$A$ Zener diode,having a breakdown voltage equal to $15 \, V$,is used in a voltage regulator circuit as shown in the figure. The current through the diode is.....$mA$.

The least count of a stopwatch is $\frac{1}{5} \, s$. The time of $20$ oscillations of a pendulum is measured to be $25 \, s$. The maximum percentage error in the measurement of time will be ..... $\%$

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

In a biprism experiment,if the $5^{\text{th}}$ bright band with wavelength $\lambda_{1}$ coincides with the $6^{\text{th}}$ dark band with wavelength $\lambda_{2}$,then the ratio $\left(\frac{\lambda_{2}}{\lambda_{1}}\right)$ is:

The two surfaces of a biconvex lens have the same radii of curvature. This lens is made of glass with a refractive index of $1.5$ and has a focal length of $10 ~cm$ in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index $=$ $4/3$),its focal length (in $cm$) is:

$A$ projectile is fired at a speed of $100 \, m/s$ at an angle of $37^\circ$ above the horizontal. At the highest point,the projectile breaks into two parts of mass ratio $1:3$,the smaller coming to rest. Then the distance of the heavier part from the launching point is ............... $m$.