$r$ and $n$ are positive integers such that $r > 1,n > 2$ and coefficients of ${\left( {r + 2} \right)^{{\rm{th}}}}$ term and${\left( {3r} \right)^{{\rm{th}}}}$ term in the expansion of ${\left( {1 + x} \right)^{2n}}$ are equal, then $n$ equals

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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Application +4 | -1

r

and

n

are positive integers such that

r > 1,n > 2

and coefficients of

{\left( {r + 2} \right)^{\mathrm{th}}}

term and

{\left( {3r} \right)^{\mathrm{th}}}

term in the expansion of

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

are equal, then

n

equals

View answer and explanation

Correct option: C

2r

Option C (2r) is correct because equating the coefficients and solving for n yields n = 2r.

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