AP EAMCET · Maths · Binomial Theorem
If the coefficients of \(x^{10}\) and \(x^{11}\) in the expansion of \(\left(1+\alpha x+\beta x^2\right)(1+x)^{11}\) are 396 and 144 respectively, then \(\alpha^2+\beta^2=\)
- A \(10\)
- B \(13\)
- C \(25\)
- D \(20\)
Answer & Solution
Correct Answer
(B) \(13\)
Step-by-step Solution
Detailed explanation
\(C(x^{10}): \binom{11}{10} + \alpha\binom{11}{9} + \beta\binom{11}{8} = 396\) \(11 + 55\alpha + 165\beta = 396\) \(\alpha + 5\alpha + 15\beta = 36 \implies \alpha + 3\beta = 7 \quad (1)\) \(C(x^{11}): \binom{11}{11} + \alpha\binom{11}{10} + \beta\binom{11}{9} = 144\)…
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