JEE Main 2026 Question Paper (05-Apr-2026) (Shift 2)

Question 1

Let $\alpha$, $\beta$ be the roots of the equation $x^{2}-x+p=0$ and $\gamma$, $\delta$ be the roots the equation $x^{2}-4x+q=0$; $p$, $q \in \mathbf{Z}$. If $\alpha$, $\beta$, $\gamma$, $\delta$ are in G.P., then $|p+q|$ equals :

Accepted Answer

34

Answer

16

Answer

32

Answer

38

Question 2

Let $z_{1}$, $z_{2} \in \mathbb{C}$ be the distinct solutions of the equation $z^{2}+4z-(1+12i)=0$. Then $|z_{1}|^{2}+|z_{2}|^{2}$ is equal to :

Accepted Answer

34

Answer

18

Answer

22

Answer

29

Question 3

If $f: \mathbf{N} ightarrow \mathbf{Z}$ is defined by$f(n) = \begin{vmatrix} n & -1 & -5 \ -2n^2 & 3(2k+1) & 2k+1 \ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix}, k \in \mathbf{N},$and $\sum_{n=1}^{k} f(n) = 98$, then $k$ is equal to :

Accepted Answer

3

Answer

4

Answer

5

Answer

6

Question 4

Let $M$ be a $3 	imes 3$ matrix such that$M \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}, M \begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix} = \begin{pmatrix} 0 \ 1 \ 2 \end{pmatrix} 	ext{ and } M \begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix} = \begin{pmatrix} -1 \ 1 \ 1 \end{pmatrix}. 	ext{ If } M \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 1 \ 7 \ 11 \end{pmatrix}, 	ext{ then } x+y+z 	ext{ equals :}$

Accepted Answer

5

Answer

4

Answer

7

Answer

11

Question 5

If the sum of the first 10 terms of the series $\frac{1}{1+1^{4} 	imes 4} + \frac{2}{1+2^{4} 	imes 4} + \frac{3}{1+3^{4} 	imes 4} + \frac{4}{1+4^{4} 	imes 4} + \dots$ is $\frac{m}{n}$, $\operatorname{gcd}(m, n) = 1$, then $m+n$ is equal to :

Accepted Answer

276

Answer

256

Answer

264

Answer

284