If the coefficients of $ x^{7} $ in $ \left(a x^{2}+\frac{1}{2 b x}\right)^{11} $ and $ x^{-7} $ in $ \left(a x-\frac{1}{3 b x^{2}}\right)^{11} $ are equal, then

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

If the coefficients of

x^{7}

\left(a x^{2}+\frac{1}{2 b x}\right)^{11}

and

x^{-7}

\left(a x-\frac{1}{3 b x^{2}}\right)^{11}

are equal, then

View answer and explanation

Correct option: A

729 a b=32

Option A (

729 a b=32

) is correct because equating the coefficients of

x^7

and

x^{-7}

and simplifying leads to the relationship

729ab = 32

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