(A) The general term $T_{r+1}$ in the expansion of $(x^2 - x^{-2})^{16}$ is given by: $T_{r+1} = ^{16}C_{r} (x^2)^{16-r} (-x^{-2})^r$ $T_{r+1} = ^{16}

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(A) The general term $T_{r+1}$ in the expansion of $(x^2 - x^{-2})^{16}$ is given by: $T_{r+1} = ^{16}C_{r} (x^2)^{16-r} (-x^{-2})^r$ $T_{r+1} = ^{16}C_{r} (-1)^r x^{32-2r} x^{-2r}$ $T_{r+1} = ^{16}C_{r} (-1)^r x^{32-4r}$ For the constant term,the power of $x$ must be $0$: $32 - 4r = 0 \implies 4r = 32 \implies r = 8$ Substituting $r = 8$ into the expression: $T_{8+1} = ^{16}C_{8} (-1)^8 x^{32-4(8)} = ^{16}C_{8} (1) (1) = ^{16}C_{8}$

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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The constant term in the expansion of $\left(x^{2}-\frac{1}{x^{2}}\right)^{16}$ is

KCET 2018 All KCET

A
$^{16}C_{8}$
B
$^{16}C_{7}$
C
$^{16}C_{9}$
D
$^{16}C_{10}$

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Binomial Theorem

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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