GATE & PSUs - Engineering Mathematics & General Aptitude (Common) previous year questions (PYQ)

2025 (42 questions)

Q1.

[Mean, Variance, Correlation & Linear Regression Concept 3] An unbiased coin is tossed 10 times independently. What is the probability of obtaining exactly 6 heads?

(A)

$\frac{105}{512} \approx 0.205$

(B)

$\frac{63}{256} \approx 0.246$

(C)

$\frac{1}{2}$

(D)

$\frac{15}{64} \approx 0.234$

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Q2.

[Verbal Ability (Grammar, Vocabulary, Sentence Completion, Reading Comprehension) Concept 22] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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2024 (84 questions)

Q1.

[Orthogonalization & Quadratic Forms Concept 4] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)

$22$ and $0$

(B)

$8$ and $1$

(C)

$27$ and $1$

(D)

$24$ and $2$

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Q2.

GATE Technical Standard: In computational modeling of 'Systems of Linear Equations (Consistency & Solutions) - Advanced Problem Solving', what constitutes the primary performance trade-off regarding asymptotic efficiency and resource conservation?

(A)

Minimizing peak algorithmic runtime and memory latency through optimal dynamic constraints (Systems of Linear Equations (Consistency & Solutions) - Advanced Problem Solving)

(B)

Maximizing redundant register transfers to force artificial synchronization

(C)

Arbitrary thread serialization without mutex coordination or race mitigation

(D)

Unbounded stack consumption with circular recursive invocation

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2023 (36 questions)

Q1.

[Numerical Integration (Trapezoidal, Simpson’s 1/3 and 3/8 Rules) Concept 8] Newton-Raphson method is used to find the root of $f(x) = x^2 - 7 = 0$ with initial guess $x_0 = 2.0$. What is the value of $x_1$ after the first iteration?

(A)

$2.75$

(B)

$2.50$

(C)

$2.64$

(D)

$3.00$

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Q2.

[Logical & Analytical Reasoning (Syllogisms, Blood Relations, Seating Arrangements) Concept 11] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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2022 (42 questions)

Q1.

[Eigenvalues & Eigenvectors (Cayley-Hamilton Theorem) Concept 19] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)

$22$ and $0$

(B)

$8$ and $1$

(C)

$27$ and $1$

(D)

$24$ and $2$

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Q2.

[Eigenvalues & Eigenvectors (Cayley-Hamilton Theorem) Concept 23] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)

$22$ and $0$

(B)

$8$ and $1$

(C)

$27$ and $1$

(D)

$24$ and $2$

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2021 (42 questions)

Q1.

[Numerical Computation & Data Interpretation (Percentages, Ratios, Speed & Work) Concept 5] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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Q2.

What is the value of $\lim_{x \to 0} \frac{x - \sin x}{x^3}$?

(A)

$\frac{1}{6}$

(B)

$0$

(C)

$\frac{1}{3}$

(D)

$\infty$

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2020 (42 questions)

Q1.

[Indeterminate Forms & L’Hôpital’s Rule Concept 12] What is the value of $\lim_{x \to 0} \frac{x - \sin x}{x^3}$?

(A)

$\frac{1}{6}$

(B)

$0$

(C)

$\frac{1}{3}$

(D)

$\infty$

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Q2.

[Hypothesis Testing & Confidence Intervals Concept 16] An unbiased coin is tossed 10 times independently. What is the probability of obtaining exactly 6 heads?

(A)

$\frac{105}{512} \approx 0.205$

(B)

$\frac{63}{256} \approx 0.246$

(C)

$\frac{1}{2}$

(D)

$\frac{15}{64} \approx 0.234$

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2019 (42 questions)

Q1.

[Partial Differential Equations (Heat, Wave & Laplace Equations) Concept 16] What is the general solution of the second-order ordinary differential equation $\frac{d^2 y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$?

(A)

$y(x) = (C_1 + C_2 x) e^{-2x}$

(B)

$y(x) = C_1 e^{-2x} + C_2 e^{2x}$

(C)

$y(x) = C_1 \cos(2x) + C_2 \sin(2x)$

(D)

$y(x) = C_1 e^{-4x} + C_2$

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Q2.

[Higher-Order Linear ODEs with Constant Coefficients Concept 2] What is the general solution of the second-order ordinary differential equation $\frac{d^2 y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$?

(A)

$y(x) = (C_1 + C_2 x) e^{-2x}$

(B)

$y(x) = C_1 e^{-2x} + C_2 e^{2x}$

(C)

$y(x) = C_1 \cos(2x) + C_2 \sin(2x)$

(D)

$y(x) = C_1 e^{-4x} + C_2$

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2018 (42 questions)

Q1.

[Maxima, Minima & Saddle Points of Multivariable Functions Concept 13] What is the value of $\lim_{x \to 0} \frac{x - \sin x}{x^3}$?

(A)

$\frac{1}{6}$

(B)

$0$

(C)

$\frac{1}{3}$

(D)

$\infty$

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Q2.

[Numerical Computation & Data Interpretation (Percentages, Ratios, Speed & Work) Concept 9] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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2017 (42 questions)

Q1.

[Numerical Computation & Data Interpretation (Percentages, Ratios, Speed & Work) Concept 13] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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Q2.

[Numerical Integration (Trapezoidal, Simpson’s 1/3 and 3/8 Rules) Concept 2] Newton-Raphson method is used to find the root of $f(x) = x^2 - 7 = 0$ with initial guess $x_0 = 2.0$. What is the value of $x_1$ after the first iteration?

(A)

$2.75$

(B)

$2.50$

(C)

$2.64$

(D)

$3.00$

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2016 (42 questions)

Q1.

[Random Variables & Probability Distributions (Binomial, Poisson, Normal, Exponential) Concept 6] An unbiased coin is tossed 10 times independently. What is the probability of obtaining exactly 6 heads?

(A)

$\frac{105}{512} \approx 0.205$

(B)

$\frac{63}{256} \approx 0.246$

(C)

$\frac{1}{2}$

(D)

$\frac{15}{64} \approx 0.234$

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Q2.

[Euler-Cauchy Equations & Method of Variation of Parameters Concept 3] What is the general solution of the second-order ordinary differential equation $\frac{d^2 y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$?

(A)

$y(x) = (C_1 + C_2 x) e^{-2x}$

(B)

$y(x) = C_1 e^{-2x} + C_2 e^{2x}$

(C)

$y(x) = C_1 \cos(2x) + C_2 \sin(2x)$

(D)

$y(x) = C_1 e^{-4x} + C_2$

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2015 (42 questions)

Q1.

[Numerical Computation & Data Interpretation (Percentages, Ratios, Speed & Work) Concept 21] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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Q2.

[Solutions of Non-linear Equations (Bisection, Regula-Falsi, Newton-Raphson) Concept 25] Newton-Raphson method is used to find the root of $f(x) = x^2 - 7 = 0$ with initial guess $x_0 = 2.0$. What is the value of $x_1$ after the first iteration?

(A)

$2.75$

(B)

$2.50$

(C)

$2.64$

(D)

$3.00$

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