JEE Main 2014 April 11 Paper & Solutions - JEE MCQ

A cone of base radius R and height h is located in a uniform electric field  parallel to its base. The electric flux entering the cone is:

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows :

Make the correspondence of these bars with their material being diamagnetic (D) ferromagnetic (F) and paramagnetic (P)

The average mass of rain drops is 3.0 × 10^–5 kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square meter of the surface at a place which receives 100 cm of rain in a year.

An ideal monoatomic gas is confinedinacy linder by a spring loaded piston of cross section 8.0 × 10^–3 m². Initially, the gas is at 300K and occupies a volume of 2.4 × 10^–3 m³ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 10⁵ N/m² The cylinder and the piston are thermally insulated.
The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible):

The angular frequency of the damped oscillator is given by where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio is 8%, the change in time period compared to the undamped oscillator is approximate as follows:

A coil of circular cross-section having 1000 turns and 4 cm² face area is placed with its axis parallel to a magnetic field which decreases by 10^-2 Wb m^-2 in 0.01 s. The e.m.f. induced in the coil is:

Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:

A body of mass 5kg under the action of constant force  has velocity at t = 0 s as and at t = 10 s as  :-

In the circuit diagrams (A, B, C, and D) shown below, R is a high resistance and S is a resistance the order of galvanometer G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as:

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly:
(take g = 10 ms^-2 and density of water = 10³ kg m^-3)

A photon of wavelength λ is scattered from an electron, which was at rest. The wavelength shift Δλ is three times of λ and the angle of scattering θ is 60°. The angle at which the electron recoiled is φ The value of tan φ is:
(electron speed is much smaller than the speed of light)

The Bulk moduli of Ethanol, Mercury and Water are given as 0.9, 25 and 2.2 respectively in units of 10⁹ Nm^-2. For a given value of pressure, the fractional compression in volume is  Which of the following statements about  for these three liquids is correct? :-

A hot body, obeying Newton's law of cooling is cooling down from its peak value 80ºC to an ambient temperature of 30ºC. It takes 5 minutes in cooling down from 80°C to 40°C. How much time will it take to cool down from 62°C to 32°C? (Given ln 2 = 0.693, ln 5 = 1.609)

A Zener diode is connected to a battery and a load as shown below :
The currents I, I_Z and I_L are respectively.

An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density 10³ kg/m³. The pressure inside the bubble is 1100 Nm^-2 greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g = 9.8 ms^-2):-

In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively:-

During an adiabatic compression, 830J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: (R = 8.3 JK^-1mol^-1)

A small ball of mass m starts at a point A with speed v₀ and moves along a frictionless track AB as shown. The track BC has coefficient of friction μ. The ball comes to stop at C after traveling a distance L which is:

In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be :

A thin bar of length L has a mass per unit length λ, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λ₀, then the distance of the centre of mass from the lighter end is :

In terms of resistance R and time T, the dimensions of ratio of the permeability μ and permittivity ε is :-

The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object?

Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is :

From a sphere of mass M and radius R, a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is:

An electromagnetic wave of frequency 1 x 10¹⁴ hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ε₀ = 8.8 × 10^-12 C²/N-m², then average energy density of electric field will be:

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be :