JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Analyzing +4 | -1

Coefficient of

x^m

in the expansion of

S=(1+x)^{2 m}+x(1+x)^{2 m-1}+x^2(1 +x)^{2 m-2} +\ldots .+x^{2 m}

View answer and explanation

Correct option: B

{ }^{2 m+1} C_m

Option B,

{ }^{{2 m+1}} C_m

, is correct because the given series is a geometric progression that simplifies to

(1+x)^{2m+1} - x^{2m+1}

, and the coefficient of

x^m

{ }^{{2m+1}} C_m

More Questions from BINOMIAL THEOREM

Practice All Chapter MCQs →

\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

d

\left( {n + 1} \right)

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

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

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

{x^5}

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

\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