Pure ammonia is placed in a vessel at a temperature where its dissociation constant $(\alpha)$ is appreciable. At equilibrium,

Three rods $AB$,$BC$,and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$,$C$,and $D$ are held at temperatures of $20^{\circ}C$,$80^{\circ}C$,and $80^{\circ}C$ respectively. If each rod is of the same length,then the temperature at the junction $B$ of the three rods is: (in $^{\circ}C$)

The osmotic pressure of equimolar solutions of $BaCl_2, NaCl$ and glucose at the same temperature follows the order:

$2 \tanh^{-1} \frac{1}{2}$ is equal to

The logical statement $(\sim(\sim p \vee q) \vee(p \wedge r)) \wedge(\sim q \wedge r)$ is equivalent to

If the line $y=mx$ is one of the bisectors of $x^2+4xy-y^2=0$,then the value of $2m$ is: