Engineering & entrance exams

GATE & PSUs - Mechanical Engineering (ME) previous year questions (PYQ)

516 previous year GATE & PSUs - Mechanical Engineering (ME) questions, grouped by year, with answers and solutions.

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2025 (42 questions)

Q1.
[Metrology & Limits, Fits, Tolerances Concept 11] 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.
[Casting Solidification & Riser Design (Chvorinov) Concept 7] 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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2024 (102 questions)

Q1.

Engineering Analysis & Principles: In technical analysis of 'Columns & Euler Buckling - Advanced Problem Solving' within Columns & Euler Buckling, which governing relationship or mathematical model determines optimal system response under equilibrium conditions?

(A)

First-order linear differential operator with boundary conditions matching system eigenvalues (Columns & Euler Buckling - Advanced Problem Solving)

(B)

Zero-order static algebraic summation neglecting non-linear feedback

(C)

Unconstrained stochastic random walk without conservation criteria

(D)

Non-convergent divergence theorem with unbounded parameter drift

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Q2.

GATE Technical Standard: In computational modeling of 'Columns & Euler Buckling - 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 (Columns & Euler Buckling - 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.
[Welding Processes & Heat Input Concept 4] 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.
[Free, Damped & Forced Vibrations (Single DOF) Concept 4] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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2022 (42 questions)

Q1.
[Mohr’s Circle & Principal Stresses Concept 8] A simply supported beam of length $L$ carries a concentrated point load $W$ at its mid-span. What is the maximum bending moment and maximum downward deflection $\delta_{\max}$ of the beam (flexural rigidity $EI$)?

(A)
$M_{\max} = \frac{WL}{4}, \quad \delta_{\max} = \frac{WL^3}{48EI}$
(B)
$M_{\max} = \frac{WL}{8}, \quad \delta_{\max} = \frac{5WL^3}{384EI}$
(C)
$M_{\max} = \frac{WL}{2}, \quad \delta_{\max} = \frac{WL^3}{24EI}$
(D)
$M_{\max} = WL, \quad \delta_{\max} = \frac{WL^3}{3EI}$
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Q2.
[Bending & Torsional Stresses Concept 4] A simply supported beam of length $L$ carries a concentrated point load $W$ at its mid-span. What is the maximum bending moment and maximum downward deflection $\delta_{\max}$ of the beam (flexural rigidity $EI$)?

(A)
$M_{\max} = \frac{WL}{4}, \quad \delta_{\max} = \frac{WL^3}{48EI}$
(B)
$M_{\max} = \frac{WL}{8}, \quad \delta_{\max} = \frac{5WL^3}{384EI}$
(C)
$M_{\max} = \frac{WL}{2}, \quad \delta_{\max} = \frac{WL^3}{24EI}$
(D)
$M_{\max} = WL, \quad \delta_{\max} = \frac{WL^3}{3EI}$
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2021 (42 questions)

Q1.
[Balancing of Rotating & Reciprocating Masses Concept 5] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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Q2.
[Fins & Extended Surfaces Concept 12] A solid metal sphere of radius $R_1$ with uniform internal heat generation $q_g\text{ (W/m}^3\text{)}$ has thermal conductivity $k$. What is the temperature distribution $T(r)$ within the sphere if the surface temperature is maintained at $T_s$?

(A)
$T(r) = T_s + \frac{q_g}{6k} (R_1^2 - r^2)$
(B)
$T(r) = T_s + \frac{q_g}{4k} (R_1^2 - r^2)$
(C)
$T(r) = T_s + \frac{q_g}{2k} (R_1^2 - r^2)$
(D)
$T(r) = T_s + \frac{q_g}{3k} (R_1 - r)$
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2020 (42 questions)

Q1.
[Balancing of Rotating & Reciprocating Masses Concept 20] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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Q2.
[Boundary Layer Theory & Drag/Lift Concept 5] For fully developed laminar flow of an incompressible Newtonian fluid through a horizontal circular pipe of radius $R$, how does the maximum centerline fluid velocity $u_{\max}$ relate to the average cross-sectional velocity $V_{\text{avg}}$?

(A)
$u_{\max} = 2.0 \, V_{\text{avg}}$
(B)
$u_{\max} = 1.5 \, V_{\text{avg}}$
(C)
$u_{\max} = 1.25 \, V_{\text{avg}}$
(D)
$u_{\max} = V_{\text{avg}}$
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2019 (42 questions)

Q1.
[Free, Damped & Forced Vibrations (Single DOF) Concept 9] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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Q2.
[Mohr’s Circle & Principal Stresses Concept 20] A simply supported beam of length $L$ carries a concentrated point load $W$ at its mid-span. What is the maximum bending moment and maximum downward deflection $\delta_{\max}$ of the beam (flexural rigidity $EI$)?

(A)
$M_{\max} = \frac{WL}{4}, \quad \delta_{\max} = \frac{WL^3}{48EI}$
(B)
$M_{\max} = \frac{WL}{8}, \quad \delta_{\max} = \frac{5WL^3}{384EI}$
(C)
$M_{\max} = \frac{WL}{2}, \quad \delta_{\max} = \frac{WL^3}{24EI}$
(D)
$M_{\max} = WL, \quad \delta_{\max} = \frac{WL^3}{3EI}$
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2018 (42 questions)

Q1.
[Continuity & Navier-Stokes Equations Concept 20] For fully developed laminar flow of an incompressible Newtonian fluid through a horizontal circular pipe of radius $R$, how does the maximum centerline fluid velocity $u_{\max}$ relate to the average cross-sectional velocity $V_{\text{avg}}$?

(A)
$u_{\max} = 2.0 \, V_{\text{avg}}$
(B)
$u_{\max} = 1.5 \, V_{\text{avg}}$
(C)
$u_{\max} = 1.25 \, V_{\text{avg}}$
(D)
$u_{\max} = V_{\text{avg}}$
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Q2.
[Fins & Extended Surfaces Concept 17] A solid metal sphere of radius $R_1$ with uniform internal heat generation $q_g\text{ (W/m}^3\text{)}$ has thermal conductivity $k$. What is the temperature distribution $T(r)$ within the sphere if the surface temperature is maintained at $T_s$?

(A)
$T(r) = T_s + \frac{q_g}{6k} (R_1^2 - r^2)$
(B)
$T(r) = T_s + \frac{q_g}{4k} (R_1^2 - r^2)$
(C)
$T(r) = T_s + \frac{q_g}{2k} (R_1^2 - r^2)$
(D)
$T(r) = T_s + \frac{q_g}{3k} (R_1 - r)$
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2017 (42 questions)

Q1.
[Operations Research (Simplex, Transportation, PERT/CPM, EOQ) Concept 24] 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.
[Welding Processes & Heat Input Concept 10] 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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2016 (42 questions)

Q1.
[First & Second Law of Thermodynamics, Entropy Concept 21] An ideal gas undergoes a reversible polytropic process $PV^n = C$. If the heat capacity ratio is $\gamma = C_p / C_v$, for what value of $n$ does the heat transfer during the process equal zero?

(A)
$n = \gamma$
(B)
$n = 1$
(C)
$n = 0$
(D)
$n = \infty$
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Q2.
[Balancing of Rotating & Reciprocating Masses Concept 10] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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2015 (42 questions)

Q1.
[Operations Research (Simplex, Transportation, PERT/CPM, EOQ) Concept 18] 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.
[Kinematic Links, Pairs & Degrees of Freedom (Gruebler) Concept 21] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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