If the coefficient of x¹⁵ in the expansion of (a x³+1/(~b x^(1 / 3)))¹⁵ is equal to the coefficient of x⁻¹⁵ in the expansion of (a x^(1 / 3)-1/(b x³))¹⁵, where a and b are positive real numbers, then for each such ordered pair (a, b):

Binomial Theorem and Its Simple Applications: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Morning shift · Q2939

JEE Main 202330 Jan, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

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

JEE Main 202330 Jan, Morning shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

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})