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

2026 (30300 questions)

Q1.

[Quantum Mechanics & Statistical Physics Problem #285] 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)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(B)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(C)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(D)

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

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Q2.

[Quantum Mechanics & Statistical Physics Problem #27] 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)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(C)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(D)

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

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2025 (72 questions)

Q1.

[Solid State Physics & Electronics Problem #486] 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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Q2.

[Solid State Physics & Electronics Problem #223] 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)

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

(C)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(D)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

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2024 (98 questions)

Q1.

[Solid State Physics & Electronics Problem #155] 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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Q2.

[Solid State Physics & Electronics Problem #379] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

The matrix cannot be diagonalized under any orthogonal transformation

(B)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(C)

Eigenvalues must always be positive integers

(D)

All eigenvalues are pure imaginary

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2023 (72 questions)

Q1.

[Solid State Physics & Electronics Problem #389] 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)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(C)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(D)

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

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Q2.

[Solid State Physics & Electronics Problem #465] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

Eigenvalues must always be positive integers

(C)

The matrix cannot be diagonalized under any orthogonal transformation

(D)

All eigenvalues are pure imaginary

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2022 (72 questions)

Q1.

[Solid State Physics & Electronics Problem #433] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(B)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(C)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(D)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

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Q2.

[Solid State Physics & Electronics Problem #433] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(B)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(C)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(D)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

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2021 (72 questions)

Q1.

[Solid State Physics & Electronics 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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Q2.

[Solid State Physics & Electronics Problem #493] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

Eigenvalues must always be positive integers

(C)

The matrix cannot be diagonalized under any orthogonal transformation

(D)

All eigenvalues are pure imaginary

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2020 (72 questions)

Q1.

[Solid State Physics & Electronics Problem #318] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

Eigenvalues must always be positive integers

(C)

The matrix cannot be diagonalized under any orthogonal transformation

(D)

All eigenvalues are pure imaginary

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Q2.

[Solid State Physics & Electronics Problem #89] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(B)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(C)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(D)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

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2019 (72 questions)

Q1.

[Solid State Physics & Electronics Problem #430] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(B)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(C)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(D)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

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Q2.

[Solid State Physics & Electronics Problem #419] 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)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(C)

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

(D)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

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2018 (74 questions)

Q1.

[Solid State Physics & Electronics Problem #377] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

Eigenvalues must always be positive integers

(B)

All eigenvalues are pure imaginary

(C)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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Q2.

[Solid State Physics & Electronics Problem #338] 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)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(C)

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

(D)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

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2017 (74 questions)

Q1.

[Solid State Physics & Electronics Problem #237] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

All eigenvalues are pure imaginary

(C)

Eigenvalues must always be positive integers

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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Q2.

[Solid State Physics & Electronics Problem #459] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

All eigenvalues are pure imaginary

(C)

The matrix cannot be diagonalized under any orthogonal transformation

(D)

Eigenvalues must always be positive integers

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2016 (74 questions)

Q1.

[Solid State Physics & Electronics Problem #178] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

Eigenvalues must always be positive integers

(C)

All eigenvalues are pure imaginary

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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Q2.

[Solid State Physics & Electronics Problem #145] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are pure imaginary

(B)

The matrix cannot be diagonalized under any orthogonal transformation

(C)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(D)

Eigenvalues must always be positive integers

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2015 (74 questions)

Q1.

[Solid State Physics & Electronics Problem #403] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(B)

The matrix cannot be diagonalized under any orthogonal transformation

(C)

All eigenvalues are pure imaginary

(D)

Eigenvalues must always be positive integers

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Q2.

[Solid State Physics & Electronics Problem #118] 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)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

(C)

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

(D)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

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