$A$ sound source is moving towards a stationary observer with $(1/10)$ of the speed of sound. The ratio of apparent to real frequency is .........

Let $A$ and $B$ be two sets,then:

For $x > 1$,if $(2x)^{2y} = 4e^{2x - 2y}$,then $(1 + \log_e 2x)^2 \frac{dy}{dx}$ is equal to

One end of a uniform glass capillary tube of radius $r=0.025 \ cm$ is immersed vertically in water to a depth $h=1 \ cm$. The excess pressure in $N/m^2$ required to blow an air bubble out of the tube is: (Surface tension of water $T=7 \times 10^{-2} \ N/m$,Density of water $\rho=10^3 \ kg/m^3$,Acceleration due to gravity $g=10 \ m/s^2$)

$A$ particle $A$ is projected vertically upwards. Another identical particle $B$ is projected at an angle of $45^{\circ}$. Both reach the same maximum height. The ratio of the initial kinetic energy of $A$ to that of $B$ is

The rate of disintegration of a fixed quantity of a radioactive element can be increased by