A large open tank containing water has two holes to its wall. A square hole of side a is made at a depth of y and a circular hole of radius r is made at a depth of 16 y from the surface of the water. If an equal amount of water comes out through both the holes per second, then  the relation between r and a will be

A) $r=\frac{a}{2\sqrt{\pi}}$

B) $r=\frac{a}{2\pi}$

C) $r=\frac{2a}{\pi}$

D) $r=\frac{2a}{\sqrt{\pi}}$


The light of wavelength $\lambda$  incident on the surface of metal having work function $\phi$ emits the electrons. The maximum velocity of electrons emitted is 

[c= velocity of light, h= planck's constant, m= mass of electron]

A) $\left[\frac{2(hv-\phi)\lambda}{mc}\right]$

B) $\left[\frac{2(hc-\lambda\phi)}{m\lambda}\right]^{1/2}$

C) $\left[\frac{2(hc-\lambda)}{m\lambda}\right]^{1/2}$

D) $\left[\frac{2(hc-\phi)}{m\lambda}\right]^{}$


In a communication system, a repeater is used to extend the range to transmission. It is the combination of 

A) IF stage and amplifier

B) rectifier and detector

C) recevier and transmitter

D) modulator and power amplifier


An obstacle is moving towards the source with velocity v. The sound is reflected from the obstacle. If c is the speed  of sound and $\lambda$ is the wavelength, then the wavelength of the reflected wave, $\lambda_{r}$is 

A) $\lambda_{r}=\left(\frac{C-V}{C+V}\right)\lambda$

B) $\lambda_{r}=\left(\frac{C+V}{C-V}\right)\lambda$

C) $\lambda_{r}=\left(\frac{C-V}{C}\right)\lambda$

D) $\lambda_{r}=\left(\frac{C+V}{C}\right)\lambda$


 A radioactive nucleus emits 4 $\alpha$ -particles and 7 $\beta$-particles in succession. The ratio of number of neutrons  of that of protons is [A= mass number, Z= atomic number]

A) $\frac{A-Z-13}{Z-2}$

B) $\frac{A-Z-15}{Z-1}$

C) $\frac{A-Z-13}{Z-1}$

D) $\frac{A-Z-11}{Z-2}$