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

2026 (30300 questions)

Q1.

[Cell Biology, Genetics & Molecular Biology Problem #275] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Cell Biology, Genetics & Molecular Biology Problem #422] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2025 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #411] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #168] 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 and ∂u/∂y = -∂v/∂x

(D)

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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2024 (104 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #167] 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)

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

(D)

The matrix cannot be diagonalized under any orthogonal transformation

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

Higher Academic Core: In advanced conceptual study of 'G-Protein Coupled Receptors and Second Messenger Cascades' in Cell Structure & Signal Transduction, which foundational mechanism is universally verified?

(A)

Empirically validated biological, physical, or social dynamics following standard scientific methodology (G-Protein Coupled Receptors and Second Messenger Cascades)

(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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2023 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #208] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2022 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #271] 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)

The matrix cannot be diagonalized under any orthogonal transformation

(D)

Eigenvalues must always be positive integers

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #282] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2021 (72 questions)

Q1.

[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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #206] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2020 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #313] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #313] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2019 (72 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #193] 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 and ∂u/∂y = -∂v/∂x

(D)

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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #123] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2018 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #333] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #133] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2017 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #403] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #299] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2016 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #309] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #131] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

2015 (74 questions)

Q1.

[Ecology, Evolution & Biostatistics Problem #97] 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

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view

Q2.

[Ecology, Evolution & Biostatistics Problem #180] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)

Eigenvalues must always be positive integers

(B)

The matrix cannot be diagonalized under any orthogonal transformation

(C)

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

(D)

All eigenvalues are pure imaginary

Show answer & solution

Verified Answer & Solution Locked

Sign in to your free student account to reveal verified answers and step-by-step solutions.

Sign in to view