GATE 2019 Mechanical Engineering
146 questions across 4 sessions
Set 1
A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory?
_________ I permitted him to leave, I wouldn’t have had any problem with him being absent, _____ I?
John Thomas, an _______________ writer, passed away in 2018.
Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then...
The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is ____.
The minister avoided any mention of the issue of women’s reservation in the private in the private sector. He was accused of _______ the issue.
A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are...
Congo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces. H...
M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following sta...
Set 2
X is an online provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty mem...
Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is___
Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is close...
Are there enough seats here? There are _______ people here than I expected.
Mola is a digital platform for taxis in a city. It offers three types of rides- Pool, Mini and Prime. The table below presents the number of rides for the past four months. The pla...
If IMHO = JNIP; IDK =JEL: and SO =TP, then IDC = ____.
Once the team of analysis identify the problem, we _____ in a better position to comment on the issue. Which one of the following choices CANNOT fill the given blank?
The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?
A final examination is the _____ of a series of evaluations that a student has to go through.
While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and...
Set 1
John Thomas, an ________ writer, passed away in 2018.
Consider the matrix P = $\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$. The number of distinct eigenvalues of P is
________ I permitted him to leave, I wouldn't have had any problem with him being absent, I?
A parabola $x = y^2$ with $0 \le x \le 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^\circ$ around the x-axis is
A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory?
For the equation $\frac{dy}{dx} + 7x^2y = 0$, if $y(0) = 3/7$, then the value of $y(1)$ is
The lengths of a large stock of titanium rods follow a normal distribution with a mean ($\mu$) of 440 mm and a standard deviation ($\sigma$) of 1 mm. What is the percentage of rods...
The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is ________.
A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity \omega. At time t = 0, the vertical position of the follower is y(0) = 0, and...
The minister avoided any mention of the issue of women's reservation in the private sector. He was accused of ________ the issue.
Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then...
The natural frequencies corresponding to the spring-mass systems I and II are ω_I and ω_II, respectively. The ratio $\frac{\omega_I}{\omega_{II}}$ is
A spur gear with 20° full depth teeth is transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the rad...
A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are...
During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction is equal to the work interaction (Q$_{1-2}$ = W$_{1-2}$) when the process is
Congo was named by Europeans. Congo's dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces. H...
For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux (Nuq) and that at...
A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown....
M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following sta...
As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, are
A slender rod of length L, diameter d (L>> d) and thermal conductivity k1 is joined with another rod of identical dimensions, but of thermal conductivity k2, to form a composite cy...
Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which...
In a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is called
Which one of the following welding methods provides the highest heat flux (W/mm²)?
The length, width and thickness of a steel sample are 400 mm, 40 mm and 20 mm, respectively. Its thickness needs to be uniformly reduced by 2 mm in a single pass by using horizonta...
The position vector OP of point P (20, 10) is rotated anti-clockwise in X-Y plane by an angle θ = 30° such that point P occupies position Q, as shown in the figure. The coordinates...
The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is
Evaluation of $\int_2^4 x^3 dx$ using a 2-equal-segment trapezoidal rule gives a value of _________
A block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is 9.81 m/s². The coefficient of static friction between the floor and the block is 0.2. A horizo...
A cylindrical rod of diameter 10 mm and length 1.0 m is fixed at one end. The other end is twisted by an angle of 10° by applying a torque. If the maximum shear strain in the rod i...
A solid cube of side 1 m is kept at a room temperature of 32 °C. The coefficient of linear thermal expansion of the cube material is $1\times10^{-5}/^{\circ}\text{C}$ and the bulk...
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of +140 MPa, and a minimum stress of -70 MPa. The R-ratio (minimum stress to...
Water flows through a pipe with a velocity given by $\vec{V} = (\frac{4}{t} + x + y)\hat{j}$ m/s, where $\hat{j}$ is the unit vector in the y direction, $t (> 0)$ is in seconds, an...
Air of mass 1 kg, initially at 300 K and 10 bar, is allowed to expand isothermally till it reaches a pressure of 1 bar. Assuming air as an ideal gas with gas constant of 0.287 kJ/k...
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading,...
The set of equations x + y + z = 1 ax - ay + 3z = 5 5x - 3y + az = 6 has infinite solutions, if a =
A harmonic function is analytic if it satisfies the Laplace equation. If u(x, y) = 2x² - 2y² + 4xy is a harmonic function, then its conjugate harmonic function v(x, y) is
The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probab...
A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height h from the ground, midway between the front and...
In a four bar planar mechanism shown in the figure, AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with...
The rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia 10 kg-m² about the rotor axis. The rotor rotates at a constant speed of 1100 rad/s in th...
The wall of a constant diameter pipe of length 1 m is heated uniformly with flux q" by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully...
A gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section of the duct at 100 kPa and 27 °C with...
A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero. The yield strength (Sy) in uniaxial tension/compression of the materi...
In orthogonal turning of a cylindrical tube of wall thickness 5 mm, the axial and the tangential cutting forces were measured as 1259 N and 1601 N, respectively. The measured chip...
A circular shaft having diameter 65.00±0.01 mm is manufactured by turning process. A 50 µm thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness i...
Match the following sand mold casting defects with their respective causes.
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is ___...
Consider an elastic straight beam of length L = 10 πm, with square cross-section of side a = 5 mm, and Young's modulus E = 200 GPa. This straight beam was bent in such a way that t...
Consider a prismatic straight beam of length L = π m, pinned at the two ends as shown in the figure. The beam has a square cross-section of side p = 6 mm. The Young's modulus E = 2...
In a UTM experiment, a sample of length 100 mm, was loaded in tension until failure. The failure load was 40 kN. The displacement, measured using the cross-head motion, at failure,...
At a critical point in a component, the state of stress is given as σₓₓ = 100 MPa, σᵧᵧ = 220 MPa, σₓᵧ = σᵧₓ = 80 MPa and all other stress components are zero. The yield strength of...
A uniform thin disk of mass 1 kg and radius 0.1 m is kept on a surface as shown in the figure. A spring of stiffness k₁ = 400 N/m is connected to the disk center A and another spri...
A single block brake with a short shoe and torque capacity of 250 N·m is shown. The cylindrical brake drum rotates anticlockwise at 100 rpm and the coefficient of friction is 0.25....
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown bel...
A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m³. Liquid of density 1000 kg/m³ is now p...
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation...
If one mole of H₂ gas occupies a rigid container with a capacity of 1000 litres and the temperature is raised from 27 °C to 37 °C, the change in pressure of the contained gas (roun...
A steam power cycle with regeneration as shown below on the T-s diagram employs a single open feedwater heater for efficiency improvement. The fluids mix with each other in an open...
A gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when operating at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5,...
The value of the following definite integral is _________ (round off to three decimal places) $\int_{1}^{e} (x \ln x) dx$
In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are 45° and 10°, respectively. The feed during cylindrical turning is 0.1 mm/rev. The center lin...
Taylor's tool life equation is given by VTⁿ = C, where V is in m/min and T is in min. In a turning operation, two tools X and Y are used. For tool X, n = 0.3 and C = 60 and for too...
Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any of the five different machines (M1, M2, M3, M4 and M5). The time durations take...
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: If all activities other than S take...
Set 2
Once the team of analysts identify the problem, we ________ in a better position to comment on the issue. Which one of the following choices CANNOT fill the given blank?
A final examination is the ________ of a series of evaluations that a student has to go through.
If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = ________.
The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x, y)+iv(x, y)$. Then, $u(x, y)$ and $v(x, y)$ must satisfy
A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the instant shown, edge QR is parallel to the x-axis, and the body moves such that velo...
Are there enough seats here? There are ________ people here than I expected.
Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the...
Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is __...
A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is
Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is close...
While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and...
Endurance limit of a beam subjected to pure bending decreases with
Mola is a digital platform for taxis in a city. It offers three types of rides - Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The pl...
A two-dimensional incompressible frictionless flow field is given by $\vec{u} = x\hat{i} - y\hat{j}$. If $\rho$ is the density of the fluid, the expression for pressure gradient ve...
Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor F12 is
X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyal...
One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat gener...
For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure and temperature, respectively. As per Maxwell's relations, $(\frac{\partial v}{\part...
Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?
Hardenability of steel is a measure of
The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in
The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface w...
The most common limit gage used for inspecting the hole diameter is
The transformation matrix for mirroring a point in x - y plane about the line y = x is given by
If x is the mean of data 3, x, 2 and 4, then the mode is _________.
The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is _________ N.
The state of stress at a point in a component is represented by a Mohr's circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same...
A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young's modulus of the mater...
Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabo...
A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of t...
In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is 200 V and the capacitance of the RC circuit is 50 µF. The energy (in J) rele...
Given a vector $\vec{u} = \frac{1}{3}(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k})$ and $\hat{n}$ as the unit normal vector to the surface of the hemisphere $(x^2 + y^2 + z^2 = 1; z \...
A differential equation is given as $x^2 \frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + 2y = 4$. The solution of the differential equation in terms of arbitrary constants $C_1$ and $C_2$...
The derivative of $f(x) = \cos(x)$ can be estimated using the approximation $f'(x) = \frac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\left(\frac{\text{Exact value...
A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central impact with a stationary ball of mass m. After the impact is over, the kinetic ener...
Consider two concentric circular cylinders of different materials M and N in contact with each other at r = b, as shown below. The interface at r = b is frictionless. The composite...
A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young's modulus E, and area moment o...
A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For t...
The figure shows a heat engine (HE) working between two reservoirs. The amount of heat ($Q_2$) rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the...
The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid an...
The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship "X < Y, Z" means that X is predecesso...
The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r. Using exact analysis, th...
A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity EI = 200 N·m² is subjected to an applied moment MA = 1.0 N·m at the free end as shown in...
Two masses A and B having mass m_a and m_b, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicul...
A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed \omega_2. Length of...
The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts...
A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle wit...
A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of frictio...
Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow...
The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag...
Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor FIJ is defined as the fraction of radiation leaving plate I that is intercepted by plat...
Hot and cold fluids enter a parallel flow double tube heat exchanger at 100 °C and 15 °C, respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 12...
Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entrop...
An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is...
An air standard Otto cycle has thermal efficiency of 0.5 and the mean effective pressure of the cycle is 1000 kPa. For air, assume specific heat ratio γ = 1.4 and specific gas cons...
The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81 m/s². The time (in s, round off to tw...
A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of 20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net...
The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of...
A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specifi...
In an orthogonal machining with a single point cutting tool of rake angle 10°, the uncut chip thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchan...
The annual demand of valves per year in a company is 10,000 units. The current order quantity is 400 valves per order. The holding cost is Rs. 24 per valve per year and the orderin...