Physics
Section-1 : (One or More than one options correct Type)
This section contains 10 multiple choice questions. Each questions has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct.
1. Heater of 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 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 40K ?
(A) 4 if wires are in parallel
(B) 2 if wires are in series
(C) 1 if wires are in se
(D) 0.5 if wires are in parallel
2. 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 100m/s. 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) 
(B) 
(C) 
(D) 
3. 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
(A) 
(B) 
(C) 
(D) 
4. 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, the
(A) 
(B) 
(C) From the central maximum, 3rd maximum of 
overlaps with 5th minimum of 
(D) The angular separation of fringes for 
is greater than 
5. 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
(A) 
(B) 
(C) 
(D) 
6. 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) 
(B) 
(C) 
(D) 
7. A student is performing an experiment using a resonance column and a tuning fork of frequency 244s–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) m, the gas in the tube is
(Useful Information : 
The molar masses M in grams are given in the options. Take the value of 
for each gas as given there.)
(A) 
(B) 
(C) 
(D) 
8. 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. Choose the correct option/options, igonoring edge effects.
(A) 
(B) 
(C) 
(D) 
9. 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 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
(A) 
(B) 
(C) 
(D) 
10. At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and alternating current I(t) = I0cos(ωt), with I0 = 1A and ω = 500 rad s−1 starts flowing in it with the initial direction shown in the figure. At 
, 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 = 20μ1, R = 10Ω and the battery is ideal with emf of 50V, identify the correct statement (s)
(A) Magnitude of the maximum charge on the capacitor before 
(B) The current in the left part of the circuit just before 
(C) Immediately after A is connected to D. the current in R is 10A.
(D) 
Section-2 : (One Integer Value Correct Type.)
This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive)
11. 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 in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents in the two wires have direction opposite to each other, the radius of curvature of the path is 
the value of 
is
12. During Searle’s experiment, zero of the Vernier scale lies between 3.20 × 10–2 m and 3.25 × 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 × 10–2 m and 3.25 × 10–2 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 2m. and its cross-sectional area is 8 × 10–7 m2. The least count of the Vernier scale is 1.0 × 10–5 m. The maximum percentage error in the Young’s modulus of the wire is
13. 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 find that d is proportional to S1/n. The value of n is:
14. A thermodynamic system is taken form 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 fire. The work done by the system along the paths af, ib and bf are Waf = 200 J, Wib = 50 J and Wbf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qiaf, Qbf and Qib respectively. If the internal energy of the system the state b is Ub = 200 J and Qiaf = 500 J, the ratio Qbf/Qib is:
15. A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 Ω resistance, it can be converted into a voltmeter of range 0-30 V. If connected to a 
resistance, it becomes an ammeter of range 0-1.5A. The value of n is :
16. A rocket is moving in a gravity free space with a constant acceleration of 2ms−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 0.3ms−1 relative to the rocket. At the same time, another ball is thrown in –x direction with a speed of 0.2ms–1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is:
17. 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 9ms–1 with respect to the ground. The rotational speed of the platform in rad–1 after the balls leave the platform is
18. A uniform circular disc of mass 1.5 kg and radius 0.5m is initially 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 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:
19. Consider an elliptically shaped rail PQ in the vertical plane with OP = 3m and OQ= 4m. A block of mass 1kg 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)
20. Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure . The speed of A is 
At time t = 0s, 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:
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