List of top Questions asked in JEE Main

Five diagrams $A, B, C, D,$ and $E$ are given. Three out of these, when put together, form a square. Identify the correct set of diagrams.

Identify the correct mirror image of the given figure along the $XY$-axis.

If the range of the function $ f(x) = \sqrt{3 - x} + \sqrt{5 + x} $ is $[\alpha, \beta]$, then $ \alpha^2 + \beta^2 $ is equal to:

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727°C and power radiated by the wire is 94.2 W. Its emissivity is $ \frac{x}{8} $, where $ x = \ldots $

Let $f: [0, \infty) \to \mathbb{R}$ be a differentiable function such that $f(x) = 1 - 2x + \int_0^x e^{x-t} f(t) \, dt$ for all $x \in [0, \infty)$. Then the area of the region bounded by $y = f(x)$ and the coordinate axes is

Let the system of equations $ x + 5y - z = 1 $ $ 4x + 3y - 3z = 7 $ $ 24x + y + \lambda z = \mu $ where $ \lambda, \mu \in \mathbb{R} $, have infinitely many solutions. Then the number of the solutions of this system, if $x, y, z$ are integers and satisfy $7 \leq x + y + z \leq 77$, is:

The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:

In the following reactions, which one is NOT correct?

A body of mass 100 g is moving in a circular path of radius 2 m on a vertical plane as shown in the figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is: (Take acceleration due to gravity as 10 m/s$^2$)

The truth table for the circuit given below is:

Choose the correct answer from the options given below:

Which of the following circuits has the same output as that of the given circuit?

The distance of the line $ \frac{x - 2}{2} = \frac{y - 6}{3} = \frac{z - 3}{4} $ from the point $ (1, 4, 0) $ along the line $ \frac{x}{1} = \frac{y - 2}{2} = \frac{z + 3}{3} $ is:

Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is:

Let the equation of the circle, which touches x-axis at the point $ (a, 0) $ and cuts off an intercept of length $ b $ on y-axis be $ x^2 + y^2 - cx + dy + e = 0 $. If the circle lies below x-axis, then the ordered pair $ (2a, b^2) $ is equal to:

Line $ L_1 $ passes through the point (1, 2, 3) and is parallel to z-axis. Line $ L_2 $ passes through the point $ (\lambda, 5, 6) $ and is parallel to y-axis. Let for $ \lambda = \lambda_1, \lambda_2, \lambda_2<\lambda_1 $, the shortest distance between the two lines be 3. Then the square of the distance of the point $ (\lambda_1, \lambda_2, 7) $ from the line $ L_1 $ is

If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:

If $ f(x) = \frac{2^x}{2^x + \sqrt{2}} $, $x \in \mathbb{R}$, then $ \sum_{k=1}^{81} f\left(\frac{k}{82}\right) $ is equal to:

Let circle $C$ be the image of
$$ x^2 + y^2 - 2x + 4y - 4 = 0 $$
in the line
$$ 2x - 3y + 5 = 0 $$
and $A$ be the point on $C$ such that $OA$ is parallel to the x-axis and $A$ lies on the right-hand side of the centre $O$ of $C$.
If $B(\alpha, \beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $\frac{1}{6}$ of the perimeter of $C$, then $\beta - \sqrt{3}\alpha$ is equal to:

Let $ ABC $ be a triangle formed by the lines $ 7x - 6y + 3 = 0 $, $ x + 2y - 31 = 0 $, and $ 9x - 2y - 19 = 0 $.
Let the point $ (h, k) $ be the image of the centroid of $ \triangle ABC $ in the line $ 3x + 6y - 53 = 0 $. Then $ h^2 + k^2 + hk $ is equal to:

The total number of ways the word 'DAUGHTER' can be arranged so that all vowels don't occur together:

For positive integers $ n $, if $ 4 a_n = \frac{n^2 + 5n + 6}{4} $ and $$ S_n = \sum_{k=1}^{n} \left( \frac{1}{a_k} \right), \text{ then the value of } 507 S_{2025} \text{ is:} $$

Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

The remainder when $ \left( (64)^{64} \right)^{64} $ is divided by 7 is equal to:

Nature of compounds TeO₂ and TeH₂ is___________ and ______________respectively.

Which of the following is the correct order of acidic strength for the following compounds: HNO$_3$, HClO$_4$, and HClO$_3$?