If solubility product of Zr₃(PO₄)₄ is denoted by K_sp and its molar solubility is denoted by S, then which of the following relation between S and K_sp is correct ?

• S = ${\left(\frac{{\mathrm{K}}_{\mathrm{sp}}}{6912}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}$

• S = ${\left(\frac{{\mathrm{K}}_{\mathrm{SP}}}{929}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.}$

• S = ${\left(\frac{{\mathrm{K}}_{\mathrm{sp}}}{144}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$

• S = ${\left(\frac{{\mathrm{K}}_{\mathrm{sp}}}{216}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}$

The quantum number of four electrons are given below:

The correct order of these increasing energies will be:

• IV > III > II > I

• I > II > III > IV

• I > III > II > IV

• IV > II > III > I

For silver, C_P( K^-1 mol^-1) = 23 + 0.01T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of $∆$H will be close to :

• 21 kJ

• 62 kJ

• 16 kJ

• 13 kJ

The correct order of the spin only magnetic moment of metal ions in the following low spin complexes, [V(CN)₆]^4-, [Fe(CN)₆]^4-, [Ru(NH₃)₆]³⁺ and [Cr(NH₃)₆]²⁺ is

• V²⁺  > Cr²⁺ > Ru³⁺ > Fe²⁺

• V²⁺ > Ru³⁺ > Cr²⁺ > Fe²⁺

• Cr²⁺ > V²⁺ > Ru³⁺ > Fe²⁺

• Cr²⁺ > Ru³⁺ > Fe²⁺ > V²⁺

In order to oxidise a mixture of one mole of each of FeC₂O₄, Fe₂(C₂O₄)₃, FeSO₄ and Fe₂(SO₄)₃ in acidic medium, the number of moles of KMnO₄ required is:

• 1.5

• 3

• 2

• 1

In the following compounds, the decreasing order of basic strength will be:

• (C₂H₅)₂NH > NH₃ > C₂H₅NH₂

• (C₂H₅)₂NH > C₂H₅NH₂ > NH₃

• C₂H₅NH₂ > NH₃ > (C₂H₅)₂NH

• NH₃ > C₂H₅NH₂ > (C₂H₅)₂NH

The vapour pressures of pure liquids A and B are 400 and 600 mm Hg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are:

• 500 mm Hg, 0.4, 0.6

• 450 mm Hg, 0.4, 0.6

• 500 mm Hg, 0.5, 0.5

• 450 mm Hg, 0.5, 0.5

The size of the iso-electronic species Cl^-, Ar and Ca²⁺ is affected by:

• nuclear charge

• Prinicpal quantum number of valence shell

• azimuthal quantum number of valence shell

• electron-electron interaction in the outer orbitals

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)

• Isothermal process : q = -w

• Cyclic process : q = -w

• Isochoric process : $∆\mathrm{U}$ = q

• Adiabatic process : $∆\mathrm{U}$ = -w

Diborane (B₂H₆) reacts independently with O₂ and H₂O to produce, respectively:

• B₂O₃ and H₃BO₃

• H₃BO₃ and B₂O₃

• B₂O₃ and [BH₄]^-

• HBO₂ and H₃BO₃