AP EAMCET · Maths · Binomial Theorem
The sum of the coefficients of \(x^{32}\) and \(x^{-31}\) in \(\left(x^4-\frac{1}{x^3}\right)^{15}\) is \(\left(x^4-\frac{1}{x^3}\right)^{15}\)
- A 1470
- B 1260
- C -1260
- D -1470
Answer & Solution
Correct Answer
(B) 1260
Step-by-step Solution
Detailed explanation
\(T_{r+1} = \binom{15}{r} (x^4)^{15-r} (-x^{-3})^r = \binom{15}{r} (-1)^r x^{60-7r}\) For \(x^{32}\): \(60-7r = 32 \Rightarrow 7r = 28 \Rightarrow r=4\) Coefficient of \(x^{32}\) =…
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