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7.Binomial Theorem
hard
$(\mathrm{x}+\sqrt{\mathrm{x}^{2}-1})^{6}+(\mathrm{x}-\sqrt{\mathrm{x}^{2}-1})^{6}$ ના વિસ્તરણમાં $x^{4}$ અને $x^{2}$ ના સહગુણકો $\alpha$ અને $\beta$ હોય તો . . . .
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
