Q. Liquids $A$ and $B$ form ideal solution over the entire range of composition. At temperature, $T$, an equimolar binary solution of liquids $A$ and $B$ has vapour pressure $45$ Torr. At the same temperature, a new solution of $A$ and $B$ having mole fractions $X_A$ and $X_B$, respectively, has a vapour pressure of $22.5$ Torr. The value of $X_A/X_B$ in the new solution is __________.

Q. Consider an ionic solid $MX$ with $NaCl$ structure. Construct a new structure($Z$) whose unit cell is constructed from the unit cell of $MX$ following the sequential instructions given. Neglect the charge balance.
(i) Remove all the anions($X$) except the central one.
(ii) Replace all the face centered cations($M$) by anions($X$).
(iii) Remove all the corner cations($M$).
(iv) Replace the central anion($X$) with cation($M$).
The value of $\left(\frac{numberofanions}{numberofcations}\right)$ in $Z$ is ___________.

Q. The compound(s) which generate(s) $N_2$ gas upon thermal decomposition below ${300}^o$C is/are:

1. $N{H}_{4}N{O}_3$
2. $(N{H}_4{)}_{2}C{r}_2{O}_7$
3. $Ba(N_3{)}_2$
4. $M{g}_3{N}_2$

Q. A reversible cyclic process for an ideal gas is shown. Here, P, V and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.
The correct option(s) is/are?

1. $q_{AC}=\Delta U_{BC}$ and $w_{AB}=P_2(V_2-V_1)$
2. $w_{BC}=P_2(V_2-V_1)$ and $q_{BC}=\Delta H_{AC}$
3. $\Delta H_{CA}<\Delta U_{CA}$ and $q_{AC}=\Delta U_{BC}$
4. $q_{BC}=\Delta H_{AC}$ and $\Delta H_{CA}>\Delta U_{CA}$

Q. A closed tank has two compartments A and B, both filled with oxygen(assumed to be an ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator(Figure $1$). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across(Figure $2$), the volume(in $m^3$) of the compartment A after the system attains equilibrium is _________.

Q. In the following reaction sequence, the correct structure(s) of $X$ is/are:

1. 
   
2. 
   
3. 
   
4. 
   

Q. The correct statement(s) regarding the binary transition metal carbonyl compounds is/are:

1. Total number of valence shell electrons at metal centre in $Fe(CO{)}_5$ or $Ni(CO{)}_4$ is $16$.
2. These are predominantly low spin in nature.
3. Metal-carbon bond strengthens when the oxidation state of the metal is lowered.
4. The carbonyl $C-O$ bond weakens when the oxidation state of the metal is increased.

Q. For the electrochemical cell, $Mg\left(s\right)|M{g}^{2+}(aq.1M)||C{u}^{2+}(aq,1M)|Cu\left(s\right)$ the standard emf of the cell is $2.70$V at $300$K. When the concentration of $M{g}^{2+}$ is changed to $x$ M, the cell potential changes to $2.67$V at $300$K. The value of $x$ is _________.

Q. Among the species given, the total number of diamagnetic species is __________.

Q. The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by $NiC{l}_2\cdot 6H_{2}O$ to form a stable coordination compound. Assume that both the reactions are $100\%$ complete. If $1584$g of ammonium sulphate and $952$g of $NiC{l}_2\cdot 6H_{2}O$ are used in the preparation, the combined weight(in grams) of gypsum and the nickel-ammonia coordination compound thus produced is _________.
(Atomic weights in $gmo{l}^{-1}:H=1,N=14,O=16,S=32,Cl=35.5,Ca=40,Ni=59$)

Q. The reaction(s) leading to the formation of $1,3,5$-trimethylbenzene is/are:

1. 
   
2. 
   
3. 
   
4. 
   

Q. Based on the compounds of group $15$ elements, the correct statement(s) is/are:

1. $N{F}_3$ is more covalent than $Bi{F}_3$.
2. $B{i}_2{O}_5$ is more basic than $N_2{O}_5$.
3. $P{H}_3$ boils at lower temperature than $N{H}_3$.
4. The $N-N$ single bond is stronger than the $P-P$ single bond.