The number of possible enantiomeric pairs that can be produced on monochlorination of $2$-methylbutane is

The distance between the parallel lines given by $(x+7y)^2 + 4\sqrt{2}(x+7y) - 42 = 0$ is

The sensitivity of a galvanometer that measures current is decreased by $\frac{1}{40}$ times by using a shunt resistance of $10 \Omega$. Then,the value of the resistance of the galvanometer is (in $\Omega$)

Two stars of masses $M$ and $2M$ are at a distance $d$ apart and are revolving around their common center of mass. The angular velocity of the system of two stars is ($G$ is the universal gravitational constant):

The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,and $x + y + z = 0$ has a non-zero solution is:

Two circular coils $X$ and $Y$,having an equal number of turns,carry equal currents in the same sense and subtend the same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$,and if we represent the magnetic induction due to the bigger coil $Y$ at $O$ as $B_Y$ and that due to the smaller coil $X$ at $O$ as $B_X$,then $\frac{B_Y}{B_X}$ is