JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\alpha\) and \(\beta\) be the coefficients of \(x^{4}\) and \(x^{2}\) respectively in the expansion of \((\mathrm{x}+\sqrt{\mathrm{x}^{2}-1})^{6}+(\mathrm{x}-\sqrt{\mathrm{x}^{2}-1})^{6}\), then
- A \(\alpha+\beta=60\)
- B \(\alpha+\beta=30\)
- C \(\alpha-\beta=-132\)
- D \(\alpha-\beta=60\)
Answer & Solution
Correct Answer
(C) \(\alpha-\beta=-132\)
Step-by-step Solution
Detailed explanation
\(2\left[^{6} \mathrm{C}_{0} \mathrm{x}^{6}+^{6} \mathrm{C}_{2} \mathrm{x}^{4}\left(\mathrm{x}^{2}-1\right)+6 \mathrm{C}_{4} \mathrm{x}^{2}\left(\mathrm{x}^{2}-1\right)^{2}+^{6} \mathrm{C}_{6}\left(\mathrm{x}^{2}-1\right)^{3}\right]\) \(\alpha=-96 \;and\; \beta=36\)…
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