If the coefficient of $x^7$ in $\left(a x-\frac{1}{b x^2}\right)^{13}$ and the coefficient of $x^{-5}$ in $\left(a x+\frac{1}{b x^2}\right)^{13}$ are equal, then $a^4 b^4$ is equal to:

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

If the coefficient of

x^7

\left(a x-\frac{1}{b x^2}\right)^{13}

and the coefficient of

x^{-5}

\left(a x+\frac{1}{b x^2}\right)^{13}

are equal, then

a^4 b^4

is equal to:

View answer and explanation

Correct option: C

Option C (22) is correct because after equating the coefficients of x⁷ and x^-5 and simplifying, we find that a⁴b⁴ equals 22.

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