List of top Questions asked in JEE Main

A bi-convex lens has radius of curvature of both the surfaces same as $ \frac{1}{6} \, \text{cm} $. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $ (R_1 \neq R_2) $, without any change in lens power then possible combination of $ R_1 $ and $ R_2 $ is:

A sportsman runs around a circular track of radius $ r $ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are:

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

In the digital circuit shown in the figure, for the given inputs the P and Q values are:

Energy released when two deuterons $ \text{(H}_2\text{)} $ fuse to form a helium nucleus $ \text{(He}_4\text{)} $ is:

Assuming the validity of Bohr's atomic model for hydrogen-like ions, the radius of $ \text{Li}^{2+} $ ion in its ground state is given by $ \frac{1}{X} a_0 $, where $ a_0 $ is the first Bohr's radius.

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is $ V $. The potential difference between the points A and B (shown in the figure) is:

Two water drops each of radius $ r $ coalesce to form a bigger drop. If $ T $ is the surface tension, the surface energy released in this process is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason
(R): In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
In the light of the above statements, choose the most appropriate answer from the options given below:

Let $ A(4, -2), B(1, 1) $ and $ C(9, -3) $ be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and AB of the triangle ABC respectively, is __________.

If $ y = \cos \left( \frac{\pi}{3} + \cos^{-1} \frac{x}{2} \right) $, then $ (x - y)^2 + 3y^2 $ is equal to ________.

If the sum of the first 10 terms of the series \[ \frac{4 \cdot 1}{1 + 4 \cdot 1^4} + \frac{4 \cdot 2}{1 + 4 \cdot 2^4} + \frac{4 \cdot 3}{1 + 4 \cdot 3^4} + \ldots \] is $\frac{m}{n}$, where $\gcd(m, n) = 1$, then $m + n$ is equal to _____.

Let $ A $ be a $ 3 \times 3 $ real matrix such that \[ A^{2}(A - 2I) - 4(A - I) = O, \] where $ I $ and $ O $ are the identity and null matrices, respectively.
If \[ A^{5} = \alpha A^{2} + \beta A + \gamma I, \] where $ \alpha, \beta, \gamma $ are real constants, then $ \alpha + \beta + \gamma $ is equal to:

Let the point $ P $ of the focal chord $ PQ $ of the parabola $ y^2 = 16x $ be $ (1, -4) $. If the focus of the parabola divides the chord $ PQ $ in the ratio $ m : n $, gcd($m, n$) = 1, then $ m^2 + n^2 $ is equal to:

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is:

If \[ \sum_{r=0}^{10} \left( \frac{10^{r+1} - 1}{10^r} \right) \cdot {^{11}C_{r+1}} = \frac{\alpha^{11} - 11^{11}}{10^{10}}, \] then $ \alpha $ is equal to:

If $ \lim_{x \to 0} \frac{\cos(2x) + a \cos(4x) - b}{x^4} $ is finite, then $ (a + b) $ is equal to:

$$ \int \frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}} \, dx - 3 \log \left( \sqrt{3} \right) $$ is equal to:

If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then $a + b + ab$ is equal to:

Given three identical bags each containing 10 balls, whose colours are as follows:

Bag I	3 Red	2 Blue	5 Green
Bag II	4 Red	3 Blue	3 Green
Bag III	5 Red	1 Blue	4 Green

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from Bag I is $ p $ and if the ball is Green, the probability that it is from Bag III is $ q $, then the value of $ \frac{1}{p} + \frac{1}{q} $ is:

If $ \theta \in \left[ -\frac{7\pi}{6}, \frac{4\pi}{3} \right] $, then the number of solutions of \[ \sqrt{3} \csc^2 \theta - 2(\sqrt{3} - 1)\csc \theta - 4 = 0 \] is equal to ______.

If the system of equation $$ 2x + \lambda y + 3z = 5 \\3x + 2y - z = 7 \\4x + 5y + \mu z = 9 $$ has infinitely many solutions, then $ \lambda^2 + \mu^2 $ is equal to:

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is:

If the image of the point $ P(1, 0, 3) $ in the line joining the points $ A(4, 7, 1) $ and $ B(3, 5, 3) $ is $ Q(\alpha, \beta, \gamma) $, then $ \alpha + \beta + \gamma $ is equal to:

For the reaction $ A \rightarrow $ products,

The reaction was started with 2.5 mol L$^{-1}$ of A.