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7.Binomial Theorem
hard
यदि $\left( x +\sqrt{ x ^{2}-1}\right)^{6}+\left( x -\sqrt{ x ^{2}-1}\right)^{6}$ के प्रसार में $x ^{4}$ तथा $x ^{2}$ के गुणांक क्रमशः $\alpha$ तथा $\beta$ हैं, तो
A
$\alpha+\beta=60$
B
$\alpha+\beta=30$
C
$\alpha-\beta=-132$
D
$\alpha-\beta=60$
(JEE MAIN-2020)
Solution
$2\left[^{6} \mathrm{C}_{0} \mathrm{x}^{6}+^{6} \mathrm{C}_{2} \mathrm{x}^{4}\left(\mathrm{x}^{2}-1\right)+6 \mathrm{C}_{4} \mathrm{x}^{2}\left(\mathrm{x}^{2}-1\right)^{2}+^{6} \mathrm{C}_{6}\left(\mathrm{x}^{2}-1\right)^{3}\right]$
$\alpha=-96 \;and\; \beta=36$
$\therefore \alpha-\beta=-132$
Standard 11
Mathematics
