JEE Advanced 2009 · Paper 1

Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q₁, Q₂, Q₃, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q₁ : Q₂ : Q₃, is

1. A1 : 2 : 3
2. B1 : 3 : 5
3. C1 : 4 : 9
4. D1 : 8 : 18

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is √3. The inclination θ of this inclined plane from the horizontal plane is gradually increased from 0°. Then

1. Aat θ = 30°, the block will start sliding down the plane
2. Bthe block will remain at rest on the plane up to certain θ and then it will topple
3. Cat θ = 60°, the block will start sliding down the plane and continue to do so at higher angles
4. Dat θ = 60°, the block will start sliding down the plane and on further increasing θ, it will topple at certain θ

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as [Take g = 10 m/s².]

1. A9 m/s
2. B12 m/s
3. C16 m/s
4. D21.33 m/s

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

1. Alinear momentum of the system does not change in time
2. Bkinetic energy of the system does not change in time
3. Cangular momentum of the system does not change in time
4. Dpotential energy of the system does not change in time

A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are: (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

1. A(42, 56)
2. B(48, 48)
3. C(66, 33)
4. D(78, 39)

Cᵥ and Cₚ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then

1. ACₚ − Cᵥ is larger for a diatomic ideal gas than for a monoatomic ideal gas
2. BCₚ + Cᵥ is larger for a diatomic ideal gas than for a monoatomic ideal gas
3. CCₚ/Cᵥ is larger for a diatomic ideal gas than for a monoatomic ideal gas
4. DCₚ · Cᵥ is larger for a diatomic ideal gas than for a monoatomic ideal gas