The vapour pressure in $mm$ of $Hg$,of an aqueous solution obtained by adding $18 \ g$ of glucose $(C_6H_{12}O_6)$ to $180 \ g$ of water at $100^{\circ} C$ is

If $f(x) = \frac{x}{1+|x|}$, for $x \in \mathbb{R}$, then $f^{\prime}(0)$ is equal to :

An unbiased coin is tossed to get $2$ points for turning up a head and $1$ point for the tail. If three unbiased coins are tossed simultaneously,then the probability of getting a total of an odd number of points is

$A$ baby has been born with a small tail. It is a case exhibiting:

$SiCl_4$ on hydrolysis forms '$X$' and $HCl$. Compound '$X$' loses water at $1000^\circ C$ and gives '$Y$'. Compounds '$X$' and '$Y$' respectively are:

Two tangent galvanometers $A$ and $B$ have coils of radii $8 \, cm$ and $16 \, cm$ respectively and resistance $8 \, \Omega$ each. They are connected in parallel with a cell of emf $4 \, V$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30°$ and $60°$ respectively. If $A$ has $2$ turns, then $B$ must have: (in $turns$)