KVPY SB SX Exam 2011 Question Paper

Question : 12 of 120

Marks: +1, -0

f(x)=(2011+x)^n

, where x is a real variable and n is a positive integer, then the value of

f(0)+f'(0)+{f"(0)}/2!+

...+{f^(n-1)(0)}/(n-1)!

Solution:

(2011)^n + ^nC_1(2011)^{n-1}

+ ^nC_2(2011)^{n-2}

+…+ ^nC_{n-1} 2011 + ^nC_{n-1}

= (2011 + 1)^{n - 1 }

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