TS EAMCET · Maths · Binomial Theorem
If \(n\) is a positive integer and the coefficient of \(x^{10}\) in the expansion of \((1+x)^{15}\) is equal to the coefficient of \(x^5\) in the expansion of \((1-x)^{-n}\), then \(n=\)
- A 15
- B 12
- C 11
- D 10
Answer & Solution
Correct Answer
(C) 11
Step-by-step Solution
Detailed explanation
In the expansion of \((1+x)^{15}\) the coefficient of \[ x^{10}={ }^{15} C_{10} \text {. } \] And the expansion of \[ (1-x)^{-n}=1+n x+\frac{n(n+1)}{2 !} x^2+\frac{n(n+1)(n+2) x^3}{3 !}+\ldots \] So, coefficient of \(x^5=\frac{n(n+1)(n+2)(n+3)(n+4)}{5 !}\) According to the…
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