JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2026, Shift 1, Maths Q7

Question 7 of 75 in this shift, Maths question 7 of 25, Section A.

The number of elements in the set

S=\left\{(r,k) : k \in \mathbf{Z} \text{ and } {}^{36}C_{r+1}=\frac{6\left({}^{35}C_r\right)}{\left(k^2-3\right)}\right\}

, is :

(1) $2$
(2) $4$ Official answer
(3) $8$
(4) $16$

Official answer

Option 2

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Absorption Identity

Same topic in other shifts

All Binomial Coefficients questions

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
4 Apr 2026, Shift 1 · Q9Let the smallest value of $k\in\mathbb{N}$ , for which the coefficient of $x^3$ in…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.