JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficients of \(x\) and \(x^{2}\) in the expansion of \((1+x)^{p}(1-x)^{q}, p, q \leq 15\), are \(-3\) and \(-5\) respectively, then the coefficient of \(x ^{3}\) is equal to \(............\)
- A \(22\)
- B \(23\)
- C \(52\)
- D \(53\)
Answer & Solution
Correct Answer
(B) \(23\)
Step-by-step Solution
Detailed explanation
Since coefficient of \(x\) is \(-3\) \({ }^{p} C _{1}-{ }^{9} C _{1}=-3\) \(p - q =-3\) \(\text { Comparing coefficients of } x ^{2}\) \({ }^{9} C _{1}{ }^{9} C _{1}+{ }^{ p } C _{2}+{ }^{9} C _{2}=-5\) \(- pq +\frac{ p ( p -1)}{2}+\frac{ q ( q -1)}{2}=-5\) Solving \((1)\) and…
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