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GATE (Graduate Aptitude Test in Engineering) Mechanical Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Mechanical Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of General Aptitude exam of GATE Mechanical Engineering. We advise candidates to solve the online GATE Mechanical Engineering mock tests to get good marks in the exam. Start practicing Mechanical GATE 2018 Mock tests here online for free GATE Mechanical Engineering exam is conducted by Indian Institute of science and seven Indian Institute of Technology. The exam is divided into two different parts General Aptitude and Core subjects. In this section, you can practice mock test of complete exam

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Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 1:

“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.” The words that best fill the blanks in the above sentence are

A	principle, principal	B	principal, principle
C	principle, principle	D	principal, principal

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 2:

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

A	cleanliness	B	punctuality
C	frugality	D	greatness

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 3:

Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toy?

A	1	B	7
C	100	D	700

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 4:

A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?

A	1125	B	2250
C	2924	D	4500

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 5:

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

A	63	B	72
C	81	D	90

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 6:

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?

A	-3 and 3	B	-1 and 1
C	-1 and 3	D	1 and 3

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 7:

Given that 𝑎 and 𝑏 are integers and

α + α^{2} b^{3}

is odd, which one of the following statements is correct?

A	𝑎 and 𝑏 are both odd	B	𝑎 and 𝑏 are both even
C	𝑎 is even and 𝑏 is odd	D	𝑎 is odd and 𝑏 is even

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 8:

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

A	210 and 140	B	162.5 and 187.5
C	245 and 130	D	175 and 200

All of these

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 9:

Which of the following functions describe the graph shown in the below figure?

A	𝑦 = \|\|𝑥\| + 1\| − 2	B	𝑦 = \|\|𝑥\| − 1\| − 1
C	𝑦 = \|\|𝑥\| + 1\| − 1	D	𝑦 = \|\|𝑥 − 1\| − 1\|

Category: GATE Mechanical Engineering 2018 set 1 General Aptitude

Question 10:

Consider the following three statements: (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly. Which of the following statements can be logically inferred from the above statements?

A	If (i) is true and (ii) is false, then (iii) is false.	B	If (i) is true and (ii) is false, then (iii) is true.
C	If (i) and (ii) are true, then (iii) is true.	D	If (i) and (ii) are false, then (iii) is false.

Category: GATE Mechanical Engineering 2018 set 1

Question 11:

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

A	1/72	B	1/55
C	1/36	D	1/27

Category: GATE Mechanical Engineering 2018 set 1

Question 12:

The rank of the matrix

[\begin{matrix} - 4 & 1 & - 1 \\ - 1 & - 1 & - 1 \\ 7 & - 3 & 1 \end{matrix}]

A	1	B	2
C	3	D	4

Category: GATE Mechanical Engineering 2018 set 1

Question 13:

According to the Mean Value Theorem, for a continuous function

f (x)

in the interval

[α, b]

,there exists a value ξ in this interval such that

\int_{a}^{b} f (x) d x =

A	f (ξ)(b-a)	B	f (b)(ξ-a)
C	f (a)(b-ξ)	D	0

Category: GATE Mechanical Engineering 2018 set 1

Question 14:

F (z)

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

F(z) = i z + k Re(z) + i Im(z).

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

A	0	B	1
C	-1	D	y

Category: GATE Mechanical Engineering 2018 set 1

Question 15:

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

The tensions in the strings are

A	$T_{1} = 100 N a n d T_{2} = 0 N$	B	$T_{1} = 0 N a n d T_{2} = 100 N$
C	$T_{1} = 75 N a n d T_{2} + 25 N$	D	$T_{1} = 25 N a n d T_{2} = 75 N$

Category: GATE Mechanical Engineering 2018 set 1

Question 16:

σ_{1} a n d σ_{3}

are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

A	$\frac{σ_{1} + σ_{3}}{2}$	B	$\frac{σ_{1} - σ_{3}}{2}$
C	$\sqrt{\frac{σ_{1} + σ_{3}}{2}}$	D	$\sqrt{\frac{σ_{1} - σ_{3}}{2}}$

Category: GATE Mechanical Engineering 2018 set 1

Question 17:

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

M \ddot{x} + K x = F \cos (ω t),

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 ω is equal to

A	$\sqrt{\frac{M}{k}}$	B	$\frac{1}{2 π} \sqrt{\frac{K}{M}}$
C	$2 π \sqrt{\frac{K}{M}}$	D	$\sqrt{\frac{k}{M}}$

Category: GATE Mechanical Engineering 2018 set 1

Question 18:

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.

A	I and III	B	I and IV
C	II and III	D	II and IV

Category: GATE Mechanical Engineering 2018 set 1

Question 19:

For a two-dimensional incompressible flow field given by

\vec{u} = A (x \hat{i} - y \hat{j}),

where

A > 0

, which one of the following statements is FALSE?

A	It satisfies continuity equation
B	It is unidirectional when $x \to 0 a n d y \to \infty$ .
C	Its streamlines are given by x = y.
D	It is irrotational.

Category: GATE Mechanical Engineering 2018 set 1

Question 20:

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

A	Its pressure is less than the saturation pressure at a given temperature.
B	Its temperature is less than the saturation temperature at a given pressure.
C	Its volume is less than the volume of the saturated vapour at a given temperature.
D	Its enthalpy is less than the enthalpy of the saturated vapour at a given pressure.

Category: GATE Mechanical Engineering 2018 set 1

Question 21:

In a linearly hardening plastic material, the true stress beyond initial yielding

A	increases linearly with the true strain
B	decreases linearly with the true strain
C	first increases linearly and then decreases linearly with the true strain
D	remains constant

Category: GATE Mechanical Engineering 2018 set 1

Question 22:

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

A	groove	B	spot
C	fillet	D	plug

Category: GATE Mechanical Engineering 2018 set 1

Question 23:

Using the Taylor’s tool life equation with exponent

n = 0.5,

if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

A	4	B	2
C	1	D	0.5

Category: GATE Mechanical Engineering 2018 set 1

Question 24:

A grinding ratio of 200 implies that the

A	grinding wheel wears 200 times the volume of the material removed
B	grinding wheel wears 0.005 times the volume of the material removed
C	aspect ratio of abrasive particles used in the grinding wheel is 200
D	ratio of volume of abrasive particle to that of grinding wheel is 200

Category: GATE Mechanical Engineering 2018 set 1

Question 25:

Interpolator in a CNC machine

A	controls spindle speed	B	coordinates axes movements
C	operates tool changer	D	commands canned cycle

Category: GATE Mechanical Engineering 2018 set 1

Question 26:

The time series forecasting method that gives equal weightage to each of the m most recent observations is

A	Moving average method
B	Exponential smoothing with linear trend
C	Triple Exponential smoothing
D	Kalman Filter

Category: GATE Mechanical Engineering 2018 set 1

Question 27:

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

A	3, 3	B	3, 12
C	4, 12	D	4, 48

Category: GATE Mechanical Engineering 2018 set 1

Question 28:

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

A	33.3	B	3.33
C	0.33	D	0.0033

Category: GATE Mechanical Engineering 2018 set 1

Question 29:

A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is ____ (correct to two decimal places).

1.00 to 1.20

1.15 to 1.20

1.05 to 1.20

1.00 to 1.15

Category: GATE Mechanical Engineering 2018 set 1

Question 30:

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 __________.

0 to 1

-1 to 1

1 to 1

0 to 0

Category: GATE Mechanical Engineering 2018 set 1

Question 31:

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).

8.25 to 8.50

8.00 to 8.50

8.00 to 8.25

8.00 to 8.75

Category: GATE Mechanical Engineering 2018 set 1

Question 32:

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_{a v g}

of the fluid (in m/s) draining out at the instant shown in the figure is _____________(correct to three decimal places).

0.055 to 0.060

0.035 to 0.045

0.025 to 0.035

0.045 to 0.055

Category: GATE Mechanical Engineering 2018 set 1

Question 33:

An ideal gas undergoes a process from state 1 (

T_{1} = 300 k, p_{1} = 100 k P a

) to state 2 (

T_{2} = 600 K, p_{2} = 500 k P a)

. The specific heats of the ideal gas are :

C_{p}

= 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).

0.20 to 0.22

0.21 to 0.22

0.20 to 0.25

0.20 to 0.21

Category: GATE Mechanical Engineering 2018 set 1

Question 34:

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).

0.45 to 0.55

0.40 to 0.52

0.45 to 0.52

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 35:

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).

56.000 to 58.000

57.000 to 58.000

55.000 to 56.000

50.000 to 58.000

Category: GATE Mechanical Engineering 2018 set 1

Question 36:

Let

X_{1}, X_{2}

be two independent normal random variables with means

μ_{1}, μ_{2}

and standard deviations

σ_{1}, σ_{2},

respectively. Consider Y =

X_{1} - X_{2}; μ_{1} = μ_{2} = 1, σ_{1} = 1, σ_{2} = 2

Then,

A	Y is normally distributed with mean 0 and variance 1
B	Y is normally distributed with mean 0 and variance 5
C	Y has mean 0 and variance 5, but is NOT normally distributed
D	Y has mean 0 and variance 1, but is NOT normally distributed

Category: GATE Mechanical Engineering 2018 set 1

Question 37:

The value of the integral

$∯_{S} \vec{r} \cdot \vec{n}$ dS

over the closed surface S bounding a volume V, where

$\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$

is the position vector and

$\vec{n}$

is the normal to the surface S, is

A	V	B	2V
C	3V	D	4V

Category: GATE Mechanical Engineering 2018 set 1

Question 38:

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 10

m / s^{2}

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	1	B	2
C	4	D	∞

Category: GATE Mechanical Engineering 2018 set 1

Question 39:

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

σ_{y}

(in kPa) is

A	9.45	B	18.88
C	37.78	D	75.50

Category: GATE Mechanical Engineering 2018 set 1

Question 40:

An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is

A	240	B	-240
C	375	D	-375

Category: GATE Mechanical Engineering 2018 set 1

Question 41:

A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30° 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

A	fails only because of criterion 1	B	fails only because of criterion 2
C	fails because of both criteria 1 and 2	D	does not fail

Category: GATE Mechanical Engineering 2018 set 1

Question 42:

A self-aligning ball bearing has a basic dynamic load rating (

C_{10}

, for

10^{6}

revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in

10^{6}

revolutions) is

A	below 0.5	B	0.5 to 0.8
C	0.8 to 1.0	D	above 1.0

Category: GATE Mechanical Engineering 2018 set 1

Question 43:

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	0.5	B	1.0
C	2.0	D	4.0

Category: GATE Mechanical Engineering 2018 set 1

Question 44:

In a Lagrangian system, the position of a fluid particle in a flow is described as

x = x_{o} e^{- k t}

and

y = y_{o} e^{k t}

where t is the time while

x_{o}

y_{o}

, and k are constants. The flow is

A	unsteady and one-dimensional
B	steady and two-dimensional
C	steady and one-dimensional
D	unsteady and two-dimensional

Category: GATE Mechanical Engineering 2018 set 1

Question 45:

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

R = 1 - e^{- (n + 1),}

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

A	0.865	B	0.826
C	0.777	D	0.632

Category: GATE Mechanical Engineering 2018 set 1

Question 46:

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

53.00 to 54.00

52.00 to 53.00

52.00 to 54.00

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 47:

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

\frac{d y}{d t} = y

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).

2.55 to 2.65

2.25 to 2.50

2.50 to 2.65

2.55 to 2.75

Category: GATE Mechanical Engineering 2018 set 1

Question 48:

F (s )is the Laplace transform of the function

f (t) = 2 t^{2} e^{- t}

F(1) is ________ (correct to two decimal places).

0.40 to 0.50

0.50 to 0.52

0.48 to 0.52

0.40 to 0.50

Category: GATE Mechanical Engineering 2018 set 1

Question 49:

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).

28.9 to 31.1

29.8 to 30.1

29.8 to 31.1

28.8 to 30.1

Category: GATE Mechanical Engineering 2018 set 1

Question 50:

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 translatory motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is ______ (correct to two decimal places).

33.50 to 33.50

33.00 to 33.00

33.50 to 33.50

33.00 to 33.50

Category: GATE Mechanical Engineering 2018 set 1

Question 51:

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).

1.00 to 1.20

1.20 to 1.20

1.00 to 1.00

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 52:

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 1

c m^{2}

. Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).

9.00 to 10.50

9.50 to 10.00

9.50 to 10.50

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 53:

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 = 0.15 mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oil film is 0.04

m^{2}

. The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7×

10^{- 3}

Pa-s and acceleration due to gravity as 10

m / s^{2} .

Neglect weight of the oil. The terminal velocity V (in m/s) of the block is _________ (correct to one decimal place).

10.4 to 10.5

10.6 to 10.8

10.2 to 10.4

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 54:

A tank of volume 0.05

m^{3}

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 to two decimal places). Property data for saturated steam and water are. At 200°C,

p_{s a t}

= 1.5538 MPa

v_{f} = 0.001157 m^{3} / k g, v_{g} = 0.12736 m^{3} / k g

S_{f g} = 4.1014 K J / K g K, s_{f} = 2.3309 K J / k g K

2.55 to 2.75

2.25 to 2.75

2.35 to 2.45

2.45 to 2.55

Category: GATE Mechanical Engineering 2018 set 1

Question 55:

Steam flows through a nozzle at a mass flow rate of

\dot{m} = 0.1

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 inlet (

C_{1} \approx 0

), the velocity (

C_{2}

) of steam (in m/s) at the nozzle exit is _________ (correct to two decimal places).

An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air:

c_{p}

= 1.005 kJ/kg K,

c_{v}

= 0.718 kJ/kg K,R= 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

1405.5 to 1405.5

1405.0 to 1405.0

1405.5 to 1406.0

1402.0 to 1406.0

Category: GATE Mechanical Engineering 2018 set 1

Question 56:

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,

T_{Q}

of 25°C, as shown in the figure. The fluid is at 45°C and the surface heat transfer coefficient, h, is 10 W/

m^{2}

K. The steady state temperature,

T_{p}

, (in °C) of the side which is exposed to the fluid is_______(correct to two decimal places).

33.50 to 34.30

33.50 to 33.50

33.50 to 33.00

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 57:

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}

) is _________ (correct to three decimal places).

0.498 to 0.498

1.498 to 0.498

0.400 to 0.450

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 58:

An orthogonal cutting operation 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).

0.29 to 0.49

0.29 to 0.99

0.79 to 0.89

0.39 to 0.49

Category: GATE Mechanical Engineering 2018 set 1

Question 59:

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).

0.69 to 0.70

0.69 to 0.79

0.59 to 0.90

0.90 to 0.70

Category: GATE Mechanical Engineering 2018 set 1

Question 60:

The minimum value of 3𝑥 + 5𝑦 such that: 3𝑥 + 5𝑦 ≤ 15 4𝑥 + 9𝑦 ≤ 8 13𝑥 + 2𝑦 ≤ 2 𝑥 ≥ 0, 𝑦 ≥ 0 is _______.

0 to 1

1 to 1

0 to 0

-1 to 0

Category: GATE Mechanical Engineering 2018 set 1

Question 61:

Processing times (including setup 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).

Job	Processing time (days)	Due date (days)
A	3	8
B	7	16
C	4	4
D	9	18
E	5	17
F	13	19

5.31 to 6.35

6.31 to 7.35

6.30 to 6.30

6.31 to 6.35

Category: GATE Mechanical Engineering 2018 set 1

Question 62:

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 = 100 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).

6.00 to 7.00

7.00 to 8.00

8.00 to 9.00

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 63:

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 g = 10

m / s^{2}

, the normal force (in N) at Q is _______ (correct to two decimal places).

419.00 to 421.00

409.00 to 421.00

420.00 to 421.00

419.50 to 421.50

Category: GATE Mechanical Engineering 2018 set 1

Question 64:

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 ×

10^{- 2}

m m^{3}

/(A s), the current (in A) required is __________ (correct to two decimal places).

968.20 to 969.00

968.00 to 969.00

968.80 to 969.20

None of these

Category: GATE Mechanical Engineering 2018 set 1

Question 65:

An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air:

c_{p}

= 1.005 kJ/kg K,

c_{v}

= 0.718 kJ/kg K, R= 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

1402.0 to 1406.0

1403.0 to 1406.0

1402.0 to 1406.0

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Question 1:

“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.” The words that best fill the blanks in the above sentence are

A	principle, principal	B	principal, principle
C	principle, principle	D	principal, principal

Correct Answer : A

Question 2:

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

A	cleanliness	B	punctuality
C	frugality	D	greatness

Correct Answer : C

Question 3:

Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toy?

A	1	B	7
C	100	D	700

Correct Answer : B

Question 4:

A	1125	B	2250
C	2924	D	4500

Correct Answer : B

Question 5:

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

A	63	B	72
C	81	D	90

Correct Answer : B

Question 6:

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?

A	-3 and 3	B	-1 and 1
C	-1 and 3	D	1 and 3

Correct Answer : A

Question 7:

Given that 𝑎 and 𝑏 are integers and

α + α^{2} b^{3}

is odd, which one of the following statements is correct?

A	𝑎 and 𝑏 are both odd	B	𝑎 and 𝑏 are both even
C	𝑎 is even and 𝑏 is odd	D	𝑎 is odd and 𝑏 is even

Correct Answer : D

Question 8:

A	210 and 140	B	162.5 and 187.5
C	245 and 130	D	175 and 200

Correct Answer : All of these

Question 9:

Which of the following functions describe the graph shown in the below figure?

A	𝑦 = \|\|𝑥\| + 1\| − 2	B	𝑦 = \|\|𝑥\| − 1\| − 1
C	𝑦 = \|\|𝑥\| + 1\| − 1	D	𝑦 = \|\|𝑥 − 1\| − 1\|

Correct Answer : B

Question 10:

A	If (i) is true and (ii) is false, then (iii) is false.	B	If (i) is true and (ii) is false, then (iii) is true.
C	If (i) and (ii) are true, then (iii) is true.	D	If (i) and (ii) are false, then (iii) is false.

Correct Answer : C

Question 11:

A	1/72	B	1/55
C	1/36	D	1/27

Correct Answer : B

Question 12:

The rank of the matrix

[\begin{matrix} - 4 & 1 & - 1 \\ - 1 & - 1 & - 1 \\ 7 & - 3 & 1 \end{matrix}]

A	1	B	2
C	3	D	4

Correct Answer : B

Question 13:

According to the Mean Value Theorem, for a continuous function

f (x)

in the interval

[α, b]

,there exists a value ξ in this interval such that

\int_{a}^{b} f (x) d x =

A	f (ξ)(b-a)	B	f (b)(ξ-a)
C	f (a)(b-ξ)	D	0

Correct Answer : A

Question 14:

F (z)

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

F(z) = i z + k Re(z) + i Im(z).

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

A	0	B	1
C	-1	D	y

Correct Answer : B

Question 15:

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

The tensions in the strings are

A	$T_{1} = 100 N a n d T_{2} = 0 N$	B	$T_{1} = 0 N a n d T_{2} = 100 N$
C	$T_{1} = 75 N a n d T_{2} + 25 N$	D	$T_{1} = 25 N a n d T_{2} = 75 N$

Correct Answer : B

Question 16:

σ_{1} a n d σ_{3}

are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

A	$\frac{σ_{1} + σ_{3}}{2}$	B	$\frac{σ_{1} - σ_{3}}{2}$
C	$\sqrt{\frac{σ_{1} + σ_{3}}{2}}$	D	$\sqrt{\frac{σ_{1} - σ_{3}}{2}}$

Correct Answer : B

Question 17:

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

M \ddot{x} + K x = F \cos (ω t),

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 ω is equal to

A	$\sqrt{\frac{M}{k}}$	B	$\frac{1}{2 π} \sqrt{\frac{K}{M}}$
C	$2 π \sqrt{\frac{K}{M}}$	D	$\sqrt{\frac{k}{M}}$

Correct Answer : D

Question 18:

A	I and III	B	I and IV
C	II and III	D	II and IV

Correct Answer : B

Question 19:

For a two-dimensional incompressible flow field given by

\vec{u} = A (x \hat{i} - y \hat{j}),

where

A > 0

, which one of the following statements is FALSE?

A	It satisfies continuity equation
B	It is unidirectional when $x \to 0 a n d y \to \infty$ .
C	Its streamlines are given by x = y.
D	It is irrotational.

Correct Answer : C

Question 20:

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

A	Its pressure is less than the saturation pressure at a given temperature.
B	Its temperature is less than the saturation temperature at a given pressure.
C	Its volume is less than the volume of the saturated vapour at a given temperature.
D	Its enthalpy is less than the enthalpy of the saturated vapour at a given pressure.

Correct Answer : A

Question 21:

In a linearly hardening plastic material, the true stress beyond initial yielding

A	increases linearly with the true strain
B	decreases linearly with the true strain
C	first increases linearly and then decreases linearly with the true strain
D	remains constant

Correct Answer : A

Question 22:

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

A	groove	B	spot
C	fillet	D	plug

Correct Answer : C

Question 23:

Using the Taylor’s tool life equation with exponent

n = 0.5,

if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

A	4	B	2
C	1	D	0.5

Correct Answer : A

Question 24:

A grinding ratio of 200 implies that the

A	grinding wheel wears 200 times the volume of the material removed
B	grinding wheel wears 0.005 times the volume of the material removed
C	aspect ratio of abrasive particles used in the grinding wheel is 200
D	ratio of volume of abrasive particle to that of grinding wheel is 200

Correct Answer : B

Question 25:

Interpolator in a CNC machine

A	controls spindle speed	B	coordinates axes movements
C	operates tool changer	D	commands canned cycle

Correct Answer : B

Question 26:

The time series forecasting method that gives equal weightage to each of the m most recent observations is

A	Moving average method
B	Exponential smoothing with linear trend
C	Triple Exponential smoothing
D	Kalman Filter

Correct Answer : A

Question 27:

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

A	3, 3	B	3, 12
C	4, 12	D	4, 48

Correct Answer : C

Question 28:

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

A	33.3	B	3.33
C	0.33	D	0.0033

Correct Answer : C

Question 29:

Correct Answer : 1.00 to 1.20

Question 30:

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 __________.

Correct Answer : 1 to 1

Question 31:

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).

Correct Answer : 8.00 to 8.50

Question 32:

u_{a v g}

of the fluid (in m/s) draining out at the instant shown in the figure is _____________(correct to three decimal places).

Correct Answer : 0.045 to 0.055

Question 33:

An ideal gas undergoes a process from state 1 (

T_{1} = 300 k, p_{1} = 100 k P a

) to state 2 (

T_{2} = 600 K, p_{2} = 500 k P a)

. The specific heats of the ideal gas are :

C_{p}

= 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).

Correct Answer : 0.20 to 0.22

Question 34:

Correct Answer : 0.45 to 0.52

Question 35:

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).

Correct Answer : 57.000 to 58.000

Question 36:

Let

X_{1}, X_{2}

be two independent normal random variables with means

μ_{1}, μ_{2}

and standard deviations

σ_{1}, σ_{2},

respectively. Consider Y =

X_{1} - X_{2}; μ_{1} = μ_{2} = 1, σ_{1} = 1, σ_{2} = 2

Then,

A	Y is normally distributed with mean 0 and variance 1
B	Y is normally distributed with mean 0 and variance 5
C	Y has mean 0 and variance 5, but is NOT normally distributed
D	Y has mean 0 and variance 1, but is NOT normally distributed

Correct Answer : B

Question 37:

The value of the integral

$∯_{S} \vec{r} \cdot \vec{n}$ dS

over the closed surface S bounding a volume V, where

$\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$

is the position vector and

$\vec{n}$

is the normal to the surface S, is

A	V	B	2V
C	3V	D	4V

Correct Answer : C

Question 38:

m / s^{2}

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	1	B	2
C	4	D	∞

Correct Answer : C

Question 39:

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

σ_{y}

(in kPa) is

A	9.45	B	18.88
C	37.78	D	75.50

Correct Answer : C

Question 40:

A	240	B	-240
C	375	D	-375

Correct Answer : C

Question 41:

A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30° as shown in the figure.

A	fails only because of criterion 1	B	fails only because of criterion 2
C	fails because of both criteria 1 and 2	D	does not fail

Correct Answer : C

Question 42:

A self-aligning ball bearing has a basic dynamic load rating (

C_{10}

, for

10^{6}

revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in

10^{6}

revolutions) is

A	below 0.5	B	0.5 to 0.8
C	0.8 to 1.0	D	above 1.0

Correct Answer : A

Question 43:

A	0.5	B	1.0
C	2.0	D	4.0

Correct Answer : B

Question 44:

In a Lagrangian system, the position of a fluid particle in a flow is described as

x = x_{o} e^{- k t}

and

y = y_{o} e^{k t}

where t is the time while

x_{o}

y_{o}

, and k are constants. The flow is

A	unsteady and one-dimensional
B	steady and two-dimensional
C	steady and one-dimensional
D	unsteady and two-dimensional

Correct Answer : B

Question 45:

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

R = 1 - e^{- (n + 1),}

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

A	0.865	B	0.826
C	0.777	D	0.632

Correct Answer : D

Question 46:

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

Correct Answer : 52.00 to 54.00

Question 47:

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

\frac{d y}{d t} = y

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).

Correct Answer : 2.55 to 2.65

Question 48:

F (s )is the Laplace transform of the function

f (t) = 2 t^{2} e^{- t}

F(1) is ________ (correct to two decimal places).

Correct Answer : 0.48 to 0.52

Question 49:

Correct Answer : 29.8 to 30.1

Question 50:

Correct Answer : 33.00 to 33.50

Question 51:

Correct Answer : 1.00 to 1.20

Question 52:

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 1

c m^{2}

. Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).

Correct Answer : 9.50 to 10.50

Question 53:

m^{2}

. The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7×

10^{- 3}

Pa-s and acceleration due to gravity as 10

m / s^{2} .

Neglect weight of the oil. The terminal velocity V (in m/s) of the block is _________ (correct to one decimal place).

Correct Answer : 10.6 to 10.8

Question 54:

A tank of volume 0.05

m^{3}

p_{s a t}

= 1.5538 MPa

v_{f} = 0.001157 m^{3} / k g, v_{g} = 0.12736 m^{3} / k g

S_{f g} = 4.1014 K J / K g K, s_{f} = 2.3309 K J / k g K

Correct Answer : 2.45 to 2.55

Question 55:

Steam flows through a nozzle at a mass flow rate of

\dot{m} = 0.1

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 inlet (

C_{1} \approx 0

), the velocity (

C_{2}

) of steam (in m/s) at the nozzle exit is _________ (correct to two decimal places).

An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air:

c_{p}

= 1.005 kJ/kg K,

c_{v}

= 0.718 kJ/kg K,R= 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

Correct Answer : 1402.0 to 1406.0

Question 56:

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,

T_{Q}

of 25°C, as shown in the figure. The fluid is at 45°C and the surface heat transfer coefficient, h, is 10 W/

m^{2}

K. The steady state temperature,

T_{p}

, (in °C) of the side which is exposed to the fluid is_______(correct to two decimal places).

Correct Answer : 33.50 to 33.50

Question 57:

ε_{B}

) is _________ (correct to three decimal places).

Correct Answer : 0.498 to 0.498

Question 58:

Correct Answer : 0.39 to 0.49

Question 59:

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).

Correct Answer : 0.69 to 0.70

Question 60:

The minimum value of 3𝑥 + 5𝑦 such that: 3𝑥 + 5𝑦 ≤ 15 4𝑥 + 9𝑦 ≤ 8 13𝑥 + 2𝑦 ≤ 2 𝑥 ≥ 0, 𝑦 ≥ 0 is _______.

Correct Answer : 0 to 0

Question 61:

Job	Processing time (days)	Due date (days)
A	3	8
B	7	16
C	4	4
D	9	18
E	5	17
F	13	19

Correct Answer : 6.31 to 6.35

Question 62:

Correct Answer : 8.00 to 9.00

Question 63:

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 g = 10

m / s^{2}

, the normal force (in N) at Q is _______ (correct to two decimal places).

Correct Answer : 419.00 to 421.00

Question 64:

10^{- 2}

m m^{3}

/(A s), the current (in A) required is __________ (correct to two decimal places).

Correct Answer : 968.80 to 969.20

Question 65:

An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air:

c_{p}

= 1.005 kJ/kg K,

c_{v}

= 0.718 kJ/kg K, R= 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

Correct Answer : 1402.0 to 1406.0

Back
Scrore Card
Total Question		Total Attempted
Correct Answers		Incorrect Answers
Score

A	𝑦 = \|\|𝑥\| + 1\| − 2	B	𝑦 = \|\|𝑥\| − 1\| − 1
C	𝑦 = \|\|𝑥\| + 1\| − 1	D	𝑦 = \|\|𝑥 − 1\| − 1\|

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