In a quadrilateral $ABCD$,the point $P$ divides $DC$ in the ratio $1:2$ and $Q$ is the midpoint of $AC$. If $\overrightarrow{AB}+2\overrightarrow{AD}+\overrightarrow{BC}-2\overrightarrow{DC}=k\overrightarrow{PQ}$,then $k$ is equal to

As shown in the figure,charges $+q$ and $-q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

$A$ long straight wire carrying a current of $30 ~A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} ~T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 ~cm$ away from the wire is
$\left(\mu_0=4 \pi \times 10^{-7} ~H/m\right)$

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere in seconds is (acceleration due to gravity,$g = 10 \ m/s^2$). (in $\pi$)

$A$ circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$. What is its translational kinetic energy in $J$?

$A$ particle is projected from the ground with an initial speed of $v$ at an angle of projection $\theta$. The average velocity of the particle between its time of projection and the time it reaches the highest point of its trajectory is