JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

p(x)=x^n

, then the value of

p(1)+\frac{p^{\prime}(1)}{1 !}+\frac{p^{\prime \prime}(1)}{2 !}+\cdots+\frac{p^{(n)}(1)}{n !}

, where

p^{(r)}(x)

stands for the

r^{\text {th }}

derivative of

p(x)

with respect to

x

, is

View answer and explanation

Correct option: A

2^n

Option A (

2^n

) is correct because the given expression is equivalent to the binomial expansion of (1+1)^n, which equals 2^n.

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

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(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

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\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n