# Short cuts & techniques CAT QA -1

Read the question carefully and mark the best choice or fill in the blanks:

1. Find the remainder when 7^131 is divided by 6.
a) 1 b)2 c)3 d)5
2. Find the remainder when 101! is divided by 103 .
a)1 b) 102 c) 0 d) none of these
3. Find the remainder when 10^42 is divided by 21.
a) 1 b) 17 c) 20 d) 5
4. Find the last non zero digit of 20!.
a) 6 b)8 c) 7 d)9
5. Find the number of intergral solutions that satisfy the equation IxI + IyI < = 3
a)24 b)25 c)12 d) 11
6. If x^5 – x^4 + 2x^3 -7x^2+ 6x+10=0, Find the value of (1+a)(1+b)(1+c)(1+d)(1+e) where a,b,c,d,e are
roots of the given equation.
7. 1. A:B = 2:3 B:C = 4:5 C:D = 6:11 D:E = 12:17 Find A:B:C:D:E ………………………….
8. Find the minimum value of the expression Ix-2I + Ix+6I +Ix+3I +Ix-6I +Ix-1I +Ix-4I
a) 15 b)18 c)20 d) 24
9. Sum the series S= 1.2 +3.2^2 +6. 2^3 + 10.2^4+………..55.2^10
10. Find the number of ways in which 576 can be represented as a product of two of its factors.
a ) 10 b) 12 c)36 d)21
11. Find the number of ways in which 6 can be represented as a product of two co primes.
a) 4 b)3 c)2 d)1
12. Find the number of trailing zeroes in 12! in base 6.
a)4 b) 5 c)2 d)3