The de-Broglie wavelength of a particle moving with a velocity $2.25 \times 10^8 \ m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the energy of the photon is (velocity of light is $3 \times 10^8 \ m/s$). (in $/8$)

$ABC$ is a triangular plate of uniform thickness. Its sides are as shown in the figure. If $I_{AB}$,$I_{BC}$,and $I_{CA}$ are the moments of inertia of the plate about axes $AB$,$BC$,and $CA$ respectively,then which of the following relations is correct?

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $\frac{T_1}{T_2}$ is given by:

In which of the following reactions,$MgO$ is not formed?

At a certain place,the horizontal component of the Earth's magnetic field is $B_0$ and the angle of dip is $45^o$. The total intensity of the field at that place will be: