$A$ plane passes through the point $A(2, 1, -3)$. If the distance of this plane from the origin is maximum,then its equation is:

Which of the following compounds is both paramagnetic and colored?

Consider the statements given below regarding contraception and answer as directed thereafter:
$(1)$ Medical Termination of Pregnancy $(MTP)$ during the first trimester is generally safe.
$(2)$ Generally,chances of conception are nil until the mother breast-feeds the infant up to two years.
$(3)$ Intrauterine devices like Copper-$T$ are effective contraceptives.
$(4)$ Contraception pills may be taken up to one week after coitus to prevent conception.
Which two of the above statements are correct?

$A$ heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The ratio of radii of the fragments is

If $\alpha, \beta, \gamma$ are the roots of $2x^3 - 2x - 1 = 0$,then $(\Sigma \alpha \beta)^2$ is equal to

Two insulated metallic spheres of $3\,\mu F$ and $5\,\mu F$ capacitances are charged to $300\,V$ and $500\,V$ respectively. The energy loss,when they are connected by a wire is (in $,J$)