If the coefficient of … in the expansion of … is equal to the coefficient of … in the expansion of …, where … and … are positive real numbers, then for each such ordered pair … :

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Binomial Theorem

JEE Main 2023 · 30 Jan, Morning shift · Q2939

MathematicsMedium64×since 2002Q2939

If the coefficient of

x^{15}

in the expansion of

\left(\mathrm{a} x^{3}+\frac{1}{\mathrm{~b} x^{1 / 3}}\right)^{15}

is equal to the coefficient of

x^{-15}

in the expansion of

\left(a x^{1 / 3}-\frac{1}{b x^{3}}\right)^{15}

, where

a

and

b

are positive real numbers, then for each such ordered pair

(\mathrm{a}, \mathrm{b})

JEE Main 2023 · 30 Jan, Morning shift · Q2939

MathematicsMedium64×since 2002Q2939

If the coefficient of

x^{15}

in the expansion of

\left(\mathrm{a} x^{3}+\frac{1}{\mathrm{~b} x^{1 / 3}}\right)^{15}

is equal to the coefficient of

x^{-15}

in the expansion of

\left(a x^{1 / 3}-\frac{1}{b x^{3}}\right)^{15}

, where

a

and

b

are positive real numbers, then for each such ordered pair

(\mathrm{a}, \mathrm{b})