JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficients of \(x\) and \(x^2\) in \((1+x)^p(1-x)^q\) are \(4\) and \(-5\) respectively, then \(2 p+3 q\) is equal to
- A \(63\)
- B \(69\)
- C \(66\)
- D \(60\)
Answer & Solution
Correct Answer
(A) \(63\)
Step-by-step Solution
Detailed explanation
\((1+x)^p(1-x)^q\) \(\left(1+p x+\frac{p(p-1)}{2 !} x^2+\ldots\right)\) \(\left(1-q x+\frac{q(q-1)}{2 !} x^2-\ldots\right)\) \(p-q=4\) \(\frac{p(p-1)}{2}+\frac{q(q-1)}{2}-p q=-5\) \(p^2+q^2-p-q-2 p q=-10\) \((q+4)^2+q^2-(q+4)-q-2(4+q) q=-10\)…
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