jee-main 2012 Q66

jee-main · India · 26may Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions
The middle term in the expansion of $\left( 1 - \frac { 1 } { x } \right) ^ { n } \left( 1 - x ^ { n } \right)$ in powers of $x$ is
(1) ${ } ^ { 2 n } \mathrm { C } _ { n - 1 }$
(2) ${ } ^ { - 2 n } \mathrm { C } _ { n }$
(3) ${ } ^ { 2 n } \mathrm { C } _ { n - 1 }$
(4) ${ } ^ { 2 n } \mathrm { C } _ { n }$ 
The middle term in the expansion of $\left( 1 - \frac { 1 } { x } \right) ^ { n } \left( 1 - x ^ { n } \right)$ in powers of $x$ is\\
(1) ${ } ^ { 2 n } \mathrm { C } _ { n - 1 }$\\
(2) ${ } ^ { - 2 n } \mathrm { C } _ { n }$\\
(3) ${ } ^ { 2 n } \mathrm { C } _ { n - 1 }$\\
(4) ${ } ^ { 2 n } \mathrm { C } _ { n }$
Paper Questions
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