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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