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B
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C
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D
All of these
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Solution
The correct option is B (1+x)n=1+nx+n(n−1)2!x2+n(n−2)3!x3+⋯ ⇒(1+x)n−nx−1 =x2[n(n−1)2!+n(n−1)(n−2)3!x+⋯] From above it is clear that (1+x)n−nx−1 is divisible by x2 Trick : (1+x)n−nx−1. Put n=2 and x=3; Then 42−2.3−1=9 is not divisible by 6, 54 but divisible by 9. Which is given by option (b) i.e., x2=9