JEE Advanced 2014 — Set 1

At time 𝑡𝑡= 0, terminal A in the circuit shown in the figure is connected to B by a keyand an alternating current 𝐼𝐼(𝑡𝑡) = 𝐼𝐼0cos⁡(𝜔𝜔𝜔𝜔), with 𝐼𝐼0 = 1Aand ω = 500 rad s-1 starts flowing in it with the initial direction shown in the figure. At t = 7𝜋𝜋 6𝜔𝜔 , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C=20µF, R= 10 Ω and the battery is ideal with emf of 50V, identify the correct statement (s).

A light source, which emits two wavelengths 𝜆𝜆1 = 400 𝑛𝑛𝑛𝑛 and 𝜆𝜆2 = 600 𝑛𝑛𝑛𝑛, is used in a Young’s double slit experiment. If recorded fringe widths for 𝜆𝜆1 and𝜆𝜆2 are𝛽𝛽1 and𝛽𝛽2 © number of fringes for them within a distance yon one side of the central maximum are m1 and m2, respectively, then

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 𝑚𝑚𝑠𝑠−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 parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.

Let𝐸𝐸1(𝑟𝑟), 𝐸𝐸2(𝑟𝑟) and 𝐸𝐸3(𝑟𝑟) 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 𝐸𝐸1(𝑟𝑟0) = 𝐸𝐸2(𝑟𝑟0) = 𝐸𝐸3(𝑟𝑟0) at a given distance r0, then

A student is performing an experiment using a resonance column and a tuning fork of frequency 244𝑠𝑠−1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 ± 0.005) 𝑚𝑚, the gas in the tube is (Useful information:√167𝑅𝑅𝑅𝑅= 640 𝐽𝐽1 2 ⁄ mole−1 2 ⁄ ;√140𝑅𝑅𝑅𝑅= 590 𝐽𝐽1 2 ⁄ mole−1 2 ⁄ .The molar masses Min grams are given in the options. Take the values of ට 10 𝑀𝑀for each gas as given there.)

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 0.5kgwater by 40K. 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 40 K?

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 𝜇𝜇1 and that between the floor and the ladder is 𝜇𝜇2. 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

A transparent thin film of uniform thickness and refractive index n1= 1.4 is coated on the convex spherical surface of radius Rat 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

Two ideal batteries of emfV1 and V2 and three resistancesR1, R2 andR3 are connected as shown in the figure. The current in resistanceR2 would be zero if