If the coefficient of ${x^7}$ in ${\left( {a{x^2} + \frac{1}{{bx}}} \right)^{11}}$ equal the coefficient of ${x^{ - 7}}$ in ${\left( {ax - \frac{1}{{b{x^2}}}} \right)^{11}},$ then $a$ and $b$ satisfy the relation

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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Analyzing +4 | -1

If the coefficient of

{x^7}

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

equal the coefficient of

{x^{ - 7}}

{\left( {ax - \frac{1}{{b{x^2}}}} \right)^{11}},

then

a

and

b

satisfy the relation

View answer and explanation

Correct option: A

ab = 1

Option A (

ab = 1

) is correct because equating the coefficients of

{x^7}

and

{x^{ - 7}}

leads to this relationship between

a

and

b

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