List of top Questions asked in WBJEE

Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity \( v_1 \) in time \( t_1 \). On another day if she remains stationary on the escalator moving with velocity \( v_2 \), then the escalator takes her up in time \( t_2 \). The time taken by her to walk up with velocity \( v_1 \) on the moving escalator will be
For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin electric outlet in a room is given by
A force \( \vec{F}=ai+bj+ck \) is acting on a body of mass \( m \). The body was initially at rest at the origin. The coordinates of the body after time \( t \) will be
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 \( E_0=2 \) N/C and \( \omega=1000 \) rad/sec. The maximum speed attained by the particle is
The number of reflexive relations on a set \( A \) of \( n \) elements is equal to:
If \( f(x) = \int_{0}^{\sin^2 x} \sin^{-1} \sqrt{t} \, dt \) and \( g(x) = \int_{0}^{\cos^2 x} \sin^{-1} \sqrt{t} \, dt \), then the value of \( f(x) + g(x) \) is:
The value of the integral \( \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} \, dx \) is:
The number of lone pair of electrons and the hybridization of Xenon (Xe) in XeOF$_2$ are
Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with velocity \( v_1 \) in time \( t_1 \). On another day, if she remains stationary on the escalator moving with velocity \( v_2 \), the escalator takes her up in time \( t_2 \). The time taken by her to walk up with velocity \( v_1 \) on the moving escalator will be:
The apparent coefficient of expansion of a liquid, when heated in a copper vessel, is \( C \) and when heated in a silver vessel is \( S \). If \( A \) is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is:
The minimum wavelength of Lyman series lines is \( P \), then the maximum wavelength of the Lyman series lines is:
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.)
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?
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 \( Y = 2.0 \times 10^{11} \, \text{N/m}^2 \)).
Oneendofasteelwireisfixedtotheceiling
If \( {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( 'r' \) is:
If \( x = \int_0^y \frac{1}{\sqrt{1+9t^2}} \, dt \) and \( \frac{d^2y}{dx^2} = ay \), then the value of \( a \) is:
An \( n \times n \) matrix is formed using 0, 1 and -1 as its elements. The number of such matrices which are skew symmetric 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?
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?
The value of \( \displaystyle \int_0^{1.5} \left\lfloor x^2 \right\rfloor \, dx \) is:
If \( x = -1 \) and \( x = 2 \) are extreme points of \( f(x) = \alpha \log|x| + \beta x^2 + x \), \( x \neq 0 \), then:
The value of \( \int_{-100}^{100} \frac{x + x^3 + x^5}{1 + x^2 + x^4 + x^6} dx \) is:
If for a matrix \( A \), \( |A| = 6 \) and \( \text{adj } A = \begin{bmatrix} 1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0 \end{bmatrix} \), then \( k \) is equal to:
If \( \cos^{-1} \alpha + \cos^{-1} \beta + \cos^{-1} \gamma = 3\pi \), then the value of \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is:
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