WBJEE 2018 Paper 2 (Physics & Chemistry) Question Paper with Solutions

A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loop of radius 2r, made of same material, having the same cross-section is connected to the same voltage source, what will be the magnetic field at its centre?

What will be the approximate terminal velocity of a rain drop of diameter ${1.8 \times {{10}^{ - 3}}}$ m, when density of rain water $\approx$ ${1.8 \times {{10}^{ - 5}}}$ N-sm^$-$2 (Neglect buoyancy of air)

A block of mass m₂ is placed on a horizontal table and another block of mass m₁ is placed on top of it. An increasing horizontal force F = at is exerted on the upper block but the lower block never moves as a result. If the coefficient of friction between the blocks is $\mu$₁ and that between the lower block and the table is $\mu$₂, then what is the maximum possible value of $\mu$₁ / $\mu$₂ ?

In the circuit shown, inputs A and B are in states 1 and 0 respectively. What is the only possible stable state of the outputs X and Y?

If the half-life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the third day? (Given, $\root 3 \of {0.25} \approx 0.63$)

How the linear velocity v of an electron in the Bohr orbit is related to its quantum number n?

Four equal charges of value + Q are placed at any four vertices of a regular hexagon of side 'a'. By suitably choosing the vertices, what can be maximum possible magnitude of electric field at the centre of the hexagon?

A spherical liquid drop is placed on a horizontal plane. A small distance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius (r) of the drop, density ($\rho$) and surface tension (S) of th liquid. Which among the following will be a possible expression for T (where, k is a dimensionless constant)?

There is a small air bubble at the centre of a solid glass sphere of radius r and refractive index $\mu$. What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius R. The magnetic field B produced at a perpendicular distance d from the axis of the cylinder is plotted in a graph. Which of the following figures looks like the plot?

A point charge $-$ q is carried from a point A to another point B on the axis of a charged ring of radius r carrying a charge + q. If the point A is at a distance ${4 \over 3}r$ from the centre of the ring and the point B is ${3 \over 4}r$ from the centre but on the opposite side, what is the net work that need to be done for this?

An alternating current is flowing through a series L-C-R circuit. It is found that the current reaches a value of 1 mA at both 200 Hz and 800 Hz frequency. What is the resonance frequency of the circuit?

An electric bulb, a capacitor, a battery and a switch are all in series in a circuit. How does the intensity of light vary when the switch is turn on?

The bob of a pendulum of mass m, suspended by an inextensible string of length L as shown in the figure carries a small charge q. An infinite horizontal plane conductor with uniform surface charge density $\sigma$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

Two identical equiconvex lenses, each of focal length f are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If refractive index of the material of the lenses is greater than that of water, how the combined focal length F is related to f?

What will be current through the 200$\Omega$ resistor in the given circuit, a long time after the switch K is made on?

What will be the current flowing through the 6k$\Omega$ resistor in the circuit shown, where the breakdown voltage of the Zener is 6V?

Which of the following statement(s) is/are true?

"Internal energy of an ideal gas .............."

The ratio of accelerations due to gravity g₁ : g₂ on the surfaces of two planets is 5 : 2 and the ratio of their respective average densities ${{\rho _1}}$ : ${{\rho _2}}$ is 2 : 1. What is the ratio of respective escape velocities v₁ : v₂ from the surface of the planets?

As shown in the figure, a rectangular loop of conducting wire is moving away with a constant velocity v in a perpendicular direction from a very long straight conductor carrying a steady current I. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf. E induced in the loop vary with time t?

In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibrium position) is plotted along the Y-axis, the resultant curve happens to be an ellipse with the ratio ${{major\,axis\,(along\,X)} \over {minor\,axis\,(along\,Y)}} = 20\pi$

What is the frequency of the simple harmonic motion?

A solid spherical ball and a hollow spherical ball of two different materials of densities $\rho$₁ and $\rho$₂ respectively have same outer radii and same mass. What will be the ratio, the moment of inertia (about an axis passing through the centre) of the hollow sphere to that of the solid sphere?

A non-zero current passes through the galvanometer G shown in the circuit when the key K is closed and its value does not change when the key is opened. Then, which of the following statement(s) is/are true?

If Young's double slit experiment is done with white light, which of the following statements will be true?

The intensity of a sound appears to an observer to be periodic. Which of the following can be the cause of it?

Four resistors, 100$\Omega$, 200$\Omega$, 300$\Omega$ and 400$\Omega$ are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square?

An electron accelerated through a potential of 10000 V from rest has a de-Broglie wave length $\lambda$. What should be the accelerating potential, so that the wavelength is doubled?

The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) $v \propto {1 \over {\sqrt x }}$. Find how the magnitude of the force (F) on the particle depends on x?

In a triangle ABC, the sides AB and AC are represented by the vectors $3\widehat i + \widehat j + \widehat k$ and $\widehat i + 2\widehat j + \widehat k$, respectively. Calculate the angle $\angle ABC$.

A light charged particle is revolving in a circle of radius r in electrostatic attraction of a static heavy particle with opposite charge. How does the magnetic field B at the centre of the circle due to the moving charge depend on r?

Two positive charges Q and 4Q are placed at points A and B respectively, where B is at a distance d units to the right of A. The total electric potential due to these charges is minimum at P on the line through A and B. What is (are) the distance (s) of P from A?

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length a as shown in the figure. A charge + Q is placed at the centre O of the cube. P is such a point outside the cube that the line OP perpendicularly intersects the surface ABCD at R and also OR = RP = a/2. A charge + Q is placed at point P also. What is the total electric flux through the five faces of the cube other than ABCD?