JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2026, Shift 1, Maths Q9

Question 9 of 75 in this shift, Maths question 9 of 25, Section A.

Let the smallest value of

k\in\mathbb{N}

, for which the coefficient of

x^3

(1+x)^3+(1+x)^4+(1+x)^5+\ldots+(1+x)^{99}+(1+kx)^{100},\ x\neq0

, is

\left(43n+\frac{101}{4}\right)\left({}^{100}C_3\right)

for some

n\in\mathbb{N}

, be

p

. Then the value of

p+n

is:

(1) $10$
(2) $11$ Official answer
(3) $12$
(4) $13$

Official answer

Option 2

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Hockey Stick Identity

Same topic in other shifts

All Binomial Coefficients questions

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2 Apr 2026, Shift 2 · Q6If for $3 \le r \le 30$ , $\binom{30}{C_{30-r}} + 3\binom{30}{C_{31-r}} + 3\binom{30}{C_{32-r}} + \binom{30}{C_{33-r}} = ^m C_r$ , then $m$ …MediumSingle correct
5 Apr 2026, Shift 1 · Q23If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3} - x^4\right)^n$ , $x \neq 0$ , is zero, then…MediumNumerical value
6 Apr 2026, Shift 1 · Q8If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}$ , $\alpha\neq 0$ , are…EasySingle correct
8 Apr 2026, Shift 2 · Q8If…HardSingle correct
2 Apr 2025, Shift 2 · Q7If $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right)\cdot {}^{11}C_{r+1} = \frac{\alpha^{11}-11^{11}}{10^{10}}$ , then $\alpha$ is equal…HardSingle correct

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.