List of top Questions asked in WBJEE

A 2V cell is connected across the points A and B as shown in the figure. Assume that the resistance of each diode is zero in forward bias and infinity in reverse bias. The current supplied by the cell is:

The acceleration-time graph of a particle moving in a straight line is shown in the f igure. If the initial velocity of the particle is zero, then the velocity-time graph of the particle will be:

A particle of mass \( m \) moves in one dimension under the action of a conservative force whose potential energy has the form \( U(x) = \frac{\alpha x}{x^2 + \beta^2} \), where \( \alpha \) and \( \beta \) are dimensional parameters. The angular frequency \( \omega \) of the oscillation is proportional to:

Two straight conducting plates form an angle θ where their ends are joined. A conducting bar in contact with the plates and forming an isosceles triangle with them, starts at the vertex at time t = 0 and moves with constant velocity v to the right as shown in the figure. A magnetic field B points out of the page. The magnitude of emf induced at t = 1 second will be:

Light of wavelength \(6000 \, \text{Å}\) is incident on a thin glass plate of refractive index \(1.5\) such that the angle of refraction into the plate is \(60^\circ\). Calculate the smallest thickness of the plate which will make a dark fringe by reflected beam interference.

Which of the following quantity has the dimension of length? (where \(h\) is Planck’s constant, \(m\) is the mass of electron and \(c\) is the velocity of light):

In the given network of AND and OR gates, output Q can be written as (assuming n even):

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:

A charged particle moving with a velocity \(\vec{v} = v_1\hat{i} + v_2\hat{j} + v_3\hat{k}\) in a magnetic field \(\vec{B}\) experiences a force \(\vec{F} = F_1\hat{i} + F_2\hat{j}\). Here \(v_1, v_2, F_1, F_2\) are all constants. Then \(\vec{B}\) can be:

A small sphere of mass m and radius R slides down the smooth surface of a large hemispherical bowl of radius R. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point A of the bowl will be:

Which of the following statement(s) is/are true in respect of nuclear binding energy?
(i) The mass energy of a nucleus is larger than the total mass energy of its individual protons and neutrons.
(ii) If a nucleus could be separated into its nucleons, an energy equal to the binding energy would have to be transferred to the particles during the separating process.
(iii) The binding energy is a measure of how well the nucleons in a nucleus are held together.
(iv) The nuclear fission is somehow related to acquiring higher binding energy.

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 \(1.8v_0\)?

In a series LCR circuit, the rms voltage across the resistor and the capacitor are \(30 \, \text{V}\) and \(90 \, \text{V}\) respectively. If the applied voltage is \(50\sqrt{2}\sin\omega t\), then the peak voltage across the inductor is:

Consider the integral form of the Gauss's law in electrostatics:
\( \oint \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0} \)
Which of the following statements are correct?

The acceleration \( f \) (in ft/sec\(^2\)) of a particle after a time \( t \) seconds starting from rest is given by:
\[ f = 6 - \sqrt{1.2t}. \]
Then the maximum velocity \( v \) and the time \( T \) to attain this velocity are:

The points of extremum of \[ \int_{0}^{x^2} \frac{t^2 - 5t + 4}{2 + e^t} \, dt \] are:

If \( \triangle ABC \) is an isosceles triangle and the coordinates of the base points are \( B(1, 3) \) and \( C(-2, 7) \), the coordinates of \( A \) can be:

Choose the correct statement:

If \( n \) is a positive integer, the value of:
\[ (2n + 1) \binom{n}{0} + (2n - 1) \binom{n}{1} + (2n - 3) \binom{n}{2} + \dots + 1 \cdot \binom{n}{n} \] is:

If the quadratic equation \( ax^2 + bx + c = 0 \) (\( a > 0 \)) has two roots \( \alpha \) and \( \beta \) such that \( \alpha < -2 \) and \( \beta > 2 \), then:

If \( a_i, b_i, c_i \in \mathbb{R} \) (\( i = 1, 2, 3 \)) and \( x \in \mathbb{R} \), and
\[ \begin{vmatrix} a_1 + b_1x & a_1x + b_1 & c_1 \\ a_2 + b_2x & a_2x + b_2 & c_2 \\ a_3 + b_3x & a_3x + b_3 & c_3 \end{vmatrix} = 0, \]
then:

A square with each side equal to \( a \) lies above the \( x \)-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle \( \alpha \) (\( 0 < \alpha < \frac{\pi}{4} \)) with the positive direction of the \( x \)-axis. The equation of the diagonals of the square is:

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = e^x + e^{-x} \) is:

Let \( \Gamma \) be the curve \( y = b e^{-x/a} \) and \( L \) be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then: