12) 2^60 = 8^20 = (7+1)^20 = 1 + C1.7 + C2.72 + ..... + 720
so remainder will be 1.
Q1.The coefficient of X6 in {(1+x)6+(1+x)7+...+(1+x)15} is
(a)16C9 (b)16C5-6C5 (c)16C6-1 (d)None of these
Q2.260 when divided by 7 leaves the remainder
(a)1 (b)6 (c)5 (d)2
Please also explain the respective method used for solving the problem.
Thanx.
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6 Answers
1
1for the first one, evaluate the sum of the GP first...which is basically
(1+x)6[(1+x)10-1]/(x)
=[(1+x)16-(1+x)6]/x
coeff of x6 in this is, 16C7= 16C9
for the second one,
260
=820
=(1+7)20
= 20C0+20C17 +20C272 .....
=1+7K
so the remaider is 1
cheers!!!