Total internal reflection of light is possible when light enters from

The period of oscillation of a simple pendulum of length $l$ suspended from the roof of a vehicle,which moves without friction down an inclined plane of inclination $\alpha$,is given by

The largest group of insecticides produced by plants is .......

If $4x^2 - 5xy + y^2 = 0$ represents a pair of lines with slopes $m_1$ and $m_2$,then the value of $|m_1 - m_2|$ equals

$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\,N,$ the mass of the block (in $kg$) is (take $g = 10\,m/s^2$)

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is