An ideal refrigerator has a freezer at a temperature of $-13^{\circ}C$. The coefficient of performance of the refrigerator is $5$. The temperature of the air (to which heat is rejected) will be:

$A$ ball is allowed to fall from a height of $10\, m$. If there is $40\%$ loss of energy due to impact,then after one impact,the ball will rise to a height of ......... $m$.

$A$ certain prism is found to produce a minimum deviation of $38^{\circ}$. It produces a deviation of $44^{\circ}$ when the angle of incidence is either $42^{\circ}$ or $62^{\circ}$. What is the angle of incidence when it is undergoing minimum deviation? (in degrees)

The point of contact of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2-2x+2y+1=0$ is

$Ni$ anode is used in the electrolytic extraction of

$\int_0^{\pi/6} \cos^4 3\theta \cdot \sin^2 6\theta \, d\theta$ is equal to