JEE Advanced 2007 · Paper 1

A resistance of 2 Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

1. A3 Ω
2. B4 Ω
3. C5 Ω
4. D6 Ω

In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

1. Ax < f
2. Bf < x < 2f
3. Cx = 2f
4. Dx > 2f

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

1. AA potential difference appears between the two cylinders when a charge density is given to the inner cylinder
2. BA potential difference appears between the two cylinders when a charge density is given to the outer cylinder
3. CNo potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders
4. DNo potential difference appears between the two cylinders when same charge density is given to both the cylinders

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

1. Anegative and distributed uniformly over the surface of the sphere
2. Bnegative and appears only at the point on the sphere closest to the point charge
3. Cnegative and distributed non-uniformly over the entire surface of the sphere
4. Dzero

A ray of light traveling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

1. Aonly a reflected ray and no refracted ray
2. Bonly a refracted ray and no reflected ray
3. Ca reflected ray and a refracted ray and the angle between them would be less than 180° − 2θ
4. Da reflected ray and a refracted ray and the angle between them would be greater than 180° − 2θ

In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

1. AE(²³⁶₉₂U) > E(¹³⁷₅₃I) + E(⁹⁷₃₉Y) + 2E(n)
2. BE(²³⁶₉₂U) < E(¹³⁷₅₃I) + E(⁹⁷₃₉Y) + 2E(n)
3. CE(²³⁶₉₂U) < E(¹⁴⁰₅₆Ba) + E(⁹⁴₃₆Kr) + 2E(n)
4. DE(²³⁶₉₂U) = E(¹⁴⁰₅₆Ba) + E(⁹⁴₃₆Kr) + 2E(n)

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

1. A802 nm
2. B823 nm
3. C1882 nm
4. D1648 nm

STATEMENT-1 A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because STATEMENT-2 The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

1. AStatement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
2. BStatement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
3. CStatement-1 is True, Statement-2 is False
4. DStatement-1 is False, Statement-2 is True