jee-main 2020 Q54

jee-main · India · session1_08jan_shift2 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion

If $\alpha$ and $\beta$ be the coefficients of $x^{4}$ and $x^{2}$, respectively in the expansion of $\left(x + \sqrt{x^{2} - 1}\right)^{6} + \left(x - \sqrt{x^{2} - 1}\right)^{6}$, then
(1) $\alpha + \beta = 60$
(2) $\alpha + \beta = -30$
(3) $\alpha - \beta = 60$
(4) $\alpha - \beta = -132$

If $\alpha$ and $\beta$ be the coefficients of $x^{4}$ and $x^{2}$, respectively in the expansion of $\left(x + \sqrt{x^{2} - 1}\right)^{6} + \left(x - \sqrt{x^{2} - 1}\right)^{6}$, then\\
(1) $\alpha + \beta = 60$\\
(2) $\alpha + \beta = -30$\\
(3) $\alpha - \beta = 60$\\
(4) $\alpha - \beta = -132$

Paper Questions

Q1 Q3 Q4 Q5 Q6 Q7 Q21 Q22 Q23 Q24 Q51 Q52 Q53 Q54 Q55 Q56 Q57 Q58 Q59 Q60 Q61