If an electric heater is rated at $1000\, W$,then the time required to heat one litre of water from $20\, ^oC$ to $60\, ^oC$ is

If $x=a\left[\cos \theta+\log \left\{\tan \left(\frac{\theta}{2}\right)\right\}\right]$ and $y=a \sin \theta$,then $\frac{dy}{dx}$ is equal to

When $KMnO_4$ solution is added to hot oxalic acid solution,the decolourisation is slow in the beginning but becomes instantaneous after some time. This is because

The curve given by $x + y = e^{xy}$ has a tangent parallel to the $y$-axis at the point

Data Entry - Physics

Two adjacent sides of a parallelogram $ABCD$ are given by $\overline{AB}=2 \hat{i}+10 \hat{j}+11 \hat{k}$ and $\overline{AD}=-\hat{i}+2 \hat{j}+2 \hat{k}$. The side $AD$ is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that $AD$ becomes $AD^{\prime}$. If $AD^{\prime}$ makes a right angle with side $AB$,then the cosine of the angle $\alpha$ is given by