**Some Basic Formula**

i. (a + b)(a – b) = (a2 – b2)

ii. (a + b)2 = (a2 + b2 + 2ab)

iii. (a – b)2 = (a2 + b2 – 2ab)

iv. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

v. (a3 + b3) = (a + b)(a2 – ab + b2)

vi. (a3 – b3) = (a – b)(a2 + ab + b2)

:-

vii. (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)

viii. When a + b + c = 0, then a3 + b3 + c3 = 3abc

**QUESTION**

1.Which one of the following is not a prime number?

A.31

B.61

C.71

D.91

2.(112 x 54) = ?

A.67000

B.70000

C.76500

D.77200

3.It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

A.(216 + 1)

B.(216 – 1)

C.(7 x 223)

D.(296 + 1)

4.What least number must be added to 1056, so that the sum is completely divisible by 23 ?

A.2

B.3

C.18

D.21

E.None of these

5.1397 x 1397 = ?

A.1951609

B.1981709

C.18362619

D.2031719

E.None of these

6.How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336

A.4

B.5

C.6

D.7

7.(935421 x 625) = ?

A.575648125

B.584638125

C.584649125

D.85628125

8.The largest 4 digit number exactly divisible by 88 is:

A.9944

B.9768

C 9988

D.8888

E.None of these

9.Which of the following is a prime number ?

A.33

B.81

C.93

D.97

10.What is the unit digit in {(6374)1793 x (625)317 x (341491)}?

A.0

B.2

C.3

D.5