JEE Main 2014 April 12 Paper & Solutions - JEE MCQ

A 4 g bullet is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately?

A spring of unstitched length l has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is:

A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The center of circle is marked by 'C. The angular momentum from the origin O can be written as:

Two hypothetical planets of masses m₁ and m₂ are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is 'd' ? (Speed of m₁ is v₁ and that of m₂ is v₂):

Steel ruptures when a shear of 3.5 ×10⁸ Nm^–2 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly :

A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius 'a'. The time in which it will be emptied is :

Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S the change in total surface area, T is the surface tension and P atmospheric pressure, which of the following relation is correct?

Hot water cools from 60°C to 50°C in the first 10 minutes and to 42°C in the next 10 minutes. The temperature of the surroundings is :​

A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127°C and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be :

At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms^–1. The gas is :

Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?

A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground, of frequency nearly : (Speed of sound =343 m/s)

A spherically symmetric charge distribution is characterised by a charge density having the following variation:

Where r is the distance from the centre of the charge distribution and ρ₀ is a constant. The electric field at an internal point (r <R ) is :

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation:
K(x) = K_o + λx (λ = a constant)
The capacitance C, of this capacitor, would be related to its ‘vacuum’ capacitance C_o as per the relation :

The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3 Ω, 9 Ω and 9 Ω and a capacitor 5.0 µF.

How much is the current I in the circuit in steady state?

A positive charge 'q' of mass 'm' is moving along the +x axis. We wish to apply a uniform magnetic field B for time ∆t so that the charge reverses its direction crossing the y axis at a distance d. Then :

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B₁, at its centre when a current (I) passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B₂ at the centre of the loops when current 1/3 passes through it. The ratio B₁ : B₂ is :

A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is :

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly :

The refractive index of the material of a concave lens is µ. It is immersed in a medium of refractive index µ₁. A parallel beam of light is incident on the lens. The path of the emergent rays when µ₁ > µ is :

Interference pattern is observed at 'P' due to superimposition of two rays coming out from a source 'S' as shown in the figure. The value ‘l’ for which maxima is obtained at 'P' is (R is perfect reflecting surface) :

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is 6600 Å , then wavelength of first maximum will be:

A beam of light has two wavelengths 4972 Å and 6216 Å with a total intensity of 3.6 ×10^–3 Wm⁻² equally distributed among the two wavelengths. The beam falls normally on an area of 1 cm² of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photo electrons liberated in 2s is approximately:

A piece of bone of an animal from a ruin is found to have ¹⁴C activity of 12 disintegrations per minute per gm of its carbon content. The ¹⁴C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die ? (Given half life of ¹⁴C is t_1/2 = 5760 years):

For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range of:

For sky wave propagation, the radio waves must have a frequency range in between:

In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potentiometer wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of voltmeter will be: