Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 1)

“Her _______ should not be confused with miserliness, she is ever willing to assist those in need.” The word that best fills the bank in the above sentence is :

Going by the __________ that many hands make light work, the school __________ involved all the students in the task.”

Given that a and b are integers and a + a²b³ is odd, which one of the following statementsis correct?

Consider the following three statements:
1. Some roses are red
2. All red flowers fade quickly.
3. Some roses fade quickly.
Q. Which of the following statements can be logically inferred from the above statements?

Which of the following functions describe the graph shows in the below figure.

For integers a, b and c, what would be the minimum and maximum values respectively of a + b + c if log| a|+ log| b |+ log| c | = 0

From the time the front of a train enters a platform, it takes 25 seconds for the back ofthe train to leave the platform, while travelling at a constant speed of 54 km/h. At thesame speed, it takes 14 seconds to pass a man running at 9 km/h in the same directionas the train. What is the length of the train and that of the platform in meter,respectively?​

For a two-dimensional incompressible flow field given by where A > 0, whichone of the following statements is FALSE?

An ideal gas undergoes a process from state 1 (T₁ = 300 K,p₁ = 100 kPa) to state( ) 2(T₂ = 600k,p₂ = 500 kPa . The specific heats of the ideal gas are: cp=1 kJ/kg-k = and c_v 0.7 kJ/kg-K. The change in specific entropy of the ideal gas from state 1 to state 2 (in kJ/kg-K) is ________ (correct to two decimal places)

A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S₁ and S₂ as shows in the figure.

Tension in the springs are

For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is_______ (correct to two decimal places).

A six- faced fair dice is rolled five times. The probability (in%)of obtaining “ONE” at leastfour times is

Using the Taylors tool life equation with exponent n = 0.5, if the cutting speed is reducedby 50% the ratio of new tool life to original tool life is

A grinding ratio of 200 implies that the

The number of atoms per unit cell and the number of slip systems, respectively, for aface-centered cubic (FCC) crystal are

The type of weld represented by the shaded region in the figure is

The height (in mm) for a 125 mm sine bar to measure a taper of 27°32’ on a flat work piece is __________ (correct to three decimal places).

Interpolator in a CNC machine

If the wire diameter of a compressive helical spring is increased by 2% the change in spring stiffness (in %) is __________ (correct to two decimal places)

A four bar mechanism is made up of links of length 100,200,300 and 350 mm. if the 350 mm link is fixed, the number of links that can rotate fully is _________

Four red balls, four green balls and four blue balls are put in a box. Three balls are pulledout of the box at random one after another without replacement. The probability thatall the three balls are red is

The rank of the matrix is

According to the Mean Value Theorem for a continuous function f (x) in the interval [a,b], there exists a value  in this interval such that

A flat plate of width L = 1 m is pushed down with a velocity U = 0.01 m/s towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, U_avg of the fluid (in m/s) draining out at the instant shows in the figure is ___________ (correct to three decimal places).

F (z) is a function of the complex variable z = x + iy given by

For what value of k will f(z) satisfy the Cauchy-Riemann equations?

If σ₁ and σ₃  are the algebraically largest and smallest principal stresses respectively the value of the maximum shear stress is.

The time series forecasting method that gives equal weightage to each of the M mostrecent observation is

In a linearly hardening plastic material. The true stress beyond initial yielding

A steel column of rectangular section (15 mm x10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200GPa for steel, the critical axial load (in kN) is _______ (correct to two decimal places)

Which one of the following statement is correct for a superheated vapour?

The equation of motion for a spring-mass system excited by a harmonic force is

Where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when is equal to.

For an Oldham coupling used between two shafts, which among the following statements are correct?
I. Torsional load is transferred along shaft axis.
II. A velocity ratio of 1:2 between shafts is obtained without using gears
III. Bending load is transferred transverse to shaft axis.
IV. Rotation is transferred along shaft axis.

The minimum value of 3x + 5y such that:

is __________.

A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is ________ (correct to two decimal places).

An epicyclic gear train is shown in the figure below. The number of teeth on the gearsA, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotatesat 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is​

An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35oC.
The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air:
_cp = 1.005jJ/kgk, c_v0.718kJ/kgk, R = 0.287 kJ/kgK. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

A solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall as shown in the figure below. A thin oil film of thickness h=0.15mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oilfilm is 0.04 m² . The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7x10⁻³ Pa-s and acceleration due to gravity as 10 m/s² Neglect weight of the oil. The terminal velocity V (in m/s) of the block is _________ (correct to one decimal place).

A self-aligning ball bearing has a basic dynamic load rating ( C₁₀ , for 10⁶ revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in 10⁶ revolutions) is

The maximum reduction in cross-sectional area per pass (R) of a cold wire drawing process is

where n represents the strain hardening coefficient. For the case of a perfectly plastic material, R is

The value of integral

over the closed surface S bounding a volume, whereis the position vector and  is the normal to the surface S, is

The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure ______ (correct to two decimal places)

An orthogonal cutting operations is being carried out in which uncut thickness is 0.010 mm, cutting speed is 130 m/min, rake angle is 15o and width of cut is 6 mm. It is observed that the chip thickness is 0.015 mm, the cutting force is 60 N and the thrust force is 25 N. The ratio of friction energy to total energy is __________ (correct to two decimal places)

Let 1 2 X , X be two independent normal random variables with means  and standard deviations  respectively. Consider Then,

An electrochemical machining (ECM) is to be used to cut a through hole into a 12 mm thick aluminum plate. The hole has a rectangular cross-section, 10 mm × 30 mm The ECM operation will be accomplished in 2 minutes, with efficiency of 90%. Assuming specific removal rate for aluminum as 3.44 x10^-2 mm³ /(As), the current (in A) required is __________(correct to two decimal places).

Steam flows through a nozzle at mass flow rate of kg/s with a heat loss of 5 kW.The enthalpies at inlet and exit are 2500 kJ/kg and 2350 kJ/kg, respectively. Assuming negligible velocity at inletthe velocityof steam (in m/s) at the nozzle exit is _________ (correct to two decimal places)

A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is _________ (correct to one decimal place)

 

The state of stress at a point, for a body in place stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress σy (in kPa) is

A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles.

The total flow rate Q through the sprinkler is 1 litre/sec and the cross-sectional area of each exit nozzle is 1cm². Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (rad/s) of the sprinkler is _________ (correct to two decimal places).

A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45° and a force of 40 N is acting towards the left on the slider. The length of the crank is 30 mm and the connecting rod is 70 mm. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is ________(correct to two decimal places).

A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of as shown in the figure.

The glue used at the interface fails if
Criterion 1 : the maximum normal stress exceeds 2.5 MPa
Criterion 2 : the maximum shear stress exceeds 1.5 MPa
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface

The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force F = 10 N is applied at the free end of the lever as shown. Given that the coefficient of friction between the shoe and the drum is 0.3, the braking torque (in Nm)
applied on the drum is ____________ (correct to two decimal places).

Processing times (including step times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is _________(correct to two decimal places).

 

An explicit forward Euler method is used to numerically integrate the differential equation

Using a time step of 0.1. With the initial condition y (0) = 1, the value of y(1) computed by this method is ___________ (correct to two decimal places).

A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m) where the jet strikes the floor is

A machine of mass m = 200 kg is supported on two mounts, each of stiffness k = 10 kN/m. The machine is subjected to an external force (in N) F (t) = 50 cos 5t.  Assuming only vertical translator motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is _________(correct to two decimal places).

A plane slab of thickness L and thermal conductivity k is heated with a fluid on one side (P) , and the other side (Q) is maintained at a constant temperature, TQ of 25°C, as shown in the figure. The fluid is at 45°C and the surface heat transfer coefficient, h, is 2 10 W/mK. The steady state temperature. TP (in °C) of the side which is exposed to the fluid is _________ (correct to two decimal places).

F (s) is the Laplace transform of the function
f (t) = 2t²e^-t
F(1) is __________ (correct to two decimal places).

Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q where the local radius of curvature is 2 m as shown in the figure. Assuming 2 g = 10 m/s , the normal force (in N) at Q is ________ (correct to two decimal places).

In a Lagrangian system, the position of a fluid particle in a flow is described asandwhere t is the time whileand k are constants. The flow is

The true stress (σ ) , true strain (ε ) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e. up to stress of 500 MPa and strain of 0.5. then from point A, there is unloading up to point B, i.e. to stress of 100 MPa, Given that the Young’s modulus E = 200 GPa, the natural strain at point B (ε_B ) ________ (correct to two decimal places).

A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 2 10 m/s and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in
seconds) of

A tank of volume 0.05 m³ contains a mixture of saturated water and saturated steam at 200°C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg/K) of the mixture is __________ (correct of two decimal places)
Property data for saturated steam and water are:
At o 200°C, Psat = 1.5538 MPa