jee-main 2018 Q67

jee-main · India · 15apr Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion

If $n$ is the degree of the polynomial, $\left[ \frac { 2 } { \sqrt { 5 x ^ { 3 } + 1 } - \sqrt { 5 x ^ { 3 } - 1 } } \right] ^ { 8 } + \left[ \frac { 2 } { \sqrt { 5 x ^ { 3 } + 1 } + \sqrt { 5 x ^ { 3 } - 1 } } \right] ^ { 8 }$ and $m$ is the coefficient of $x ^ { n }$ in it, then the ordered pair $( n , m )$ is equal to
(1) $\left( 8,5 ( 10 ) ^ { 4 } \right)$
(2) $\left( 12,8 ( 10 ) ^ { 4 } \right)$
(3) $\left( 12 , ( 20 ) ^ { 4 } \right)$
(4) $\left( 24 , ( 10 ) ^ { 8 } \right)$

If $n$ is the degree of the polynomial, $\left[ \frac { 2 } { \sqrt { 5 x ^ { 3 } + 1 } - \sqrt { 5 x ^ { 3 } - 1 } } \right] ^ { 8 } + \left[ \frac { 2 } { \sqrt { 5 x ^ { 3 } + 1 } + \sqrt { 5 x ^ { 3 } - 1 } } \right] ^ { 8 }$ and $m$ is the coefficient of $x ^ { n }$ in it, then the ordered pair $( n , m )$ is equal to\\
(1) $\left( 8,5 ( 10 ) ^ { 4 } \right)$\\
(2) $\left( 12,8 ( 10 ) ^ { 4 } \right)$\\
(3) $\left( 12 , ( 20 ) ^ { 4 } \right)$\\
(4) $\left( 24 , ( 10 ) ^ { 8 } \right)$

Paper Questions

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