The condition for the lines $lx + my + n = 0$ and $l_1x + m_1y + n_1 = 0$ to be conjugate with respect to the circle $x^2 + y^2 = r^2$ is

Compound $A$ $(C_3H_6O)$ undergoes the following reactions to form $B$ and $C$. Identify $A$,$B$,and $C$.

If ${x^p}{y^q} = {(x + y)^{p + q}},$ then $\frac{dy}{dx} = $

During cell division,sometimes there is a failure of separation of sister chromatids or homologous chromosomes. This event is called

The potential energy of a particle of mass $1\, kg$ in motion along the $x-$axis is given by $U = 4(1 - \cos 2x)$,where $x$ is in $meters$. The period of small oscillation (in $seconds$) is

One mole of $A_{(g)}$ is heated to $200^{\circ} C$ in a one litre closed flask,till the following equilibrium is reached.
$A_{(g)} \rightleftharpoons B_{(g)}$
The rate of forward reaction at equilibrium is $0.02 \ mol \ L^{-1} \ min^{-1}$. What is the rate (in $mol \ L^{-1} \ min^{-1}$) of the backward reaction at equilibrium?