GATE 2023 Mechanical Engineering
96 questions across 2 sessions
Gate Me 2023
Consider a laterally insulated rod of length L and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperatu...
A linear transformation maps a point (𝑥, 𝑦) in the plane to the point (𝑥̂, 𝑦̂) according to the rule 𝑥̂ = 3𝑦, 𝑦̂ = 2𝑥. Then, the disc 𝑥 2 + 𝑦 2 ≤ 1 gets transformed to a...
The value of k that makes the complex-valued function 𝑓(𝑧) = 𝑒 −𝑘𝑥 (cos 2𝑦 − 𝑖 sin 2𝑦) analytic, where 𝑧 = 𝑥 + 𝑖𝑦, is _________. (Answer in integer)
Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T 1, in = 300 K and T 2, in = 350 K. The heat capacity rates of the two fluids are...
Which one of the options given is the inverse Laplace transform of $\rm \frac{1}{s^3-s}$ ? 𝑢(𝑡) denotes the unit-step function.
A cylindrical rod of length ℎ and diameter 𝑑 is placed inside a cubic enclosure of side length 𝐿. 𝑆 denotes the inner surface of the cube. The view-factor F S-S is
The smallest perimeter that a rectangle with area of 4 square units can have is ______ units. (Answer in integer)
Consider the second-order linear ordinary differential equation $\rm x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0, x\ge1$ with the initial conditions $\rm y(x=1)=6, \left.\frac{dy}{dx}\...
The initial value problem $\rm \frac{dy}{dt}+2y=0, y(0)=1$ is solved numerically using the forward Euler’s method with a constant and positive time step of Δt. Let 𝑦 𝑛 represent...
The atomic radius of a hypothetical face-centered cubic (FCC) metal is (√2/10) nm. The atomic weight of the metal is 24.092 g/mol. Taking Avogadro’s number to be 6.023 × 10 23 atom...
The velocity field of a certain two-dimensional flow is given by V(𝑥, 𝑦) = 𝑘(𝑥𝑖̂ − 𝑦𝑗̂) where 𝑘 = 2 s -1 . The coordinates 𝑥 and 𝑦 are in meters. Assume gravitational eff...
Consider a unidirectional fluid flow with the velocity field given by V(𝑥, 𝑦, 𝑧, 𝑡) = 𝑢(𝑥, 𝑡) 𝑖̂ where 𝑢(0,𝑡) = 1. If the spatially homogeneous density field varies with...
The principal stresses at a point P in a solid are 70 MPa, −70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORREC...
Ignoring the small elastic region, the true stress (𝜎) – true strain (𝜀) variation of a material beyond yielding follows the equation 𝜎 = 400𝜀 0.3 MPa. The engineering ultimate...
A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. While operating at 500 rpm, the angle of t...
Which one of the sentence sequences in the given options creates a coherent narrative? (i) I could not bring myself to knock. (ii) There was a murmur of unfamiliar voices coming fr...
He did not manage to fix the car himself, so he _______ in the garage.
A heat engine extracts heat (𝑄 H ) from a thermal reservoir at a temperature of 1000 K and rejects heat (𝑄 L ) to a thermal reservoir at a temperature of 100 K, while producing w...
Which one of the following statements is FALSE?
Consider a mixture of two ideal gases, X and Y, with molar masses M̅ X = 10 kg/kmol and M̅ Y = 20 kg/kmol, respectively, in a container. The total pressure in the container is 100...
Planting : Seed :: Raising : _____ (By word meaning)
The minute-hand and second-hand of a clock cross each other _______ times between 09:15:00 AM and 09:45:00 AM on a day.
In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi’s f...
Consider the following inequalities 𝑝 2 − 4𝑞 < 4 3𝑝 + 2𝑞 < 6 where 𝑝 and 𝑞 are positive integers. The value of (𝑝 + 𝑞) is _______.
How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a...
The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?
Air (density = 1.2 kg/m 3 , kinematic viscosity = 1.5 × 10 -5 m 2 /s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from t...
Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profile...
Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?
In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correc...
Set Master
He did not manage to fix the car himself, so he ________ in the garage.
Planting : Seed :: Raising : ________ (By word meaning)
A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts. What is the percentage, correct to one...
The minute-hand and second-hand of a clock cross each other ________ times between 09:15:00 AM and 09:45:00 AM on a day.
The symbols O, *, Δ, and □ are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows. 1) Every row and every column must contain e...
In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi's f...
Consider the following inequalities p² - 4q < 4 3p + 2q < 6 where p and q are positive integers. The value of (p + q) is _________.
Which one of the sentence sequences in the given options creates a coherent narrative? (i) I could not bring myself to knock. (ii) There was a murmur of unfamiliar voices coming fr...
How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?
An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented per...
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a...
The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?
With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?
Which one of the options given represents the feasible region of the linear programming model: Maximize 45X1 + 60X2 X1 ≤ 45 X2 ≤ 50 10X1 + 10X2 ≥ 600 25X1 + 5X2 ≤ 750
A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylind...
The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is
The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?
The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?
Air (density = 1.2 kg/m³, kinematic viscosity = 1.5×10⁻⁵ m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the lead...
Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The fl...
Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profile...
A heat engine extracts heat (QH) from a thermal reservoir at a temperature of 1000 K and rejects heat (QL) to a thermal reservoir at a temperature of 100 K, while producing work (W...
Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?
A beam is undergoing pure bending as shown in the figure. The stress (σ)-strain (ε) curve for the material is also given. The yield stress of the material is σY. Which of the optio...
In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correc...
The principal stresses at a point P in a solid are 70 MPa, -70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORREC...
Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)
Consider a laterally insulated rod of length L and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperatu...
Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |ω₂|/|ω₁| = 1/4, have their centers 30 mm apart. The number of teeth on the driv...
The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizo...
A vector field B(x, y, z) = x î + y ĵ – 2z k is defined over a conical region having height h = 2, base radius r = 3 and axis along z, as shown in the figure. The base of the cone...
A linear transformation maps a point (x, y) in the plane to the point (x̂, ŷ) according to the rule x̂ = 3y, ŷ = 2x. Then, the disc x² + y² ≤ 1 gets transformed to a region with an...
The value of k that makes the complex-valued function f(z) = e⁻ᵏˣ (cos 2y – i sin 2y) analytic, where z = x + iy, is __________. (Answer in integer)
The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over...
Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T₁, in = 300 K and T₂, in = 350 K. The heat capacity rates of the two fluids are C₁...
Which one of the options given is the inverse Laplace transform of $\frac{1}{s^3-s}$? u(t) denotes the unit-step function.
A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum v...
The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity $\omega_1$. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the f...
A beam of length L is loaded in the xy -plane by a uniformly distributed load, and by a concentrated tip load parallel to the z -axis, as shown in the figure. The resulting bending...
The figure shows a thin-walled open-top cylindrical vessel of radius r and wall thickness t. The vessel is held along the brim and contains a constant-density liquid to height h fr...
Which one of the following statements is FALSE?
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder i...
A cylindrical rod of length h and diameter d is placed inside a cubic enclosure of side length L. S denotes the inner surface of the cube. The view-factor Fs-s is
In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool α = 5°, and the shear angle, φ, is known to be 45°. Applying the id...
A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is...
Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of Q are...
A very large metal plate of thickness d and thermal conductivity k is cooled by a stream of air at temperature T∞ = 300 K with a heat transfer coefficient h, as shown in the figure...
The smallest perimeter that a rectangle with area of 4 square units can have is ________ units. (Answer in integer)
Consider the second-order linear ordinary differential equation $x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0, x \geq 1$ with the initial conditions $y(x = 1) = 6, \frac{dy}{dx}...
The initial value problem $\frac{dy}{dt} + 2y = 0$, $y(0) = 1$ is solved numerically using the forward Euler's method with a constant and positive time step of $\Delta t$. Let $y_n...
The atomic radius of a hypothetical face-centered cubic (FCC) metal is $(\sqrt{2}/10)$ nm. The atomic weight of the metal is 24.092 g/mol. Taking Avogadro's number to be $6.023 \ti...
A steel sample with 1.5 wt.% carbon (no other alloying elements present) is slowly cooled from 1100 °C to just below the eutectoid temperature (723 °C). A part of the iron-cementit...
A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data...
A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the dat...
A solid part (see figure) of polymer material is to be fabricated by additive manufacturing (AM) in square-shaped layers starting from the bottom of the part working upwards. The n...
An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewing via the optical flat using a monochromatic light of wavel...
Ignoring the small elastic region, the true stress (σ) – true strain (ε) variation of a material beyond yielding follows the equation σ = 400ε^0.3 MPa. The engineering ultimate ten...
The area moment of inertia about the y-axis of a linearly tapered section shown in the figure is ________ m^4. (Answer in integer)
A cylindrical bar has a length L = 5 m and cross section area S = 10 m². The bar is made of a linear elastic material with a density ρ = 2700 kg/m³ and Young's modulus E = 70 GPa....
A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. While operating at 500 rpm, the angle of t...
Consider a mixture of two ideal gases, X and Y, with molar masses M_X = 10 kg/kmol and M_Y = 20 kg/kmol, respectively, in a container. The total pressure in the container is 100 kP...
The velocity field of a certain two-dimensional flow is given by V(x, y) = k(xî – yĵ) where k = 2 s^-1. The coordinates x and y are in meters. Assume gravitational effects to be ne...
Consider a unidirectional fluid flow with the velocity field given by V(x, y, z, t) = u(x, t) î where u(0, t) = 1. If the spatially homogeneous density field varies with time t as...
The figure shows two fluids held by a hinged gate. The atmospheric pressure is P_a = 100 kPa. The moment per unit width about the base of the hinge is ________ kNm/m. (Rounded off...
An explosion at time t = 0 releases energy E at the origin in a space filled with a gas of density ρ. Subsequently, a hemispherical blast wave propagates radially outwards as shown...