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A refrigerator is driven by 1000 W electric motor having an efficiency of 60%. The refrigerator is considered as a reversible heat engine operating between 273 K and 303 K. Time required by it to freeze 32.5 kg of water at 0°C is. (Given, latent heat of fusion of ice = 336 × 10³ J-kg^-1 and heat lost may be neglected).

• 53 min 20 s

• 33 min 20 s

• 48 min 40 s

• 28 min 32 s

A boat strikes an under water rock which punctures a hole 5 cm in diameter in its hull which is 1.5 m below the water line. At what rate in litre per second does water enter.

• 2.65 Ls^-1

• 8.85 Ls^-1

• 10.65 Ls^-1

• 624 Ls^-1

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T₂ and T₁ (T₂ > T₁) . The rate of flow of heat through the slab in steady state is

• $\frac{\mathrm{KA} \left({\mathrm{T}}_1 - {\mathrm{T}}_2\right)}{3\mathrm{x}}$

• $\frac{\mathrm{KA} \left({\mathrm{T}}_2 - {\mathrm{T}}_1\right)}{3\mathrm{x}}$

• $\frac{\mathrm{KA}\hspace{0.17em}\left({\mathrm{T}}_1 - {\mathrm{T}}_2\right)}{2\mathrm{x}}$

• $\frac{\mathrm{KA} \left({\mathrm{T}}_2 - {\mathrm{T}}_1\right)}{2\mathrm{x}}$

One mole of oxygen is heated at a constant pressure from 0°C. What must be the quantity of heat that should be supplied to the gas for the volume to be doubled . (specific heat of oxygen is 0.218 calg^-1K^-1)

• 1700 cal

• 1805 cal

• 1904 cal

• 1612 cal

A steel wire of length 15 m has density = 7.7 × 10³ kg/m³ and Young's modulus = 2.2 × 10¹¹ N/m². It is subjected to a tension which produces an elastic strain of 1%. Its fundamental frequency of vibration must be

• 256 Hz

• 178 Hz

• 170 Hz

• 200 Hz

Determine the mean free path of argon molecules under normal condition knowing that the molecule diameter is 0.4 nm.

• 48 nm

• 60 nm

• 52 nm

• 71 nm

Two soap bubbles A & B are kept in a closed chamber where the air is maintained at pressure 8 N/m² . The radii of bubbles A & B are 2cm and 4cm, respectively. Surface tension of the soap water used to make bubbles is 0.04 N/m. If n_A and n_B are the number of moles of air in bubbles A and B, respectively, then $\frac{{\mathrm{n}}_{\mathrm{B}}}{{\mathrm{n}}_{\mathrm{A}}}$ = ?[Neglect the effect of gravity]

• 2

• 8

• 9

• 6

By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density 13.6 g/cm³). Using the straw, he can drink water from a glass upto a maximum depth of

• 10 cm

• 13.6 cm

• 75 cm

• 1.36 cm

The self-inductance of the motor of an electric fan is 10H. In order to impart maximum power at 50 Hz, it should be
connected to a capacitance of

• 4µF

• 8µF

• 1µF

• 2µF

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be

• 400 %

• 66.6 %

• 33.3 %

• 200 %