JEE (Advanced) 2018 Paper-1

Based on the compounds of group 15 elements, the correct statement(s) is (are)

In the following reaction sequence, the correct structure(s) of X is (are)

The reaction(s) leading to the formation of 1, 3, 5-trimethylbenzene is (are)

A reversible cyclic process for an ideal gas is shown below. 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 options(s) is (are)

Among the species given below, the total number of diamagnetic species is ___
H atom , $$NO_{2}$$ manometer, $${O_{2}}^{-}$$ (superoxide),dimeric sulphur in vapour phase , $$Mn_{3}O_{4}, (NH_{4})_{2}[FeCl_{4}],(NH_{4})_{2}[NiCl_{4}],K_{2}MnO_{4}, K_{2}CrO_{4}$$

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

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
below. 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 $$\left(\frac{number of anions}{number of cations}\right)$$ in Z is ..........

For the electrochemical cell,
$$Mg(s) \mid Mg^{2+}$$ (aq,1M) $$\parallel Cu^{2+}$$ (aq,1M) $$\mid Cu(s)$$ the standard emf of the cell is 2.70 V at 300 K. When the concentration of $$Mg^{2+}$$ is changed to 𝒙 M, the cell potential changes to 2.67 V at 300 K. The value of 𝒙 is ____.
(given $$\frac{F}{R} = 11500 KV^{-1}$$, where F is the Faraday constant and 𝑅 is the gas constant, $$\ln(10) = 2.30)$$

A closed tank has two compartments A and B, both filled with oxygen (assumed to be 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 ____.

Liquids A and B form ideal solution over the entire range of composition. At temperature T, 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 vapour pressure of 22.5 Torr. The value of $$\frac{x_{A}}{x_{B}}$$ in the new solution is ____.
(given that the vapour pressure of pure liquid A is 20 Torr at temperature T)