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:

1

Let the line $x = -1$ divide the area of the region ${(x,y) : 1 + x^2 \le y \le 3 - x}$ in the ratio $m : n$, $\gcd(m,n…

Topic: JEE Main 2026 (22 January Morning Shift)

2

Let the relation $R$ on the set $M = {1,2,3,\ldots,16}$ be given by $R = {(x,y) : 4y = 5x - 3,; x,y \in M}$. Then the…

Topic: JEE Main 2026 (22 January Morning Shift)

3

Let $\overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k}$ and $\overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda \hat…

Topic: JEE Main 2026 (22 January Morning Shift)

1

Let $f(x) = x^{2025} - x^{2000},; x \in [0,1]$ and maximum value of the function $f(x)$ in the interval $[0,1]$ be $\le…

Topic: JEE Main 2026 (22 January Morning Shift)

2

Let $P(\alpha,\beta,\gamma)$ be the point on the line $\frac{x-1}{2} = \frac{y+1}{-3} = z$ at a distance $4\sqrt{14}$…

Topic: JEE Main 2026 (22 January Morning Shift)

3

If a random variable $x$ has the probability distributionthen $P(3 < x \le 6)$ is equal to:

Topic: JEE Main 2026 (22 January Morning Shift)

4

The number of distinct real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 is

Topic: JEE Main 2026 (22 January Morning Shift)

5

Let $f : [1,\infty) \to \mathbb{R}$ be a differentiable function. If $6\int_{1}^{x} f(t),dt = 3xf(x) + x^3 - 4$ for al…

Topic: JEE Main 2026 (22 January Morning Shift)

6

If the line $\alpha x + 2y = 1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^2 - 9y^2 = 9$, then a po…

Topic: JEE Main 2026 (22 January Morning Shift)

7

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

Topic: JEE Main 2026 (22 January Morning Shift)

8

Let the set of all values of $r$, for which the circles $(x + 1)^2 + (y + 4)^2 = r^2$ and $x^2 + y^2 - 4x - 2y - 4 = 0…

Topic: JEE Main 2026 (22 January Morning Shift)

9

If $A = \begin{bmatrix} 2 & 3 \ 3 & 5 \end{bmatrix}$, then the determinant of the matrix $(A^{2025} - 3A^{2024} + A^{2…

Topic: JEE Main 2026 (22 January Morning Shift)

10

If the domain of the function $f(x) = \sin^{-1}\left(\frac{5 - x}{3 + 2x}\right) + \log\left(\frac{1}{10 - x}\right)$ …

Topic: JEE Main 2026 (22 January Morning Shift)