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

The ratio of the magnetic field at the centre of a current-carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$,then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$,is (in $\text{cm}^2/\text{sec}$): (in $\pi$)

$A$ road is $10\, m$ wide. Its radius of curvature is $50\, m$. The outer edge is raised above the inner edge by a distance of $1.5\, m$. This road is most suited for the velocity .......... $m/s$. (in $.5$)

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

The points whose position vectors are $2i+3j+4k$,$3i+4j+2k$,and $4i+2j+3k$ are the vertices of