If the pair of lines $ax^2-7xy-3y^2=0$ and $2x^2+xy-6y^2=0$ have exactly one line in common and $a$ is an integer,then the equation of the pair of bisectors of the angles between the lines $ax^2-7xy-3y^2=0$ is

Which of the following is a Dobereiner's triad?

If $x^2+y^2=t+\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $x^3 y \frac{d y}{d x}$ is equal to

Which substance is used as a smoke screen in warfare?

The potential energy for a force field $\vec{F}$ is given by $U(x, y) = \cos(x + y)$. The force acting on a particle at the position given by coordinates $(0, \pi/4)$ is:

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 angle $\alpha$ in the plane of the parallelogram so that $AD$ becomes $AD^{\prime}$. If $AD^{\prime}$ makes a right angle with the side $AB$,then the cosine of the angle $\alpha$ is given by