A carnot  engine  with efficiency $\eta$ operates between two heat  reservoirs with temperatures $T_{1}$ and $T_{2}$  , where $T_{1} >T_{2}$ . If only $T_{1}$ is changed by 0.4% , the  change in efficiency is $\triangle\eta_{1}$ , whereas if only  $T_{2}$  is changed by 0.2% , the efficiency is changed by $\triangle\eta_{2}$ . The ratio  $\frac{\triangle\eta_{1}}{\triangle\eta_{2}}$ is approximately

A) -2

B) -4

C) +3

D) +4


A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent? [ Assume  g=10 m/s2, $\rho_{water}$= 103 kg/m3, viscosity =1 centi-poise]

A) 3 cm

B) 4 cm

C) 6 cm

D) 2 cm


A body of mass 0.3 kg hangs by a spring with a force constant of 50N/m . The amplitude of oscillations is damped and reaches $\frac{1}{e}$ of its original value in about 100 oscillations. If $\omega$ and $\omega'$ are the angular frequencies of undamped and damped oscillations respectively , then percentage of  $\left(\frac{\omega-\omega'}{\omega}\right)$ is 

A) $\left(\frac{1}{800 \pi}\right)$

B) $\left(\frac{\pi^{2}}{600 }\right)$

C) $\left(\frac{1}{800\pi^{2} }\right)$

D) $\left(\frac{\pi}{400 }\right)$


A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 5 km/s. The speed of the rocket when its mass is  reduced to  $\frac{1}{20}^{th}$  of its initial mass, is [Assume initial speed  to be zero and ignored gravitational and viscous forces]

A) 20 km/s

B) 40 in (2) km/s

C) 5 in (20) km/s

D) 10 in (10) km/s


A particle A moves along the line, y=30m with a constant velocity, v parallel to the x-axis. At the momemt particle A passes the y-axis, particle  B starts from the origin  witrh zero  initial speed and a constant acceleration  .$a=0.40 m/sec^{2}$ . The angle between a and y-axis is $60^{0}$. If the particles A and B collide after sometimes , then the value of |v|  will be

A) 2 m/s

B) 3 m/s

C) 4 m/s

D) 5 m/s