List of top Questions asked in WBJEE- 2024

If \[ A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \] and \(\theta = \frac{2\pi}{7}\), then \(A^{100} = A \times A \times \ldots\) (100 times) is equal to:

\(f(x) = \cos x - 1 + \frac{x^2}{2!}, \, x \in \mathbb{R}\)
Then \(f(x)\) is:

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:

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? (\(\mu_s = 0.6\)).

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 \(1.8v_0\)?

A uniform rod AB of length 1 m and mass 4 kg is sliding along two mutually perpendicular frictionless walls OX and OY. The velocity of the two ends of the rod A and Bare 3 m/s and 4 m/s respectively, as shown in the figure. Then which of the following statement(s) is/are correct?

The equivalent capacitance of a combination of connected capacitors shown in the figure between the points P and N is:

If \(a, b, c\) are distinct odd natural numbers, then the number of rational roots of the equation \(ax^2 + bx + c = 0\) is:

The locus of the midpoint of the system of parallel chords parallel to the line \( y = 2x \) to the hyperbola \( 9x^2 - 4y^2 = 36 \) is:

With origin as a focus and x = 4 as the corresponding directrix, a family of ellipses are drawn. Then the locus of an end of the minor axis is:

Let \(f\) be a differential function with
\[ \lim_{x \to \infty} f(x) = 0. \text{ If } y' + y f'(x) - f(x) f'(x) = 0, \lim_{x \to \infty} y(x) = 0 \text{ then,} \]

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: