$A$ simple pendulum has a periodic time $T_1$ when it is on the surface of the Earth of radius $R$. Its periodic time is $T_2$ when it is taken to a height $R$ above the Earth's surface. The value of $\frac{T_2}{T_1}$ is

Find the derivative of the function $(x+\sec x)(x-\tan x)$.

The wavelength of the light used in Young's double slit experiment is $\lambda$. The intensity at a point on the screen is $I$,where the path difference is $\lambda/6$. If $I_0$ denotes the maximum intensity,then the ratio of $I$ and $I_0$ is

All the springs in figures $(a)$,$(b)$,and $(c)$ are identical,each having a force constant $K$. The mass attached to each system is $m$. If $T_a, T_b$,and $T_c$ are the time periods of oscillations of the three systems respectively,then:

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere in seconds is (acceleration due to gravity,$g = 10 \ m/s^2$). (in $\pi$)

$A$ photoelectric surface is illuminated successively by monochromatic light of wavelengths $\lambda$ and $\frac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is $3$ times that in the first case,the work function of the surface is: