$A$ renewable exhaustible natural resource is

If the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines,then the square of the distance of their point of intersection from the origin is

$A$ circle passes through the point $(3, 4)$ and cuts the circle $x^2 + y^2 = a^2$ orthogonally. The locus of its centre is a straight line. If the distance of this straight line from the origin is $25$,then $a^2$ is equal to

If $x$ is real,then the minimum value of $\frac{x^2-x+1}{x^2+x+1}$ is

Which of the following reagents would you use to separate $SO_4^{2-}$ ions from a solution containing a mixture of $SO_4^{2-}$ and $Cl^-$ ions?

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The initial temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of the air at $0^{\circ} C$ is (in $cm$ of $Hg$):