JEE Main 2018 April 16 Shift 1 Paper & Solutions - JEE MCQ

Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B the intensity of emergent light is reduced to I/3. The angle between the polarizers A and C is θ, then

The de-Broglie wav elength (λ_B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (λ_G) by :

In the given circuit the current through zener diode is :

The end correction of a resonance column is 1cm. If the shortest length resonating with the tuning fork is 10cm, the next resonating length should be :

Two sitar strings A and B playing the note 'Dha' are slightly out of tune and produce beats of frequency 5Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz. the original frequency of B is:

A power transmission line feeds input power at 2300V to a step down transformer with its primary windings having 4000 turns giving the output power at 230V. If the current in the primary of the transformer is 5A and its efficiency is 90% the output current would be :

A body of mass m starts moving from rest along x-axis so that its velocity varies as u = a√s where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :

Suppose that the angular velocity of rotation of earth is increased. Then as a consequence:

Both the nucleus and the atom of some element are in their respective first excited states. They get deexcited by emitting photons of wavelengths λ_N,λ_A respectively. The ratio λ_N/λ_A  is closest to : 

A plane electromagnetic wave of wavelength λ has an intensity I. It is propagating along the positive Y-direction. The allowed expressions for the electric and magnetic fields are given by :

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity ω with respect to normal axis then magnetic moment of the loop is :

A heating element has a resistance of 100Ω at room temperature. When it is connected to a supply of 220V a steady current of 2A passes in it and temperature is 500°C more than room temperature. What is the temperature coefficient of resistance of the heating element?

A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity ω the maximum e.m.f. induced in the coil will be :

A ray of light is incident at an angle of 60° on one face of a prism of angle 30°. The emergent ray of light makes an angle of 30° with incident ray. The angle made by the emergent ray with second face of prism will be :

A galvanometer with its coil resistance 25Ω requires a current of 1mA for its full deflection. In order to construct an ammeter to read up to a current of 2A the approximate value of the shunt resistance should be :

An oscillator of mass M is at rest in the equilibrium position in a potential V = 1/2 k(x – X)². A particle of mass m comes from right  with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)

One mole of an ideal monatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

In a circuit for finding the resistance of a galvanometer by half deflection method a 6V battery and a high resistance of 11kΩ are used. The figure of merit of the galvanometer produces a deflection of θ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of θ/2 is

In the following circuit the switch S is closed at t = 0. The charge on the capacitor C₁ as a function of time will be given by 

Let  The magnitude of a coplanar vector  is given by :

A particle executes simple harmonic motion and is located at x = a, b and c at times t₀, 2t₀ and 3t₀ respectively. The frequency of the oscillation is :

A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :

Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than their diameters and the force between them is F. A third identical conducting sphere C is uncharged. Sphere C is first touched to A then to B and then removed. As a result the force between A and B would be equal to :

Two particles of the same mass m are moving in circular orbits because of force given by  The first particle is at distance r =  1 and  the second at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to 

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity  The maximum percentage error in the value of A will be :

A carrier wave of peak voltage 14V is used for transmitting a message signal given to achieve a modulation index of 80% will be :

A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P₂ be the pressure inside the inner bubble and P₀ the pressure outside the outer bubble. Radius of another bubble with pressure difference P₂ – P₀ between its inside and outside would be :