Light is an electromagnetic wave. Its speed in vacuum is given by the expression

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base to be $30^{\circ}$. After walking $120 \ m$ towards it on level ground,the angle of elevation is found to be $60^{\circ}$. The height of the object (in metres) is:

Assertion : Between any two given energy levels,the number of absorption transitions is always less than the number of emission transitions.
Reason : Absorption transitions start from the lowest energy level only and may end at any higher energy level. But emission transitions may start from any higher energy level and end at any energy level below it.

$\begin{aligned} & f(x, y)=2(x-y)^2-x^4-y^4 \\ & \left|\left(f_{x x} f_{y y}-f_{x y}^2\right)\right|_{(0,0)} \end{aligned}$

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,then the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals

The bacteria increases at a rate proportional to the number of bacteria present. If the original number $N$ doubles in $4 \text{ hours}$,then the number of bacteria in $12 \text{ hours}$ will be (in $N$)