List of top Questions asked in JEE Main- 2023

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion (A): Acceleration due to gravity is minimum at equator. Reason (R): Rotation of earth influences acceleration. In the light of the above statements, choose the correct answer from the options given below

The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\) If the ratio of their radii respectively is\(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet B will be :

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \( \rho \) and \( \frac{\rho}{3} \) respectively. The ratio of acceleration due to gravity at their surfaces (i.e. \( g_A : g_B \)) will be:
Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:
A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E₅. The ratio \( E_5 / E_1 \) is:
As shown in the figure, a configuration of two equal point charges (q0 = + 2 \(\mu\)C) is placed on an inclined plane. Mass of each point charge is 20g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \( h = x \times 10^{-3} \, \text{m} \). The value of \( x \) is _____
configuration of two equal point charges
In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40\, cm$ from the pole of the mirror is formed at distance $120 \,cm$ from the pole of the mirror These distances are measured with a modified scale in which there are $20$ small divisions in $1 \,cm$ The value of error in measurement of focal length of the mirror is $\frac{1}{ K } cm$ The value of $K$ is _____
A monochromatic light wave with wavelength λ1 and frequency ν1, in air, enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength λ2 and frequency ν2 of the refracted wave are:

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. When viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is:

An object is placed Infront of a plane mirror 12 cm away from it. The object is kept fixed while the plane mirror is shifted towards the object by a distance of 4 cm. The length of shift in the position of image is equal to ___________ cm.
If light is passing through a medium of critical angle 45°, then the wave speed will be
An point sized object is placed 4 cm from the double convex lens of focal length 8 cm. The change in the position of image, when the object is moved 2 cm towards the lens, is?
Time taken by light to travel in two different materials $A$ and $B$ of refractive indices $\mu_{ A }$ and $\mu_{ B }$ of same thickness is $t _1$ and $t _2$ respectively If $t_2-t_1=5 \times 10^{-10} s$ and the ratio of $\mu_{ A }$ to $\mu_{ B }$ is $1: 2$ Then the thickness of material, in meter is: (Given $v_A$ and $v_B$ are velocities of light in $A$ and $B$ materials respectively)
The critical angle for a denser refractive index is 45°. The speed of light in water medium is \( 3 \times 10^8 \) m/s. The speed of light in the denser medium is:
The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be:
1 kg of water at 100°C is converted into steam at 100°C by boiling at atmospheric pressure. The volume of water changes from \(1.00 \times 10^{-3}\, \text{m}^3\) as a liquid to \(1.671 \times 10^{-3}\, \text{m}^3\) as steam. The change in internal energy of the system during the process will be:
Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions \(f : S → P(S)\), where \(P(S)\) denotes the power set of S, such that \(f(n) ⊂ f(m)\) where \(n < m,\) is:
Let \(f(x)\) be a quadratic polynomial with leading coefficient 1 such that \(f(0) = p, p≠0\) and \(f(1)=\frac{1}{3}\). If the equation \(f(x) = 0\) and \(fofofof(x) = 0\) have a common real root, then \(f(–3)\) is equal to.......................
Let \(\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c\), where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______
Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:
$Ka _1, Ka _2$ and $Ka _3$ are the respective ionization constants for the following reactions (a), (b) and (c)
(a) $H _2 C _2 O _4 \rightleftharpoons H ^{+}+ HC _2 O _4^{-}$
(b) $HC _2 O _4^{-} \rightleftharpoons H ^{+}+ HC _2 O _4^{2-}$
(c) $H _2 C _2 O _4 \rightleftharpoons 2 H ^{+}+ C _2 O _4^{2-}$
The relationship between $K _{ a _1}, K _{ a _2}$ and $K _{ a _3}$ is given as
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:
Let \( S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} \) be a sample space and \( A = \{ M \in S : M \text{ is invertible} \} \) be an event. Then \( P(A) \) is equal to:

If the x-intercept of a focal chord of the parabola \(y^2=8 x+4 y+4\) is 3 , then the length of this chord is equal to ___