GATE 2022 Mechanical Engineering

A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus?

In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?

The Clausius inequality holds good for

A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m 3 to a final volume of 2.5 m 3 . The polytropic index is given by n = 1.2. The absolute va...

In Fe-Fe 3 C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel...

Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperature side A has a surface temperature of 80 °C, and the heat tr...

In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressu...

After playing _________ hours of tennis, I am feeling _________ tired to walk back.

The average of the monthly salaries of M, N and S is ₹ 4000. The average of the monthly salaries of N, S and P is ₹ 5000. The monthly salary of P is ₹ 6000. What is the monthly sal...

Given below are three conclusions drawn based on the following three statements. Statement 1 : All teachers are professors. Statement 2 : No professor is a male. Statement 3 : Some...

A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph. What percentage...

Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning...

Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear “lost”, it was found that wallets with money are more likely to be returned...

An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle?

The limit $\rm p = \displaystyle\lim_{x \rightarrow \pi} \left( \frac{x^2 + α x + 2 \pi^2}{x - \pi + 2 \sin x} \right)$ has a finite value for a real α . The value of α and the cor...

Solution of ∇ 2 T = 0 in a square domain (0 < x < 1 and 0 < y < 1) with boundary conditions: T(x, 0) = x; T(0, y) = y; T(x, 1) = 1 + x; T(1, y) = 1 + y is

Given a function $\rm ϕ = \frac{1}{2} (x^2 + y^2 + z^2) $ in three-dimensional Cartesian space, the value of the surface integral ∯ S n̂ . ∇ϕ dS where S is the surface of a sphere...

The value of the integral $\rm \oint \left( \frac{6z}{2z^4 - 3z^3 + 7 z^2 - 3z + 5} \right) dz$ evaluated over a counter-clockwise circular contour in the complex plane enclosing o...

Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?

The Fourier series expansion of x 3 in the interval −1 ≤ x < 1 with periodic continuation has

If A = $\begin{bmatrix} 10 & 2k + 5 \\\ 3k - 3 & k + 5 \end{bmatrix} $ is a symmetric matrix, the value of k is _______.

A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed as

A CNC worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is 5 mm. The stepper motor completes one full rev...

The type of fit between a mating shaft of diameter $25.0^{\begin{matrix} +0.010 \\\ -0.010 \end{matrix}}$ mm and a hole of diameter $25.0^{\begin{matrix} +0.015 \\\ -0.015 \end{mat...

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is

Which one of the following is NOT a form of inventory?

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec V = (2x)...

In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature T ∞ (g is the gravitational acceleration, β is...

Which of the following heat treatment processes is/are used for surface hardening of steels?

Which of the following methods can improve the fatigue strength of a circular mild steel (MS) shaft?

A flat plate made of cast iron is exposed to a solar flux of 600 W/m 2 at an ambient temperature of 25 °C. Assume that the entire solar flux is absorbed by the plate. Cast iron has...

Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters. $$ \begin{array}{|l|...

Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are gi...

A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece is lubricated with a mineral oil, which gives a coefficient...

Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be complete...

A solid spherical bead of lead (uniform density = 11000 kg/m 3 ) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1...

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m 3 and 100 m/s, respectively....

Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T ∞ with convective heat transf...

The system of linear equations in real (x, y) given by $\rm \begin{pmatrix} \rm x & \rm y \end{pmatrix} \begin{bmatrix} 2 & 5- 2 α \\\ α & 1 \end{bmatrix} = \rm \begin{pmatrix} \rm...

Let a random variable X follow Poisson distribution such that Prob(X = 1) = Prob(X = 2). The value of Prob(X = 3) is __________ (round off to 2 decimal places).

Consider two vectors $\rm \vec a = 5 i + 7 j + 2 k $ $\rm \vec b = 3i - j + 6k$ Magnitude of the component of $\vec a$ orthogonal to $\vec b$ in the plane containing the vectors $\...

Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m/s. The orthogonal rake angle of the cutting tool is 5º. The...

A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is 1 m...

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine...

A steady two-dimensional flow field is specified by the stream function ψ = kx 3 y, where x and y are in meters and the constant k = 1 m -2 s -1 . The magnitude of acceleration at...

During open-heart surgery, a patient’s blood is cooled down to 25 °C from 37 ° C using a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at 4 ° C and l...

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following stat...

Consider a forced single degree-of-freedom system governed by $\rm \ddot x(t) + 2 ζ ω_n \dot x (t) + ω_n^2 x(t) = ω_n^2 \cos (ω t)$ , where ζ and ω n are the damping ratio and unda...

A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some inter...

An engine running on an air standard Otto cycle has a displacement volume 250 cm 3 and a clearance volume 35.7 cm 3 . The pressure and temperature at the beginning of the compressi...

Consider the following functions for non-zero positive integers, p and q. $\rm f(p,q)=\frac{p\times p\times p\times.......\times p}{q\ terms}=p^q;\;$ ; f(p, 1) = p $g(p,q)=p^{p^{p^...

Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality $2-5x\leq-\left(\frac{6x-5}{3}\right)\;$ on the real number l...

Which one of the following is an intensive property of a thermodynamic system?

Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume c v is equal to 750 J-kg -1...

In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg. The...

A rigid tank of volume of 8 m 3 is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacua...

At steady state, 500 kg/s of steam enters a turbine with specific enthalpy equal to 3500 kJ/kg and specific entropy equal to 6.5 kJ-kg -1 K -1 . It expands reversibly in the turbin...

Direction: Fill in the blank spaces in the given sentence selecting an appropriate set of words from the following options- Writing too many things on the ______ while teaching cou...

If $f(x)=2\ln(\sqrt{e^x})$ , what is the area bounded by f(x) for the interval [0, 2] on the x-axis?

A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information?

Fish belonging to species S in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey....

For the past m days, the average daily production at a company was 100 units per day. If today’s production of 180 units changes the average to 110 units per day, what is the value...

A polynomial ψ(s) = a n s n + a n-1 s n-1 + ......+ a 1 s + a 0 of degree n > 3 with constant real coefficients a n , a n-1 , ... a 0 has triple roots at s = -σ. Which one of the f...

Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral $\int_A \vec{F}.d\vec{A}$ of a vector fie...

Consider the definite integral $\int^2_1(4x^2+2x+6)dx$ Let I e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals...

Given $\int^{\infty}_{-\infty}e^{-x^2}dx=\sqrt{\pi}$ If a and b are positive integers, the value of $\int^{\infty}_{-\infty}e^{-a(x+b)^2}dx$ is _________.

A shaft of diameter $25^{-0.04}_{-0.07}$ mm is assembled in a hole of diameter $25^{+0.02}_{-0.00}$ mm. Match the allowance and limit parameter in Column I with its corresponding q...

Match the additive manufacturing technique in Column I with its corresponding input material in Column II. Additive manufacturing technique (Column I) Input Material (Column II) P....

Which one of the following CANNOT impart linear motion in a CNC machine?

Which of the following non-dimensional terms is an estimate of Nusselt number?

Consider sand casting of a cube of edge length a. A cylindrical riser is placed at the top of the casting. Assume solidification time, t s ∝ V/A, where V is the volume and A is the...

Which of these processes involve(s) melting in metallic workpieces?

The velocity field in a fluid is given to be $\vec{V}=(4xy)\hat{i}+2(x^2-y^2)\hat{j}$ Which of the following statement(s) is/are correct?

Parts P1 - P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time requi...

An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units. If the manufacturer uses exponential smoothing method with a...

The demand of a certain part is 1000 parts/year and its cost is Rs. 1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is Rs. 100/ord...

For the exact differential equation, $\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$ which one of the following is the solution?

A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediat...

A manufacturing unit produces two products Pl and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit ear...

The steady velocity field in an inviscid fluid of density 1.5 is given to be $\vec{V}=(y^2-x^2)\hat{i}+(2xy)\hat{j} $ . Neglecting body forces, the pressure gradient at (x =1, y =...

A is a 3 × 5 real matrix of rank 2. For the set of homogeneous equations Ax = 0, where 0 is a zero vector and x is a vector of unknown variables, which of the following is/are true...

If the sum and product of eigenvalues of a 2 × 2 real matrix $\begin{bmatrix}3&p\\\ p&q\end{bmatrix} $ are 4 and -1 respectively, then |p| is _______ (in integer).

Given z = x +iy, i = √-1 C is a circle of radius 2 with the centre at the origin. If the contour C is traversed anticlockwise, then the value of the integral $\frac{1}{2\pi}\int_c\...

In an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is 0.5 mm and the shear angle is 15°. The orthogonal rake angle...

In a direct current arc welding process, the power source has an open circuit voltage of 100 V and short circuit current of 1000 A. Assume a linear relationship between voltage and...

Saturated vapor at 200 °C condenses to saturated liquid at the rate of 150 kg/s on the shell side of a heat exchanger (enthalpy of condensation h fg = 2400 kJ/kg). A fluid with C p...

Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of...

Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?

A structural member under loading has a uniform state of plane stress which in usual notations is given by σ x = 3P, σ y = -2P and τ xy = √2 P, where P > 0. The yield strength of t...

For a dynamical system governed by the equation, $\ddot{x}(t)+2 ζ \omega_n \dot{x}(t)+\omega_n^2x(t)=0$ the damping ratio ζ is equal to $\frac{1}{2\pi}\log_e2$ . The displacement x...