If $f(x)=|x|+|sin x|$ for $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$,then its left hand derivative at $x=0$ is

$A$ positively charged $(+q)$ particle of mass $m$ has kinetic energy $K$ and enters a region with a horizontal magnetic field of induction $\vec{B}$ in a vertically downward direction. The acceleration of the particle is:

When a metallic surface is illuminated with radiation of wavelength $\lambda$,the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2\lambda$,the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is:

If a change in current of $0.01 ~A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} ~Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $~H$)

If the function $y = \sin^{-1} x$,then $(1 - x^2) \frac{d^2 y}{d x^2}$ is equal to

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$