List of top Questions asked in WBJEE

If the dimensions of length are expressed as \( G^x C^y h^z \), where \( G \), \( C \), and \( h \) are the universal gravitational constant, speed of light, and Planck's constant respectively, then:

Figure shows the graph of angle of deviation \( \delta \) versus angle of incidence \( i \) for a light ray striking a prism. The prism angle is

angle of deviation δ versus angle of incidence i

Three different liquids are filled in a U-tube as shown in the figure. Their densities are \( \rho_1 \), \( \rho_2 \), and \( \rho_3 \), respectively. From the figure, we may conclude that:

A radioactive nucleus decays as follows: \[ X \to X_1 \to X_2 \to X_3 \to X_4 \] If the mass number and atomic number of \( X_4 \) are 172 and 69 respectively, the mass number and atomic number of \( X \) are:

Consider a particle of mass 1 gm and charge 1.0 Coulomb at rest. Now, the particle is subjected to an electric field \( E(t) = E_0 \sin(\omega t) \) in the x-direction, where \( E_0 = 2 \, \text{N/C} \) and \( \omega = 1000 \, \text{rad/sec} \). The maximum speed attained by the particle is:

The variation of the density of a solid cylindrical rod of cross-sectional area \( \alpha \) and length \( L \) is given by: \[ \rho(x) = \rho_0 \frac{x^2}{L^2} \] Where \( x \) is the distance from one end of the rod. The position of its center of mass from one end is:

Temperature of a body \( \theta \) is slightly more than the temperature of the surrounding \( \theta_s \). Its rate of cooling (R) versus temperature of the body (\( \theta \)) is plotted. Its shape would be:

The minimum wavelength of Lyman series lines is \( P \), then the maximum wavelength of the Lyman series lines is:

The de-Broglie wavelength of a moving bus with speed \( v \) is \( \lambda \). Some passengers left the bus at a stop. Now, when the bus moves with twice of its initial speed, its kinetic energy is found to be twice of its initial value. What is the de-Broglie wavelength of the bus now?

A single slit diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light, then:

A simple pendulum is taken at a place where its distance from the Earth's surface is equal to the radius of the Earth. Calculate the time period of small oscillations if the length of the string is 4.0 m. (Take \( g = 9 \, \text{m/s}^2 \) at the surface of the Earth.)

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration \( 2 \, \text{m/s}^2 \) and a load of 10 kg hangs from the other end. If the cross-section of the wire is \( 2 \, \text{cm}^2 \), then the longitudinal strain in the wire will be (Take \( g = 10 \, \text{m/s}^2 \) and \( Y = 2.0 \times 10^{11} \, \text{N/m}^2 \)).

Acceleration-time (\( a \) vs. \( t \)) graph of a body is shown in the figure. Corresponding velocity-time (\( v \) vs. \( t \)) graph is:

A ball falls from a height \( h \) upon a fixed horizontal floor. The coefficient of restitution between the ball and the floor is \( e \). The total distance covered by the ball before it comes to rest is:

What are the charges stored in the 1 µF and 2 µF capacitors in the circuit as shown in the figure once the current (\( I \)) becomes steady?

A diode is connected in parallel with a resistance as shown in Figure. The most probable current (\( I \)) - voltage (\( V \)) characteristic is:

The variation of displacement with time of a simple harmonic motion (SHM) for a particle of mass \( m \) is represented by: \[ y = 2 \sin \left( \frac{\pi}{2} + \phi \right) \, \text{cm} \] The maximum acceleration of the particle is:

Six vectors \( \mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{e}, \mathbf{f} \) have the magnitudes and directions indicated in the figure. Which of the following statements is true?

The minimum force required to start pushing a body up a rough (having coefficient of friction \( \mu \)) inclined plane is \( F_1 \), while the minimum force needed to prevent it from sliding is \( F_2 \). If the inclined plane makes an angle \( \theta \) with the horizontal such that \( \tan\theta = 2\mu \), then the ratio \( \frac{F_1}{F_2} \) is:

What force \(F\) is required to start moving this 10 kg block shown in the figure if it acts at an angle of \(60^\circ\) as shown? (\(\mu_s = 0.6\)).

Consider a circuit where a cell of emf \( E_0 \) and internal resistance \( r \) is connected across the terminal A and B as shown in the figure. The value of \( R \) for which the power generated in the circuit is maximum, is given by:

A small ball of mass m is suspended from the ceiling of a floor by a string of length L. The ball moves along a horizontal circle with constant angular velocity ω, as shown in the figure. The torque about the center (O) of the horizontal circle is:

The speed distribution for a sample of \(N\) gas particles is shown below. \(P(v) = 0\) for \(v > 2v_0\). How many particles have speeds between \(1.2v_0\) and \(1.8v_0\)?

The equation \(r \cos \theta = 2a \sin^2 \theta\) represents the curve:

The expression \(\cos^2 \theta + \cos^2 (\theta + \phi) - 2 \cos \theta \cos (\theta + \phi)\) is: