Past Year Paper - Mechanical Engineering GATE : 2019

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?

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?

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 loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television.Which one of the following statements can be inferred from the above paragraph?

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 closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _________.​

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 in Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”.The writer of this passage is surprised by the creative writing assignments of his students, because __________.

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 platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?

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 material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.

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) released per spark across the IEG is __________

If x is the mean of data 3, x, 2 and 4, then the mode is _________

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 with a regular pattern is

Endurance limit of a beam subjected to pure bending decreases with

In matrix equation [A] {X} = {R}.

One of the eigenvalues of matrix [A] is

Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
R_eD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.

For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell’s relations,  is equal to

Hardenability of steel is a measure of

The directional derivative of the function f(x, y) = x² + y² along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is

A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is

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 velocities of
points P and R are V_P and V_R, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is

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

The transformation matrix for mirroring a point in x – y plane about the line y = x is given by

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 point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is ___________ MPa.

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 generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is

An analytic function f(z) of complex variable z = x + l y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy

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 the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ¼, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h₁ and that for the second plate is h₂,
the value of the ratio h₁/h₂ is____________.

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?

Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio v = 0.3 are given. The principal strains in the plane of the sheet are

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 fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in​

The most common limit gage used for inspecting the hole diameter is

The differential equation is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The
solution of the differential equation is

A two-dimensional incompressible frictionless flow field is given by u = xΠ− yj. If ρ is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

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 friction between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m (round off to two decimal places).

 

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 with angular speed ω, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical axis at ωp = ω/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming ω2r = 300 m/s2 and g = 10 m/s2, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is __________.

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 two decimal places) to fill up the mold cavity (of size 40 cm × 30 cm × 15 cm) is ____________

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 predecessor of activities Y and Z. The time to complete the activities along the critical path is ____________ weeks.

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, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

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 heat input per unit length of the weld will be ________ kJ/mm (round off to one decimal place).

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 in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates Q_B/Q_A is ______ (round off to two decimal places).

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 cylinder
system is subjected to internal pressure P. Let anddenote the radial and
tangential displacement and stress components, respectively, in material M Similarly,and  denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

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 and liquid (in weight percent) at 1250°C, respectively, will be

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 ordering cost is Rs. 400 per order. If the current order quantity is changed to Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal places).

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 the system to be critically damped, the ratio c/√km should be

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 will be
defective is __________ (round off to two decimal places).

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ω2. Length of different links
are :

The magnitude of the angular speed of the output link 4 is ω4 at the instant when link 2 makes
an angle of 90o with O2O4 as shown. The ratio  is __________ (round off to two decimal
places).

 

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 perpendicular to the figure. The radii of rotation of the masses m_a and m_b are r_a and r_b, respectively. The angle between lines OA and OB is 90°. If ma = 10 kg, mb = 20 kg, r_a = 200 mm and r_b = 400 mm, then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two decimal places).

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 of inertia I, the magnitude of the maximum deflection is

Given a vector and nˆ as the unit normal vector to the surface of the
hemisphere (x² + y² + z² = 1;z ≥0), the value of integral  evaluated on the
curved surface of the hemisphere S is

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 friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).

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 energy of the 3 kg ball is 6 J. The possible value (s) of m is/are

The derivative of f(x) = cos(x) can be estimated using the approximation The percentage error is calculated asThe percentage error in the derivative of f(x) at x = π/6 radian, choosing h = 0.1 radian, is

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 coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ________km/h (the density of air and frontal area may be assumed to be constant).

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 radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ________ kg/s (round off to two decimal places).

The Klein's method of construction for reciprocating engine mechanism

Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor FU is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of F_LM and F_NR are 0.8 and 0.4, respectively. The value of F_PQ (round off to one decimal place) is ___________.

Hot and cold fluids enter a parallel flow double tube heat exchanger at 100oC and 15oC, respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45oC, the log mean temperature difference (LMTD) of the heat exchanger is ________ K (round off to two decimal places).

A differential equation is given as

The solution of the differential equation in terms of arbitrary constants C₁ and C₂ is

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 entropy increases by
0.007 kJ/kg.K. The power input to the electric heater is 2.50 kW. There is no other work or heat
interaction between the system and the surroundings. Assuming an ambient temperature of 300
K, the irreversibility rate of the system is _________kW (round off to two decimal places).

In an orthogonal machining with a single point cutting tool of rake angle 10o, the uncut chip
thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant’s
first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool
interface is ___________(round off to two decimal places).

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 constant R = 0.287 kJ/kg.K, If the pressure and temperature at the beginning of the compression stroke are 100 kPa and 300 K, respectively, then the specific net work output of the cycle is ___________kJ/kg (round off to two decimal places).

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 specific energy required for cutting this material is 0.7 N.m/mm³, the power required for drilling is _________W (round off to two decimal places).

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 the figure. The magnitude of the vertical deflection of the free end is _____________mm (round off to one decimal place).