JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Analyzing +4 | -1

Statement-1

\sum\limits_{r=0}^n(r+1){ }^n C_r=(n+2) \cdot 2^{n-1}

Statement - 2

\sum\limits_{{r=0}}^n(r+1)^n C_r x^r

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

View answer and explanation

Correct option: A

Statement-1 is true, Statement-2 is true; Statement-2 is a
correct explanation for Statement-1

Option A is correct because both Statement-1 and Statement-2 are true, and Statement-2 provides a general formula that, when evaluated at x=1, proves Statement-1.

More Questions from BINOMIAL THEOREM

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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

equals If

a

and

d

are two complex numbers, then the sum to

\left( {n + 1} \right)

terms of the following series

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

is The number of different terms in the expansion of

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

is The sum of the coefficient of the binomial expansion of

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

is equal to 6561 . The constant term in the expansion is The coefficient of

{x^5}

in the expansion of

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

is If

\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

, then

n

equals