The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $n$) is

$A$ microscope consists of an objective of focal length $1.9 \ cm$ and an eyepiece of focal length $5 \ cm$. The two lenses are kept at a distance of $10.5 \ cm$. If the image is to be formed at the least distance of distinct vision $(25 \ cm)$,the distance at which the object is to be placed before the objective is: (in $cm$)

$A$ particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where $g$ is acceleration due to gravity)

If a solid sphere of mass $1 \ kg$ and radius $0.1 \ m$ rolls without slipping at a uniform velocity of $1 \ m/s$ along a straight line on a horizontal floor,the kinetic energy is

If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $