Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are $6$ and $3$ units, respectively. Then the area (in sq. units) of the equilateral triangle $ABC$, where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$, respectively, is:

1

The number of relations, defined on the set ${a,b,c,d}$, which are both reflexive and symmetric, is equal to:

Topic: JEE Main 2026 (21 January Morning Shift)

2

The area of the region, inside the ellipse $x^2 + 4y^2 = 4$ and outside the region bounded by the curves $y = |x| - 1$ …

Topic: JEE Main 2026 (21 January Morning Shift)

3

If the domain of the function $ f(x) = \cos^{-1}\left(\frac{2x-5}{11-3x}\right) + \sin^{-1}(2x^2 - 3x + 1) $ is the int…

Topic: JEE Main 2026 (21 January Morning Shift)

1

Let $\vec{a} = -\hat{i} + 2\hat{j} + 2\hat{k}$, $\vec{b} = 8\hat{i} + 7\hat{j} - 3\hat{k}$ and $\vec{c}$ be a vector su…

Topic: JEE Main 2026 (21 January Morning Shift)

2

Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive terms such that $a_1 a_2 a_3 a_4 = 64$ and $a_1 + a_2 + a_…

Topic: JEE Main 2026 (21 January Morning Shift)

3

Let $\vec{c}$ and $\vec{d}$ be vectors such that $|\vec{c} + \vec{d}| = \sqrt{29}$ and $\vec{c} \times (2\hat{i} + 3\ha…

Topic: JEE Main 2026 (21 January Morning Shift)

4

Let $y = y(x)$ be the solution curve of the differential equation $(1 + x^2)dy + (y - \tan^{-1}x)dx = 0$, $y(0) = 1$. T…

Topic: JEE Main 2026 (21 January Morning Shift)

5

The number of strictly increasing functions $f$ from the set ${1,2,3,4,5,6}$ to the set ${1,2,3,\ldots,9}$ such that $f…

Topic: JEE Main 2026 (21 January Morning Shift)

6

Let $f : R \to (0, \infty)$ be a twice differentiable function such that $f(3) = 18$, $f'(3) = 0$ and $f''(3) = 4$. The…

Topic: JEE Main 2026 (21 January Morning Shift)

7

Let the foci of hyperbola coincide with the foci of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$. If the eccentric…

Topic: JEE Main 2026 (21 January Morning Shift)

8

The value of $\int_{-\pi/6}^{\pi/6} \left( \frac{\pi + 4x}{1 - \sin(x + \pi/6)} \right) dx$ is equal to:

Topic: JEE Main 2026 (21 January Morning Shift)

9

Let the mean and variance of $7$ observations $2, 4, 10, x, 12, 14, y$, $x > y$, be $8$ and $16$ respectively. Two numb…

Topic: JEE Main 2026 (21 January Morning Shift)

10

Let $(\alpha, \beta, \gamma)$ be the co-ordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on th…

Topic: JEE Main 2026 (21 January Morning Shift)