The solution of the differential equation $\frac{d \theta}{d t}=-k\left(\theta-\theta_0\right)$ where $k$ is constant, is .............

A metal surface is illuminated by light of given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one fourth of its original value then the maximum KE of the emitted photoelectrons would be

Torque acting on a rectangular coil carrying current ' $l$ ' situated parallel to magnetic field of induction ' $B$ ', having number of turns ' $n$ ' and area ' $A$ ' is

A force $(F)=-5 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ acting on a particle causes a displacement $(s)=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ in its own direction. If the work done is 14 J , then the value of ' $a$ ' is