List of top Questions asked in GATE CY

The ground state of [Cr(H₂O)₆]²⁺ is

The correct statement(s) about ⁴D_5/2 state of an atom is (are) :

In the EPR spectrum of an aqueous solution of VOSO₄ at room temperature, the total number of hyperfine splitting signals is

In aqueous solution of K₄[Fe(CN)₆], the allowed transition(s) is (are)

The molecule XY₂ is microwave active and its vibration-rotation spectrum shows only P and R transitions. In the correct structure,

The order and the number of classes present in a group with the irreducible representations A₁, A₂, B₁, B₂, E₁, and E₂, are, respectively,

In thermogravimetric analysis, 12.45 mg of CuSO₄.5H₂O was subjected to heating under N₂ atmosphere. At a particular temperature, there was a weight loss of 3.6 mg. The number of water molecule(s) lost per formula unit is _____.
(Given molar mass (in g mol^-1) of H = 1.0, O = 16.0, S = 32.0, and Cu = 63.5)
(rounded off to the nearest integer)

The partial vapor pressure of 0.1 molal solution of B in liquid A is 60 kPa at 300 K. The partial vapor pressure (in kPa) of a solution containing B with mole fraction of 0.1 in liquid A at 300 K is ______.
(Assume the solute B obeys Henry's law. The molar mass of A is 80 g mol^-1.)
(rounded off to three decimal places)

¹H NMR spectrum of a mixture containing CH₃Br (x mol) and (CH₃)₃CBr (y mol) shows two singlets at 2.7 ppm and 1.8 ppm, with the relative ratio of 3:1 (integration value), respectively. The value of x/y is ______.
(rounded off to the nearest integer)

Critical micellar concentration of a surfactant is 0.008 M in water at 25 °C. If the aggregation number of the micelles is 80, the concentration of the micelles (in M) present in 0.088 M aqueous solution of the surfactant at 25 °C is

The reaction(s) that yield(s) X as the major product is (are)

2 mol of a monoatomic ideal gas with initial volume of 5 L and pressure 10 bar undergoes an irreversible adiabatic expansion against a constant final pressure of 1 bar. The final volume (in L) is _______.
(Given: R = 8.314 × 10^-2 L bar mol^-1 K^-1)
(rounded off to one decimal place)

Consider the following ¹H-NMR (400 MHz, DMSO-d₆) data of a compound :
δ in ppm: 3.85 (s, 6H), 6.73 (t, J = 2.2 Hz, 1H), 7.1 (d, J = 2.2 Hz, 2H), and 13.05 (brs, 1H).
The compound is

The following figure shows an experimental liquid-liquid phase diagram of phenol and water at the vapor pressure of the system. The total amount of phenol and water (in mol) present in the phenol-rich phase when 5 mol of water was shaken with 5 mol of phenol at 40 °C is _______.

(rounded off to one decimal place)

In the given reaction sequence, the amount of R produced (in g) is ______.

(Given: molar mass (in g mol^-1) of H = 1, C = 12, N = 14, O = 16, and S = 32)
(rounded off to two decimal places)

The correct statement(s) related to an ensemble is (are) :

The reaction of XeF₂ with HN(SO₂F)₂ at 273 K in CF₂Cl₂ solvent yields

Φ₁ and Φ₂ are normalised eigenfunctions of a Hermitian operator.
|Ψ〉 = 3i |Φ₁〉 + 2|Φ₂〉 and |X〉 = -2i |Φ₁〉 + 5 |Φ₂〉
The value of 〈Ψ|X〉 + 〈X|Ψ〉 is _______.
(rounded off to the nearest integer)

The wave function of a particle in a cubic box (of side L) is given by
\(\psi(x,y,z)=\sqrt{32/L^3}\sin\frac{\pi x}{L}\cos\frac{\pi x}{L}\sin\frac{2\pi y}{L}\sin\frac{\pi z}{L.}\).
The ratio of the energy of the state corresponding to the above wave function to the ground state energy is ________.
(rounded off to the nearest integer)

The turnover frequency (in h^-1) of a reaction where 5 mol% of a catalyst is required for 90% conversion in 3 h is ______.
(rounded off to the nearest integer)

Among the following, the correct statement(s) is (are) :

Among the following, the correct statement(s) is (are) :

ΔS° (in J mol^-1 K^-1) for the given reaction at 298 K is ________.
[Cu(H₂O)6]²⁺ + en ⇌ [Cu(H₂O)₄(en)]²⁺ + 2H₂O
(Given: log K₁ = 10.6, where K₁ is the equilibrium constant. ΔH° =-54 kJ mol^-1 and R = 8.314 J mol^-1 K^-1)
(rounded off to two decimal places)

The correct statement(s) about the relationship for the H-atoms in the following compounds is (are) :

The correct statement(s) regarding P, Q, R, and S is (are) :