:**

Let D be a recurring decimal of the form D = 0. abababab ..., where digits a and b lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D?

Topic: Digits

[1] 18

[2] 108

[3] 198

[4] 288