List of top Questions asked in WBJEE

The displacement ($x$) of a particle depends on time ($t$) as $x = \alpha t^2 - \beta t^3$. Then, $\alpha \beta$ is:

Number of particles passing in unit time through unit area perpendicular to the z-axis is given by: 
$N = D \dfrac{(N_2 - N_1)}{(Z_2 - Z_1)}$, 
where $N_2$ and $N_1$ are the number of particles in unit volume at $Z_2$ and $Z_1$. The dimensional formula of $D$ is?

If \( n = 1, 2, 3, \dots \), then \( \cos \alpha \cos 2\alpha \cos 4\alpha \dots \cos^{2n - 1} \alpha \) is equal to: 

A proton is projected with a velocity 10⁷ ms^-1 at right angles to a uniform magnetic field of induction 100 mT. The time (in seconds) taken by the proton to traverse 90^o arc is(Mass of proton = 1.65 × 10^-27 kg and charge of proton = 1.6 × 10^-19 C)

The potential energy of a particle varies with distance $x$ from a fixed origin as $\vee =\left(\frac{A\sqrt{x}}{x+B}\right),$ where $A$ and $B$ are constants. The dimensions of AB are

A small ball is connected to a block by a light string of length L. Both are initially on the ground. There is sufficient friction on the ground to prevent the block from slipping. The ball is projected vertically upwards with a velocity u, where 2gl < u² < 3gl. The centre of mass of the 'block + ball' system is C. Then,

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the root mean square speed of gas molecules is v, then at 480 K it will be

Two disks of equal mass but different diameter are connected with an axle system that allows them to roll down an inclined plane together. Both disks start and finish at the same time. Which of the following statements best describes the disks?

The value of F so as to keep the smooth wedge stationary, when it is loaded with a block of mass M, which is connected with a light inextensible string, will be

A conducting sphere of radius R, carrying charge Q, lies inside an uncharged conducting shell of radius 2R. If they are joined by a metal wire, then

Three identical thin bar magnets, each of moment M, are placed along three adjacent sides of a regular hexagon as shown in the figure. The resultant magnetic moment of the system is

A copper bar of length 1 m and cross-sectional area 10 × 10^-2 m² has its one end maintained at 100^oC by means of 0.4 kW electric heater. What is the temperature of the other end in steady state, given that the thermal conductivity of copper is 400 W/mK?

In the figure, a horizontal force F is applied such that the block remains stationary. Which of the following statements is false?

In the figure, the block B of mass m starts from rest at the top of a wedge W of mass M. All surfaces are without friction. W can slide on the ground. B slides down onto the ground, moves along it with a speed , has an elastic collision with the wall and climbs back onto W. Then,

In the following common emitter circuit, if β = 100, VCE = 7V, VBE = Negligible and RC = 2 kΩ, then IB is equal to

In the given system of three blocks, the surfaces are frictionless. The ratio T1/T2 is:

A current of i amp flows in the loop having circular arc r metre, subtending an angle  as shown in the figure. The magnetic field at centre O of circle is

Experimental investigations show that the intensity of solar radiation is maximum for a wavelength 480 nm in the visible region.Estimate the surface temperature of sun. Given Wein’s constant b = 2.88 × 10^–3 mK.

Narrow capillary tubes A and B are of length l and l/2 and of the same radius r. The rate of flow of water through the tube A under a constant pressure head 'P' is 3 cm³/sec. If A and B are connected in series and the same pressure difference 'P' is maintained between the ends of the composite tube, then the rate of flow of water is

A body of mass $40\mathrm{kg}$ is resting on a rough horizontal surface and is subjected to a force $P$, which is just enough to start the motion of the body. If ${\mu }_s=5,{\mu }_k=0.4,\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ and the force $P$ is continuously applied on the body, then the acceleration of the body is

The coercivity of a small magnet where the ferromagnet gets demagnetised is 3 x 10³ Am^–1. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetised when inside the solenoid, is

A parachutist, after bailing out, falls 50 m without friction. When parachute opens, it retards at 2 ms^-2. He reaches the ground with a speed of 3 ms^-1. At what height did he bail out?

A particle moves in xy plane according to the law x = a sin ωt and y = a(1 - cos ωt), where a and w are constant. The particle traces

At a given place where acceleration due to gravity is ' $8^{\prime }\mathrm{m}/{\mathrm{s}}^2,$ a sphere of lead of density 'd' $\mathrm{kg}/{\mathrm{m}}^3$ is gently released in a column of liquid of density $\rho \mathrm{kg}/{\mathrm{m}}^3$. If $\mathrm{d}>\rho$, the sphere will

The electric potential at a point on the axis of an electric dipole depends upon the distance r (> > a) of the point from centre of the dipole as