AP EAMCET · Maths · Binomial Theorem
Sum of the coefficients of \(x^4\) and \(x^6\) in the expansion of \(\left(1+x-x^2\right)^6\) is
- A \(121\)
- B \(-91\)
- C \(11\)
- D \(31\)
Answer & Solution
Correct Answer
(C) \(11\)
Step-by-step Solution
Detailed explanation
Coefficient of \(x^4\): \(C_4 = \frac{6!}{2!4!0!}(1)^2(1)^4(-1)^0 + \frac{6!}{3!2!1!}(1)^3(1)^2(-1)^1 + \frac{6!}{4!0!2!}(1)^4(1)^0(-1)^2 = 15 - 60 + 15 = -30\) Coefficient of \(x^6\):…
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