IIT JAM & CSIR NET - Chemical Sciences previous year questions (PYQ)

2026 (30300 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #203] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n + 1/2) ħ ω

(B)

E_n = ħ^2 k^2 / (4 m L)

(C)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(D)

E_n = (n^2 ħ^2) / (8 m L^2)

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Q2.

[Inorganic Chemistry & Coordination Compounds Problem #344] Regarding Cauchy-Riemann equations for an analytic function f(z) = u(x,y) + i v(x,y): Which of the following analytical formulations is correct?

(A)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(B)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(C)

∂u/∂x + ∂v/∂y = 0 and ∂u/∂y + ∂v/∂x = 0

(D)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

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2025 (72 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #197] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(B)

E_n = (n + 1/2) ħ ω

(C)

E_n = ħ^2 k^2 / (4 m L)

(D)

E_n = (n^2 ħ^2) / (8 m L^2)

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #116] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = ħ^2 k^2 / (4 m L)

(B)

E_n = (n + 1/2) ħ ω

(C)

E_n = (n^2 ħ^2) / (8 m L^2)

(D)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

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2024 (100 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #487] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = ħ^2 k^2 / (4 m L)

(B)

E_n = (n^2 ħ^2) / (8 m L^2)

(C)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(D)

E_n = (n + 1/2) ħ ω

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #316] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(B)

H = T - V representing the total potential Lagrangian

(C)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(D)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

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2023 (72 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #284] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(B)

H = T - V representing the total potential Lagrangian

(C)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

(D)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #217] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

(B)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(C)

H = T - V representing the total potential Lagrangian

(D)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

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2022 (72 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #183] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(B)

H = T - V representing the total potential Lagrangian

(C)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

(D)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #462] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

H = T - V representing the total potential Lagrangian

(B)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(C)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(D)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

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2021 (72 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #450] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n + 1/2) ħ ω

(B)

E_n = ħ^2 k^2 / (4 m L)

(C)

E_n = (n^2 ħ^2) / (8 m L^2)

(D)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #435] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(B)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(C)

H = T - V representing the total potential Lagrangian

(D)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

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2020 (72 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #342] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 ħ^2) / (8 m L^2)

(B)

E_n = ħ^2 k^2 / (4 m L)

(C)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(D)

E_n = (n + 1/2) ħ ω

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #323] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(B)

H = T - V representing the total potential Lagrangian

(C)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(D)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

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2019 (72 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #280] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(B)

E_n = ħ^2 k^2 / (4 m L)

(C)

E_n = (n^2 ħ^2) / (8 m L^2)

(D)

E_n = (n + 1/2) ħ ω

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #291] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 ħ^2) / (8 m L^2)

(B)

E_n = (n + 1/2) ħ ω

(C)

E_n = ħ^2 k^2 / (4 m L)

(D)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

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2018 (74 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #279] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(B)

H = T - V representing the total potential Lagrangian

(C)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(D)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #432] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 ħ^2) / (8 m L^2)

(B)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(C)

E_n = ħ^2 k^2 / (4 m L)

(D)

E_n = (n + 1/2) ħ ω

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2017 (74 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #339] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

H = T - V representing the total potential Lagrangian

(B)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(C)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

(D)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #229] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 ħ^2) / (8 m L^2)

(B)

E_n = ħ^2 k^2 / (4 m L)

(C)

E_n = (n + 1/2) ħ ω

(D)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

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2016 (74 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #441] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

(B)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(C)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(D)

H = T - V representing the total potential Lagrangian

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #406] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = (n^2 ħ^2) / (8 m L^2)

(B)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(C)

E_n = ħ^2 k^2 / (4 m L)

(D)

E_n = (n + 1/2) ħ ω

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2015 (74 questions)

Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #387] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(B)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

(C)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(D)

H = T - V representing the total potential Lagrangian

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #427] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = ħ^2 k^2 / (4 m L)

(B)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(C)

E_n = (n^2 ħ^2) / (8 m L^2)

(D)

E_n = (n + 1/2) ħ ω

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