$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is: (in $^{\circ}$)

If $\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} dt=\frac{1}{2}[g(t)]^2+c$,(where $c$ is a constant of integration),then $g(2)$ is

Sunlight of intensity $1.3 ~kW ~m^{-2}$ is incident normally on a thin convex lens of focal length $20 ~cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light,in $kW m^{-2}$,at a distance $22 ~cm$ from the lens on the other side is.

Which of the following statements is true for an $N$-type semiconductor?

In the circuit shown in the figure,the power developed across the $1 \Omega$,$2 \Omega$,and $3 \Omega$ resistors are in the ratio of:

Honey bees also produce beeswax,which finds many uses in industry,such as: