JEE Main 2026 Question Paper (Jan 22, 2026) (Shift 2)

Question 1

Among the statements(S1) : If $A(5, -1)$ and $B(-2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$, then its third vertex is $(-4, -7)$and(S2) : If positive numbers $2a, b, c$ are three consecutive terms of an A.P., then the lines $ax+by+c=0$ are concurrent at $(2, -2)$,

Accepted Answer

both are correct

Answer

only (S2) is correct

Answer

both are incorrect

Answer

only (S1) is correct

Question 2

Let n be the number obtained on rolling a fair die. If the probability that the system
$x - ny + z = 6$
$x + (n - 2)y + (n + 1)z = 8$
$(n - 1)y + z = 1$
has a unique solution is $\frac{k}{6}$, then the sum of k and all possible values of n is :

Accepted Answer

20

Answer

21

Answer

24

Answer

22

Question 3

Let the domain of the function $f(x) = \log_3 \log_5 \left(7 - \log_2 \left(x^2 - 10x + 85\right)\right) + \sin^{-1} \left(\left|\frac{3x - 7}{17 - x}\right|\right)$ be $(\alpha, \beta]$. Then $\alpha + \beta$ is equal to :

Accepted Answer

12

Answer

9

Answer

8

Answer

10

Question 4

Let $[\cdot]$ denote the greatest integer function, and let $f(x) = \min \{\sqrt{2}x, x^2\}$.
Let $S = \{x \in (-2, 2) : \text{the function } g(x) = |x|[x^2] \text{ is discontinuous at } x\}$.
Then $\sum_{x \in S} f(x)$ equals

Accepted Answer

$1 - \sqrt{2}$

Answer

$2 - \sqrt{2}$

Answer

$2\sqrt{6} - 3\sqrt{2}$

Answer

$\sqrt{6} - 2\sqrt{2}$

Question 5

If the mean deviation about the median of the numbers $k, 2k, 3k, \dots, 1000k$ is 500, then $k^2$ is equal to :

Accepted Answer

1

Answer

4

Answer

16

Answer

9