GATE CY format:nat PYQs & Answers — Page 5

Questions 41–50 of 166. Imported answers require independent review unless marked reviewed.

Topic practice 166 questionsPage 5 of 17

The wave function of a particle in a cubic box (of side

) is given by

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)

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and

are normalized eigenfunctions of a Hermitian operator.

and

The value of

is __.

(rounded off to the nearest integer)

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2 mol of a monatomic 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)

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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)

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The calculated magnetic moment of

is ______ BM. (rounded off to two decimal places)

(Given: atomic number of Ce is 58)

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The enthalpy change for the exothermic reaction between BeI₂ and HgF₂ is ______ kJ mol⁻¹ (rounded off to the nearest integer)

(Given: Bond dissociation energy (in kJ mol⁻¹) for Be–F = 632, Be–I = 289, Hg–F = 268 and Hg–I = 145)

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Number of carbon atoms connected to the metal center in [W(C₆₀)(CO)₅] is ______ (rounded off to the nearest integer)

(Given: atomic number of W is 74)

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Two-component solid-liquid system of naphthalene-benzene forms a simple eutectic mixture. Assuming that naphthalene-benzene forms an ideal solution, the mole fraction of naphthalene in benzene at 300 K and 1 bar is ______ (rounded off to two decimal places)

(Given: Freezing point (T₍fp₎) and enthalpy of fusion (ΔH₍fus₎) of naphthalene are 353 K and 19.28 kJ mol⁻¹, respectively and gas constant (R) = 8.31 J K⁻¹ mol⁻¹)

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The intrinsic viscosity of a sample of polystyrene in toluene is 84 cm³ g⁻¹ at 30 °C. It follows Mark-Houwink equation with empirical constant values of K = 1.05 × 10⁻² cm³ g⁻¹ and a = 0.75. The molecular weight of the polymer is ______ × 10³ g mol⁻¹ (rounded off to the nearest integer)

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According to Debye-Hückel limiting law, the mean molal activity coefficient for 0.87 g K₂SO₄ (molar mass = 174 g mol⁻¹) in 1 kg of water at 25 °C is ______ (rounded off to two decimal places)

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GATE CY format:nat PYQs

Question 62

Question 63

Question 64

Question 65

Question 35

Question 58

Question 59

Question 60

Question 61

Question 62