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

2026 (30300 questions)

Q1.

[Biochemistry & Plant/Animal Physiology Problem #6] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(D)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

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Q2.

[Biochemistry & Plant/Animal Physiology Problem #8] 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)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(D)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

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2025 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #318] 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.

[Ecology, Evolution & Biostatistics Problem #188] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(C)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

(D)

∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x

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2024 (104 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #443] 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 strictly real, and eigenvectors from distinct eigenvalues are orthogonal

(C)

All eigenvalues are pure imaginary

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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Q2.

Higher Academic Core: In advanced conceptual study of 'Phytohormones Auxin Cytokinin Gibberellin Signaling' in Plant & Animal System Physiology, which foundational mechanism is universally verified?

(A)

Empirically validated biological, physical, or social dynamics following standard scientific methodology (Phytohormones Auxin Cytokinin Gibberellin Signaling)

(B)

Unsubstantiated speculative claims lacking experimental replication or peer verification

(C)

Deterministic models that reject thermodynamic entropy and stochastic variance

(D)

Isolated observations taken under non-standard uncontrolled environmental extremes

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2023 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #283] 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.

[Ecology, Evolution & Biostatistics Problem #327] 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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2022 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #463] 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)

Eigenvalues must always be positive integers

(C)

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

(D)

All eigenvalues are pure imaginary

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Q2.

[Ecology, Evolution & Biostatistics Problem #104] 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)

All eigenvalues are pure imaginary

(D)

Eigenvalues must always be positive integers

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2021 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #473] 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)

Eigenvalues must always be positive integers

(C)

All eigenvalues are pure imaginary

(D)

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

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Q2.

[Ecology, Evolution & Biostatistics Problem #92] 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)

Eigenvalues must always be positive integers

(D)

All eigenvalues are pure imaginary

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2020 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #428] 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.

[Ecology, Evolution & Biostatistics Problem #439] 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 = 0 and ∂u/∂y + ∂v/∂x = 0

(D)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

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2019 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #301] 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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Q2.

[Ecology, Evolution & Biostatistics Problem #112] 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)

∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly

(D)

∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x

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2018 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #122] 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.

[Ecology, Evolution & Biostatistics Problem #289] 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)

Eigenvalues must always be positive integers

(C)

All eigenvalues are pure imaginary

(D)

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

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2017 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #110] 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.

[Ecology, Evolution & Biostatistics Problem #332] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are pure imaginary

(B)

Eigenvalues must always be positive integers

(C)

The matrix cannot be diagonalized under any orthogonal transformation

(D)

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

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2016 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #276] 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)

Eigenvalues must always be positive integers

(D)

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

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Q2.

[Ecology, Evolution & Biostatistics Problem #342] 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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2015 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #297] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are pure imaginary

(B)

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

(C)

Eigenvalues must always be positive integers

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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Q2.

[Ecology, Evolution & Biostatistics Problem #478] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

All eigenvalues are pure imaginary

(B)

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

(C)

Eigenvalues must always be positive integers

(D)

The matrix cannot be diagonalized under any orthogonal transformation

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