The coefficient of $x^{70}$ in $x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46}$ is ${}^{99}C_p-{}^{46}C_q$. Then a possible value of $p+q$ is :

JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 9 April 2024, Shift 1, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

The coefficient of

x^{70}

x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46}

{}^{99}C_p-{}^{46}C_q

. Then a possible value of

p+q

is :

(1) $55$
(2) $83$ Official answer
(3) $68$
(4) $61$

Official answer

Option 2

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Geometric Progression of Expansions

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.