JEE Main 2015 April 4 Paper & Solutions - JEE MCQ

A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction wth speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

Distance of the centre of mass of a solid uniform cone from its vertex is z₀. If the radius of its base is R and its height is h then z₀ is equal to

From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is

From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is (G = gravitational constant)

A pendulum made of a uniform wire of crosssectional area A has time period .  When an additional mass M is added to its bob, the time period changes to T_M. If the Young's modulus of the material of the wire is Y then 1/Y is equal to (g = gravitational acceleration)

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume and pressure.If the shell now undergoes an adiabatic expansion the relation between T and R is

A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways :
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.
(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat.
In both the cases body is brought from initial temperature 100°C to final temperature 200°C.
Entropy change of the body in the two cases respectively is

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as Vq, where V is the volume of the gas. The value of q is 

For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly?
(Graphs are schematic and not drawn to scale)

A train is moving on a straight track with speed 20 ms^–1. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms^–1) close to

A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge -σ in the lower half. The electric field lines around the cylinder will look like figure given in
(figures are schematic and not drawn to scale)

A uniformly charged solid sphere of radius R has potential V0 (measured with respect to ¥) on its surface. For this sphere the equipotential surfaces with potentials  have radius R₁, R₂, R₃ and R₄ respectively. Then

In the given circuit, charge Q₂ on the 2μF capacitor changes as C is varied from 1 μF to 3 μF. Q₂ as a function of C is given properly by : (Figures are drawn schematically and are not to scale)

When 5 V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is 2.5 × 10^–4 ms^–1. If the electron density in the wire is 8 × 10²⁸ m^–3, the resistivity of the material is close to

In the circuit shown, the current in the 1 W resistor is

Two coaxial solenoids of different radii carry current I in the same direction. Letbe the magnetic force on the inner solenoid due to the outer one andbe the magnetic force on the outer solenoid due to the inner one. Then

Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle θ with the vertical. If wires have mass λ per unit length then the value of I is (g = gravitational acceleration)

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below:
(a)  (b) 
(c)    (d) 

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

An inductor (L = 0.03 H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown below. The key K₁ has been kept closed for a long time. Then at t = 0, K₁ is opened and key K₂ is closed simultaneously. At t = 1 ms, the current in the circuit will be (e ≌150)

A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided.

On a hot summer night, the refractive index of air is smallest near the ground and increases with height form the ground. When a light beam is directed horizontally, the Huygen's principle leads us to conclude that as it travels, the light beam

Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion

Match List-I (Fundamental Experiment) with List-II (its conclusion) and select the correct option from the choices given below the list:

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q₀ and then connected to the L and R as shown below :

If a student plots graphs of the square of maximum charge (Q²_Max) on the capacitor with time (t) for two different values L₁ and L₂ (L₁ > L₂) of L then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale)