JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(x^{70}\) in \(x^2(1+x)^{98}+x^3(1+x)^{97}+\) \(x^4(1+x)^{96}+\ldots \ldots . .+x^{54}(1+x)^{46}\) is \({ }^{99} \mathrm{C}_p-{ }^{46} \mathrm{C}_{\mathrm{q}}\). Then a possible value to \(\mathrm{p}+\mathrm{q}\) is :
- A \(55\)
- B \(61\)
- C \(68\)
- D \(83\)
Answer & Solution
Correct Answer
(D) \(83\)
Step-by-step Solution
Detailed explanation
\( x^2(1+x)^{98}+x^3\left(1+x^{97}\right)+x^4(1+x)^{96}+\ldots \ldots . \) \( x^{54}(1+x)^{46}\) Coeff. of \(\mathrm{x}^{70}:{ }^{98} \mathrm{C}_{68}+{ }^{97} \mathrm{C}_{67}+{ }^{96} \mathrm{C}_{66}+\ldots \ldots \ldots\). \( { }^{47} \mathrm{C}_{17}+{ }^{46} \mathrm{C}_{16} \)…
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