JEE Advanced 2014 Paper -1 with Solutions - JEE MCQ

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string
is 100 ms^-1. The other end of the string is vibrating in the y direction so that stationary waves are set up in
the string. The possible waveform(s) of these stationary waves is (are)

A transparent thin film of uniform thickness and refractive index n₁ = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n₂ = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the
temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same
material, each of length L and diameter 2d. The way these wires are connected is given in the options.
How much time in minutes will it take to raise the temperature of the same amount of water by 40K?

Two ideal batteries of emf V₁ and V₂ and three resistances R₁, R₂ and R₃ are connected as shown in the figure. The current in resistance R₂ would be zero if

Let  E₁ (r), E₂ (r) and E₃ (r) be the respective electric fields at a distance r from a point charge Q, an
infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge
density σ. If E₁(r₀ ) = E₂ (r₀ ) = E₃ (r₀ ) at a given distance r0, then

A light source, which emits two wavelengths λ₁ = 400 nm and λ₂ = 600 nm, is used in a Young’s double
slit experiment. If recorded fringe widths for λ₁ and λ₂ are β₁ and β₂ and the number of fringes for them
within a distance y on one side of the central maximum are m₁ and m₂, respectively, then

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle
θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ1 and that
between the floor and the ladder is μ₂. The normal reaction of the wall on the ladder is N1 and that of the
floor is N₂. If the ladder is about to slip, then

Q. No. 11 - 20  carry 3 Marks  each

Each question, when worked out will result in one integer from 0 to 9 (both inclusive).

Q.

During Searle’s experiment, zero of the Vernier scale lies between 3.20 x 10^-2 m and 3.25 x 10^-2 m of the
main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions.
When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 x
10^-2 m and 3.25 x10^-2 m of the main scale but now the 45th division of Vernier scale coincides with one of
the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 x 10^-7
m². The least count of the Vernier scale is 1.0 x 10^-5 m. The maximum percentage error in the Young’s
modulus of the wire is

Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30⁰ and 60⁰ with
respect to the horizontal respectively as shown in the figure. The speed of A is 100√3 ms^-1. At time t = 0
s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity
perpendicular to the line of motion of A. If at t = t₀, A just escapes being hit by B, t₀ in seconds is

A thermodynamic system is taken from an initial state i with internal energy Ui = 100 J to the final state f
along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system
along the paths af, ib and bf are W_af = 200 J, W_ib = 50 J and W_bf = 100 J respectively. The heat supplied to
the system along the path iaf, ib and bf are iaf ib Q , Q and Q_bf respectively. If the internal energy of the
system in the state b is U_b = 200 J and Q_iaf = 500 J, the ratio Q_bf / Q_ib is

Two parallel wires in the plane of the paper are distance X₀ apart. A point charge is moving with speed u
between the wires in the same plane at a distance X₁ from one of the wires. When the wires carry current of
magnitude I in the same direction, the radius of curvature of the path of the point charge is R₁. In contrast,
if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R₂. id X₀/X₁  =3  the value of  R₁/ R₂  is

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses
dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity
(power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to
S^1/n. The value of n is

A rocket is moving in a gravity free space with a constant acceleration of 2 ms^–2 along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3 ms^–1 relative to the rocket. At the same time, another ball is thrown in +x direction with a speed of 0.2 ms^–1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990  resistance, it can be converted into a voltmeter of range 0 – 30 V. If connected to a 2n/249  resistance, it becomes an ammeter of range 0 – 1.5 A. The value of n is

A uniform circular disc of mass 1.5 kg and radius 0.5 m isinitially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral
triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rad s^–1 is

A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 ms^–1 with respect to the ground. The rotational speed of the platform in rad s^–1 after the balls leave the platform is

Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n×10) Joules. The
value of n is (take acceleration due to gravity = 10 ms^–2)

Q. No. 21- 30 carry 3 mark  each.

Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.

Q. The correct combination of names for isomeric alcohols with molecular formula C₄H₁₀O is/are

An ideal gas in a thermally insulated vessel at internal pressure = P₁, volume = V₁ and absolute
temperature = T₁ expands irreversibly against zero external pressure, as shown in the diagram. The final
internal pressure, volume and absolute temperature of the gas are P₂, V₂ and T₂, respectively. For this
expansion,

Hydrogen bonding plays a central role in the following phenomena:

In a galvanic cell, the salt bridge

For the reaction:

The correct statement(s) in the balanced equation is/are:

The reactivity of compound Z with different halogens under appropriate conditions is given below:

The observed pattern of electrophilic substitution can be explained by

The correct statement(s) for orthoboric acid is/are

Upon heating with Cu₂S, the reagent(s) that give copper metal is/are

The pair(s) of reagents that yield paramagnetic species is/are

In the reaction shown below, the major product(s) formed is/are