JEE Mains · Maths · 6. Binomial Theorem
If the sum of the coefficients of \(x^7\) and \(x^{14}\) in the expansion of \(\left(\dfrac{1}{x^3} - x^4\right)^n\), \(x \neq 0\), is zero, then the value of \(n\) is __________.
- A 21
- B 22
- C 23
- D 24
Answer & Solution
Correct Answer
(A) 21
Step-by-step Solution
Detailed explanation
The general term in the expansion of \(\left(\dfrac{1}{x^3} - x^4\right)^n\) is given by: \(T_{r+1} = ^{n}C_{r} \left(x^{-3}\right)^{n-r} \left(-x^4\right)^r = (-1)^r \cdot ^{n}C_{r} \cdot x^{7r - 3n}\) For the coefficient of \(x^7\), we set the exponent to \(7\):…
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