jee-main 2023 Q66

jee-main · India · session2_08apr_shift2 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion

The absolute difference of the coefficients of $x ^ { 10 }$ and $x ^ { 7 }$ in the expansion of $\left( 2 x ^ { 2 } + \frac { 1 } { 2 x } \right) ^ { 11 }$ is equal to
(1) $13 ^ { 3 } - 13$
(2) $11 ^ { 3 } - 11$
(3) $10 ^ { 3 } - 10$
(4) $12 ^ { 3 } - 12$

The absolute difference of the coefficients of $x ^ { 10 }$ and $x ^ { 7 }$ in the expansion of $\left( 2 x ^ { 2 } + \frac { 1 } { 2 x } \right) ^ { 11 }$ is equal to\\
(1) $13 ^ { 3 } - 13$\\
(2) $11 ^ { 3 } - 11$\\
(3) $10 ^ { 3 } - 10$\\
(4) $12 ^ { 3 } - 12$

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