[JEE Main 2005] if the coefficient of x 7 in ax 2 1 bx 11 equals the
If the coefficient of $x^7$ in $\left(ax^2+\frac1{bx}\right)^{11}$ equals the coefficient of $x^{-7}$ in $\left(ax-\frac1{bx^2}\right)^{11}$, then
(a) $a-b=1$
(b) $a+b=1$
(c) $\frac ab=1$
(d) $ab=1$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (d) $ab=1$
The two coefficients are $\binom{11}5a^6b^{-5}$ and $\binom{11}6a^5b^{-6}$; equality (with $\binom{11}5=\binom{11}6$) gives $ab=1$.
JEE Main 2005 · Binomial Theorem — verified solution by the Vidaara Team.
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