Consider two sets $A = {x \in \mathbb{Z} : |x - 3| - 3 \le 1}$ and $B = {x \in \mathbb{R} - {1,2} : \dfrac{(x-2)(x-4)}{x-1}\log_e(|x-2|) = 0}$ Then the number of onto functions $f : A \to B$ is equal to:

1

Let $A(1, 2)$ and $C(-3, -6)$ be two diagonally opposite vertices of a rhombus, whose sides $AD$ and $BC$ are parallel …

Topic: JEE Main 2026 (23 January Evening Shift)

1

The system of linear equations $x + y + z = 6$ $2x + 5y + az = 36$ $x + 2y + 3z = b$ has

Topic: JEE Main 2026 (23 January Evening Shift)

2

The sum of all the real solutions of the equation $\log_{x+3}(6x^2 + 28x + 30) - 5 = 2\log_{6x+10}(x^2 + 6x + 9)$ is eq…

Topic: JEE Main 2026 (23 January Evening Shift)

3

If the points of intersection of the ellipses $x^2 + 2y^2 - 6x - 12y + 23 = 0$ and $4x^2 + 2y^2 - 20x - 12y + 35 = 0$ l…

Topic: JEE Main 2026 (23 January Evening Shift)

4

Let $PQ$ be a chord of the hyperbola$\frac{x^2}{4} - \frac{y^2}{b^2} = 1$,perpendicular to the x-axis such that triangl…

Topic: JEE Main 2026 (23 January Evening Shift)

5

$\vec{a}, \vec{b}, \vec{c}$ be three vectors such that$\vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c})$.If $|\vec{a}…

Topic: JEE Main 2026 (23 January Evening Shift)

6

Bag $A$ contains $9$ white and $8$ black balls, while bag $B$ contains $6$ white and $4$ black balls. One ball is rando…

Topic: JEE Main 2026 (23 January Evening Shift)

7

The area of the region enclosed between the circles$x^2 + y^2 = 4$ and $x^2 + (y-2)^2 = 4$ is:

Topic: JEE Main 2026 (23 January Evening Shift)

8

The least value of$\cos^2\theta - 6\sin\theta\cos\theta + 3\sin^2\theta + 2$is:

Topic: JEE Main 2026 (23 January Evening Shift)

9

Let $I(x) = \int \dfrac{3dx}{(4x+6)\sqrt{4x^2 + 8x + 3}}$ and $I(0) = \dfrac{\sqrt{3}}{4} + 20$. If $I\left(\dfrac{1}{…

Topic: JEE Main 2026 (23 January Evening Shift)

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The number of ways, in which $16$ oranges can be distributed to four children such that each child gets at least one or…

Topic: JEE Main 2026 (23 January Evening Shift)