JEE Advanced 2012 · Paper 1

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

1. A(65/2)¹⁄⁴ T
2. B(97/4)¹⁄⁴ T
3. C(97/2)¹⁄⁴ T
4. D97¹⁄⁴ T

In the determination of Young’s modulus (Y = 4MLg/πld²) by using Searle’s method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement

1. Adue to the errors in the measurements of d and l are the same.
2. Bdue to the error in the measurement of d is twice that due to the error in the measurement of l.
3. Cdue to the error in the measurement of l is twice that due to the error in the measurement of d.
4. Ddue to the error in the measurement of d is four times that due to the error in the measurement of l.

Young’s double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe widths recorded are β_G, β_R and β_B, respectively. Then,

1. Aβ_G > β_B > β_R
2. Bβ_B > β_G > β_R
3. Cβ_R > β_B > β_G
4. Dβ_R > β_G > β_B

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the r ms speeds (v_rms (helium)/v_rms (argon)) is

1. A0.32
2. B0.45
3. C2.24
4. D3.16

Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 45° to the vertical JUST after release. Then X is nearly

1. A1 × 10⁻⁵ V
2. B1 × 10⁻⁷ V
3. C1 × 10⁻⁹ V
4. D1 × 10⁻¹⁰ V

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E⃗ = E₀ ĵ and B⃗ = B₀ ĵ. At time t = 0, this charge has velocity v⃗ in the x-y plane, making an angle θ with the x-axis. Which of the following option(s) is(are) correct for time t > 0?

1. AIf θ = 0°, the charge moves in a circular path in the x-z plane.
2. BIf θ = 0°, the charge undergoes helical motion with constant pitch along the y-axis.
3. CIf θ = 10°, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.
4. DIf θ = 90°, the charge undergoes linear but accelerated motion along the y-axis.

A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

1. Aa high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.
2. Ba low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.
3. Ca low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.
4. Da high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.