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Question
Assertion :STATEMENT-1 : Coefficient of x51 in the expansion of (x−1)(x2−2)(x3−3).......(x10−10)is−1 Reason:
STATEMENT-2 :If n∈I and n>3,then coefficient of xn(n+1)2−4 in the expansion of (x−1)(x2−2)(x3−3).......(xn−n) is −1
Assertion :STATEMENT-1 : Coefficient of x51 in the expansion of (x−1)(x2−2)(x3−3).......(x10−10)is−1 Reason:
STATEMENT-2 :If n∈I and n>3,then coefficient of xn(n+1)2−4 in the expansion of (x−1)(x2−2)(x3−3).......(xn−n) is −1
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Solution
The correct option is A Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
xn(n+1)2−4.
We substitute n=10 in the above expression.
x10(11)2−4
=x55−4
=x51.
Hence for n=51 coefficient is −1.
Hence both the statements are true.
xn(n+1)2−4.
We substitute n=10 in the above expression.
x10(11)2−4
=x55−4
=x51.
Hence for n=51 coefficient is −1.
Hence both the statements are true.
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