List of top Questions asked in JEE Main

The axis of a parabola is the line $ y = x $ and its vertex and focus are in the first quadrant at distances $ \sqrt{2} $ and $ 2\sqrt{2} $ units from the origin, respectively. If the point $ (1, k) $ lies on the parabola, then a possible value of $ k $ is:
Let the values of $ p $, for which the shortest distance between the lines $ \frac{x + 1}{3} = \frac{y}{4} = \frac{z}{5} $ and $ \vec{r} = (p \hat{i} + 2 \hat{j} + \hat{k}) + \lambda (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) $ is $ \frac{1}{\sqrt{6}} $, be $ a, b $, where $ a<b $. Then the length of the latus rectum of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ is:
Let $ a>0 $. If the function $ f(x) = 6x^3 - 45ax^2 + 108a^2x + 1 $ attains its local maximum and minimum values at the points $ x_1 $ and $ x_2 $ respectively such that $ x_1x_2 = 54 $, then $ a + x_1 + x_2 $ is equal to:

Let the matrix $ A = \begin{pmatrix} 1 & 0 & 0 \\1 & 0 & 1 \\0 & 1 & 0 \end{pmatrix} $ satisfy $ A^n = A^{n-2} + A^2 - I $ for $ n \geq 3 $. Then the sum of all the elements of $ A^{50} $ is:

Consider the following plots of log of rate constant $ k (log k)$ vs $ \frac{1}{T} $ for three different reactions. The correct order of activation energies of these reactions is:

Choose the correct answer from the options given below:

Consider the following molecule (X).

The Structure X is?

Half-life of zero-order reaction $ A \to $ product is 1 hour, when initial concentration of reaction is 2.0 mol L$^{-1}$. The time required to decrease concentration of A from 0.50 to 0.25 mol L$^{-1}$ is:

The IUPAC name of the following compound is:

In which pairs, the first ion is more stable than the second?

The incorrect relationship in the following pairs in relation to ionisation enthalpies is:
A particle of charge 1.6 $\mu$C and mass 16 $\mu$g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is _______ s. (Take $ \pi = 3.14 $)
In a Young's double slit experiment, two slits are located 1.5 m apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the centre maximum of the single slit diffraction pattern, then the width of each slit is $ x \times 10^{-3} \, \text{cm} $, where x-value is:
An inductor of self inductance 1 H connected in series with a resistor of 100 $ \Omega $ and an AC supply of 10 V, 50 Hz. Maximum current flowing in the circuit is:
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimensions of [M$ L^2 T^{-3} A^{-1}]$. The value of P and Q are:
A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:
Two polarisers $ P_1 $ and $ P_2 $ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $ P_3 $ is inserted in between $ P_1 $ and $ P_2 $, at the particular angle between $ P_1 $ and $ P_2 $. The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers $ P_2 $ and $ P_3 $ is:
There are ‘n’ number of identical electric bulbs, each is designed to draw a power $ p $ independently from the mains supply. They are now joined in series across the main supply. The total power drawn by the combination is:
Let the three sides of a triangle ABC be given by the vectors $$ 2\hat{i} - \hat{j} + \hat{k}, \quad \hat{i} - 3\hat{j} - 5\hat{k}, \quad \text{and} \quad 3\hat{i} - 4\hat{j} - 4\hat{k}. $$ Let G be the centroid of the triangle ABC. Then $$ 6 \left( |\vec{AG}|^2 + |\vec{BG}|^2 + |\vec{CG}|^2 \right) \text{ is equal to}$$ _______
A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\frac{11}{50}, \text{ then } n \text{ is equal to}$ _______
Let the mean and the standard deviation of the observations $ 2, 3, 4, 5, 7, a, b $ be $ 4 $ and $ \sqrt{2} $ respectively. Then the mean deviation about the mode of these observations is:
If the sum of the first 20 terms of the series $$ \frac{4.1}{4 + 3.1^2 + 1^4} + \frac{4.2}{4 + 3.2^2 + 2^4} + \frac{4.3}{4 + 3.3^2 + 3^4} + \frac{4.4}{4 + 3.4^2 + 4^4} + ... $$ is $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, then $ m + n $ is equal to:
Let the sum of the focal distances of the point $ P(4, 3) $ on the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be $ 8\sqrt{\frac{5}{3}} $. If for $ H $, the length of the latus rectum is $ \ell $ and the product of the focal distances of the point $ P $ is $ m $, then $ 9\ell^2 + 6m $ is equal to:
A line passing through the point $ A(-2, 0) $, touches the parabola $ P: y^2 = x - 2 $ at the point $ B $ in the first quadrant. The area of the region bounded by the line $ AB $, parabola $ P $, and the x-axis is:
Let the product of $ \omega_1 = (8 + i) \sin \theta + (7 + 4i) \cos \theta $ and $ \omega_2 = (1 + 8i) \sin \theta + (4 + 7i) \cos \theta $ be $ \alpha + i\beta $, where $ i = \sqrt{-1} $. Let $ p $ and $ q $ be the maximum and the minimum values of $ \alpha + \beta $ respectively.
Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $ and $ R $ be a relation on $ A $ defined by $ xRy $ if and only if $ 2x - y \in \{0, 1\} $. Let $ l $ be the number of elements in $ R $. Let $ m $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to: