List of top Questions asked in WBJEE

The light beams of intensities in the ratio of 9 : 1 are allowed to interfere. What will be the ratio of the intensities of maxima and minima ?

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

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

If the length of the second's hand in a stop-clock is 3 cm, then the angular velocity and linear velocity of the tip 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.

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,

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

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

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

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

Two mirrors at an angle θº produce 5 images of a point. The number of images produced when θ is decreased to θº – 30º 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?

A certain reaction proceeds in a sequence of three elementary steps with rate constants k1, k2 and k3. If the observed rate constant, Kobs, of the reaction is expressed as Kobs = K3 [K1/K2]^1/2, then what is the observed energy of activation of the reaction?

The area (in sq. units) enclosed by y = 1, 2x + y = 2 and x + y = 2 is

Reagents which cannot be used to distinguish allyl bromide and n-propyl bromide are

Directions: The following question has four choices, out of which one or more are correct. An infinite current-carrying wire passes through point O and in perpendicular to the plane containing a current-carrying loop ABCD as shown in the figure. Choose the correct option(s).

$$\begin{array}{l}\text{ Given: }\left|\begin{array}{ccc}a& b& a\alpha +b\\ b& c& b\alpha +c\\ ac+b& bc+c& 0\end{array}\right|=0\\ \text{ Applying }{C}_3\to C_3-(\alpha C_1+C_2)\end{array}$$If the determinant $\left|\begin{array}{ccc}a& b& 0\\ b& c& 0\\ a\alpha +b& bc+c& -(a{c}^2+2bc+c)\end{array}\right|=0$$$\Rightarrow -(a{\alpha }^2+2b\alpha +c)(ac-b^2)=0$$$$\Rightarrow a{\alpha }^2+2b\alpha +c=0\text{ or }{b}^2=ac$$$\therefore \alpha$ is root of $a{x}^2+2bx+c$ or $a,b,c$ are in GP.

Directions: The following question has four choices, out of which one or more are correct.A ray of light is incident on a reflecting surface. The ray moves in horizontal direction and is reflected vertically after striking the surface. If the surface is denoted by $y=\frac{2L}{\pi }\sin \left(\frac{\pi }{L}x\right),0\le x\le L,$ what are the coordinates of the point(s) where the ray is incident?

If log3 x + log3 y = 2 + log3 2 and log3 (x + y) = 2, then

The area enclosed between y² = x and y = x is

If $x=8+3\sqrt{7}$ and $xy=1,$ then the value of $\frac{1}{x^2}+\frac{1}{y^2}$ is

Let $Sn=\sum _{k=0}^1\frac{n}{n^2+kn+k^2}$ and $T_n=\sum _{k=0}^{1-1}\frac{n}{n^2+kn+k^2},$ for $n=1,2,3,\dots$ Then

If one of the cube roots of 1 be $\omega$, then$\left|\begin{array}{ccc}1& 1+{\omega }^2& {\omega }^2\\ 1-i& -1& {\omega }^2-1\\ -i& -1+\omega & -1\end{array}\right|=$

Let [x] denote the greatest integer less than or equal to x. If f(x) = [x sinπ x], then f(x) is