List of top Questions asked in JEE Main

(A) The drift velocity of electrons decreases with the increase in the temperature of conductor.
(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.
(C) The drift velocity does not depend on the applied potential difference to the conductor.
(D) The drift velocity of electron is inversely proportional to the length of the conductor.
(E) The drift velocity increases with the increase in the temperature of conductor.

Choose the correct answer from the options given below

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surf ace tension (S), if density of the liquid is ρ and radius of the drop is r, then $T=K\sqrt {\frac {ρr^3}{S^{\frac 32}}}$ is dimensionally correct, where K is dimensionless.
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac h3$ while going up and coming down respectively.

For a constant collector-emitter voltage of 8 V, the collector current of a transistor reached to the value of 6 mA from 4 mA, whereas base current changed from 20 μA to 25 μA value. If transistor is in active state, small signal current gain (current amplification factor) will be

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)?

A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this hall at the highest point of its flight will become

Two bodies of mass $1$ kg and $3$ kg have position vectors $\hat i+2\hat j+\hat k$ and $−3\hat i−2 \hat j+\hat k$, respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector.

Given below are two statements: One is labelled as Assertion (A) and the other· is labelled as Reason (R).
Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R) : Because the angle of contact between the oil/grease and water is obtuse.
In the light of the above statements, choose the correct answer from the option given below.

If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s modulus of the material of the wire will :

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α, is given by:

In an experiment to determine the Young’s modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm²) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young’s modulus of given steel wires is x × 10¹¹ Nm^–2, then the value of x is ______.

In the given figure of meter of bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be _______ cm.

As show in the figure, in the steady state, the charge stored in the capacitor is _________ × 10^–6 C.

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _______ ε₀ J. (Where ε₀ is the permittivity of free space).

Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor.
Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options given below.

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___

A ball is projected from the ground with a speed 15 ms¹ at an angle θ with horizontal so that its range and maximum height are equal, then ‘tan θ’ will be equal to

A particle is moving in a straight line such that its velocity is increasing at 5 ms^–1 per meter. The acceleration of the particle is _______ms^–2 at a point where its velocity is 20 ms^–1.

In Young’s double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes’ separation of 7.2 mm. Now another light is used to produce an interference pattern with consecutive bright fringes’ separation of 8.1 mm. The wavelength of the second light is ________ nm.

The acute angle between the pair of tangents drawn to the ellipse 2x² + 3y² = 5 from the point (1, 3) is

Let Q and R be two points on the line
$\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}$ at a distance $\sqrt{26}$
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

If $a = \lim_{{n \to \infty}} \sum_{{k=1}}^{n} \frac{2n}{{n^2 + k^2}}$and
$f(x) = \sqrt{\frac{1 - \cos x}{1 + \cos x}}, \quad x \in (0, 1)$ then

2 L of 0.2 M $H_2SO_4$ is reacted with 2 L of 0.1 M NaOH solution, the molarity of the resulting product $Na_2SO_4$ in the solution is _______ millimolar. (Nearest integer)

Let a vector $\vec{a}$ has a magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in R \times R-\{(0,0)\}$, the vector $(x \vec{a}+y \vec{b})$ is perpendicular to the vector $(6 y \vec{a}-18 x \vec{b})$. Then the value of $|\vec{a} \times \vec{b}|$ is equal to:

Let P(–2, –1, 1) and Q(56/17, 43/17, 111/17) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $α, –1, β,$ where both $α$ and $β$ are integers of minimum absolute values, then $α^2 + β^2$ is equal to ___________.