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UPSC NDA II 2023 Mathematics Solved Paper

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Consider the following for the next three (03) items that follow :

Let

(1+x)^n=1+T_1 x+T_2 x^2+T_3 x^3+. . .+T_n x^n

.

[NDA II 2023]

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Question : 39 of 120

Marks: +1, -0

What is

1 - T_1 + 2 T_2 - 3 T_3 + \dots + (-1)^{n} n T_n

0
$-2^{n-1}$
$n 2^{n-1}$
1

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