If the coefficient of $x^8$ in $\left(a x^2+\frac{1}{b x}\right)^{13}$ is equal to the coefficient of $x^{-8}$ in $\left(a x-\frac{1}{b x^2}\right)^{13}$, then $a$ and $b$ will satisfy the relation

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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Application +4 | -1

If the coefficient of

x^8

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

is equal to the coefficient of

x^{-8}

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

, then

a

and

b

will satisfy the relation

View answer and explanation

Correct option: A

a b+1=0

Option A (

a b+1=0

) is correct because equating the coefficients of

x^8

and

x^{-8}

leads to the relation

ab = -1

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