11.

The equation of stationary wave along a stretched string is given by $\mathrm{y} = 5 \sin \frac{\mathrm{\pi x}}{3} \cos 40\mathrm{\pi t}$ where, x and y are in cm and t in second. The separation between two adjacent nodes is :

• 1.5 cm

• 3 cm

• 6 cm

• 4 cm

Which of the following is not an inelastic collision ?

• A man jump on a cart

• A bullet embedded in a block

• Collision of two glass ball

• none of the above

A force F is given by F =at + bt² ,where, t is time. What are the dimensions of a and b ?

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -1}\right] \mathrm{and} \left[\mathrm{M} \mathrm{L} {\mathrm{T}}^0\right]$

• $\left[ \mathrm{M} \mathrm{L} \mathrm{T}{ }^{-3}\right] \mathrm{and} \left[\mathrm{M} {\mathrm{L}}^2 {\mathrm{T}}^4\right]$

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -4}\right] \mathrm{and} \left[\mathrm{M} \mathrm{L} {\mathrm{T}}^1\right]$

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -3}\right] \mathrm{and} \left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{ -4}\right]$

A river is flowing from west to east with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so, as to take the shortest possible path to go to the south?

• 30^o east of south

• 60^o east of south

• 60^o west of south

• 30^o west of north

If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period becomes :

• 3 T

• 3/2T

• 4T

• 2T

There are 26 tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives 3 beats with the next. The first one is octave of the last. What is the frequency of 18th tuning fork?

• 100 Hz

• 99 Hz

• 96 Hz

• 103 Hz

A pendulum is undergoing SHM with frequency f What is the frequency of its kinetic energy ?

• $\frac{\mathrm{f}}{2}$

• 2 f

• 3 f

• 4 f

A person is observing two trains one coming towards him and other leaving with the same
velocity 4 m/s. If their whistling frequencies are 240 Hz each, then the number of beats per second heard  by the person will be : ( if velocity of sound 320 m/s)

• 3

• 6

• 9

• zero

Two rods of same material have same length and area. The heat ΔQ flows through them for 12 minutes when they are joint side by side. If now both the rods are joined in parallel, then the same amount of heat ΔQ will flow in :

• 24 min

• 3 min

• 12 min

• 6 min

A perfect gas is found to obey the relation PV^3/2 = constant during an adiabatic process. If such a gas initially at a temperature T, is compressed to half of its initial volume, then its final temperature will be :

• 2 T

• 4T

• (2)^1/2 T

• 2 (2)^1/2 T