JEE Main 2014 Question Paper with Solutions - JEE MCQ

The current voltage relation of diode is given by I = (e^1000V/T – 1) mA, where the applied voltage V is in
volts and the temperature T is in degree Kelvin. If a student makes an error measuring 0.01 V while
measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury
level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46
cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm
of Hg)

Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct
option from the choices given below the lists:

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a
dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 10⁴ V/m,
the charge density of the positive plate will be close to :

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the
action of their mutual gravitational attraction. The speed of each particle is :

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The
voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

A particle moves with simple harmonic motion in a straight line. In first s, after starting from rest it travels
a distance a, and in next s it travels 2a, in same direction, then :

The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 x 103 Am^-1. The current
required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets
demagnetized when inside the solenoid, is:

The forward biased diode connection is:

During the propagation of electromagnetic waves in a medium:

In the circuit shown here, the point ‘C’ is kept connected to point ‘A’ till the current flowing through the circuit becomes constant. Afterward, suddenly, point ‘C’ is disconnected from point ‘A’ and connected to point ‘B’ at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to :

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct
statement:

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the
particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation
between H, u and n is:

A thin convex lens made from crown glass (μ= 3/2) has focal length f. When it is measured in two different
liquids having refractive indices 4/3 and 5/3 . it has the focal lengths f₁ and f₂ respectively. The correct
relation between the focal lengths is:

Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross –
section of each rod = 4 cm². End of copper rod is maintained at 100^oC where as ends of brass and steel are
kept at 0^oC. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are
thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are
0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air
column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 900 angle at centre. Radius joining their interface makes an angle α with
vertical. ratio d₁/d₂ is

A green light is incident from the water to the air - water interface at the critical angle (9). Select the correct statement

Hydrogen (₁H¹), Deuterium (₁H²), singly ionised Helium (₂He⁴)⁺ and doubly ionised lithium (₃Li⁶)⁺⁺ all have
one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of
emitted radiation are λ₁, λ₂, λ₃ and λ₄ respectively then approximately which one of the following is
correct?

The radiation corresponding to 3 → 2 transition of hydrogen atom falls on a metal surface to produce
photoelectrons. These electrons are made to enter a magnetic field of 3 x 10^-4T. If the radius of the largest
circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

A block of mass m is placed on a surface with a vertical cross section given by y = x3/6. If the coefficient
of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping
is :

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber band by L is :

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R, and the surface tension of water is T, value of r just before bubbles detach is : (density of water is ρ_w)

Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen
through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero
intensity), a rotation of Polaroid through 300 makes the two beams appear equally bright. If the initial
intensities of the two beams are IA and IB respectively, then I_A/I_B equals :

Assume that an electric field  exists in space. Then the potential difference V_A – V_O, where V_O is
the potential at the origin and V_A the potential at x = 2 m is :