JEE Main 2026 Question Paper (Jan 22, 2026) (Shift 1)

Question 1

Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3,..., 50$. The probability, that their product $ab$ is divisible by 3, is

Accepted Answer

$\frac{8}{25}$

Answer

$\frac{561}{1225}$

Answer

$\frac{664}{1225}$

Answer

$\frac{272}{1225}$

Question 2

If a random variable $x$ has the probability distribution$x$01234567P(x)02kk3k$2k^2$2k$k^2+k$$7k^2$then $P(3 < x \le 6)$ is equal to

Accepted Answer

0.64

Answer

0.22

Answer

0.33

Answer

0.34

Question 3

Let $f: [1, \infty) \rightarrow \mathbb{R}$ be a differentiable function. If $6\int_1^x f(t)dt = 3x f(x) + x^3 - 4$ for all $x \ge 1$, then the value of $f(2) - f(3)$ is

Accepted Answer

$-4$

Answer

3

Answer

$-3$

Answer

4

Question 4

If the image of the point $P(1, 2, a)$ in the line $\frac{x-6}{3} = \frac{y-7}{2} = \frac{7-z}{2}$ is $Q(5, b, c)$, then $a^2 + b^2 + c^2$ is equal to

Accepted Answer

283

Answer

293

Answer

298

Answer

264

Question 5

If the chord joining the points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ on the parabola $y^2 = 12x$ subtends a right angle at the vertex of the parabola, then $x_1x_2 - y_1y_2$ is equal to

Accepted Answer

284

Answer

292

Answer

288

Answer

280

$x$	0	1	2	3	4	5	6	7
P(x)	0	2k	k	3k	$2k^2$	2k	$k^2+k$	$7k^2$