51.

The temperature of equal masses of three different liquids A, Band Care 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C and when B and C are mixed is 23°C. The temperature when A and C are mixed is

• 18.2°C

• 22°C

• 20.2°C

• 24.2°C

The time period of the second's hand of a watch is

• 1 h

• 1 s

• 12 h

• 1 min

A particle starts SHM from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is 3 $\frac{\mathrm{E}}{4}$ · Its displacement at that instant is

• $\frac{\mathrm{a}}{\sqrt{2}}$

• $\frac{\mathrm{a}}{2}$

• $\frac{\mathrm{a}}{\sqrt{\left({\displaystyle \frac{3}{2}}\right)}}$

• $\frac{\mathrm{a}}{\sqrt{3}}$

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration . Then its time period in second is

• $\frac{1}{2 \mathrm{\pi }\sqrt{3}}$

• $2 \mathrm{\pi }\sqrt{3}$

• $\frac{2 \mathrm{\pi }}{\sqrt{3}}$

• $\frac{\sqrt{3}}{2\mathrm{\pi }}$

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is

• 1 : 1

• 2 : 1

• 1 : 4

• 1 : 2

An observer standing near the sea shore 54 min. If the wavelength of the water wave is 10 m, then the velocity of water wave is

• 540 ms^-1

• 5.4 ms^-1

• 0.184 ms^-1

• 9 ms^-1

A set of 24 tuning forks are so arranged that each gives 6 beats/s with the previous one. If the frequency of the last tuning fork is double than that of the first, frequency of the second tuning fork is

• 138 Hz

• 132 Hz

• 144 Hz

• 276 Hz

A 10 Ω electric heater operates on a 110 V line. The rate at which heat is developed in watts is 

• 1310 W

• 670 W

• 810 W

• 1210 W

For a certain thermocouple, if the temperature of the cold junction is 0°C, the neutral temperature and inversion temperatures are 285°C and 570°C respectively. If the cold junction is brought to 10°C, then the new neutral and inversion temperatures are respectively

• 285°C and 560°C

• 285°C and 570°C

• 295°C and 560°C

• 275°C and 560°C

In which of the following substances does resistance decrease with increase in temperature ?

• Copper

• Carbon

• Constantan

• Silver