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65 Questions MCQ Test - Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz for GATE 2024 is part of GATE preparation. The Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz questions and answers have been prepared according to the GATE exam syllabus.The Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz MCQs are made for GATE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz below.
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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 1

A motor driving a solid circular steel shaft transmits 40kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is ________MPa.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 1

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 2

Consider the following partial differential equation for u(x,y) with the constant c>1 : 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 2

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 3

The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered by the particle from t = 0 to t= 5 s is __________m.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 3

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 4

The damping ratio for a viscously damped spring mass system, governed by the relationship 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 4

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 5

The differential equation    + 16y = 0 for y (x) with the two boundary conditions 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 5

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 6

Metric thread of 0.8 mm pitch is to be cut on a lathe. Pitch of the lead screw is 1.5 mm. If the spindle rotates at 1500 rpm, the speed of rotation of the lead screw (rpm) will be _________

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 6

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 7

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t2, q (t)= t, where t is time. The kinetic energy of the particle at time t = 2 is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 7

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 8

The Poisson‟s ratio for a perfectly incompressible linear elastic material is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 8

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 9

A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300K. The Coefficient of Performance (COP) of the heat pump is ___________.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 9

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 10

Which one of the following is NOT a rotating machine?

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 10

In the given options all the pumps have rotating machine elements except Jet pump.

Centrifugal pump: It has rotating part eg.,impeller, Vane.
Gear Pump: In this pump there is gear mechanism which is rotating part.
Jet Pump: Jet pump utilizes ejector principle which have nozzle and diffuser not rotating parts.
Vane Pump: It consist of rotating disc which called as rotor in which number of radial slots are there where sliding vanes is inserted
Schematic Diagram of Jet Pump

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 11

Consider the schematic of a riveted lap joint subjected to tensile load F, as shown below. Let d be the diameter of the rivets, and Sf be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 11

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 12

Water (density =1000 kg/m3) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s. If the pressure drop across the pipe is 100 kPa, the minimum power required to pump the water across the pipe, in watts, is _______

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 12

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 13

For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 13

The average velocity in pipe flow always be same either for developing flow or fully developed flow.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 14

Cylindrical pins of diameter 15±0.020 mm are being produced on a machine. Statistical quality control tests show a mean of 14.995 mm and standard deviation of 0.004mm. The process capability index Cp is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 14

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 15

The product of Eigen values of the matrix P is 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 15

We know that, product of eigen values of P = determinant of P
= 2 (3- 6) - 0 +1(8)

= -6 +8

= 2

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 16

Match the processes with their characteristics. 

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 17

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 17

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 18

In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 18

By doubling welding speed, Area reduces by 50%

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 19

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is 


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 19

The Probabilities corresponding to the outcomes are given below:

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 20

Consider the two dimensional velocity field given by  wher a , b , a and b are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible? 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 20

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 21

Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 21

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 22

Saturated steam at 100°C condenses on the outside of a tube. Cold fluid enters the tube at 20° C and exists at 50°C. The value of the Log Mean Temperature Difference (LMTD) is ________°C.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 22

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 23

In a metal forming operation when the material has just started yielding, the principal stresses are σ1 = +180 MPa, σ2 = -100 MPa, σ3 = 0. Following Von Mises criterion, the yield stress is ________ MPa.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 23

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 24

In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 24

For mild, steel stress-strain curve is :

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 25

A parametric curve defined by x     in the range 0<u<1 is rotated 
about the X – axis by 360 degrees. Area of the surface generated is.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 25

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 26

Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is 20 mm, The central line average surface roughness Ra (in mm ) is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 26

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 27

 A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L/3 from one of its ends. The bar is further supported using springs, each of stiffness k, located at the two ends. A particle of mass m = M/4 is fixed at one end of the bar, as shown in the figure.For small rotations of the bar about O, the natural frequency of the system is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 27

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 28

A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm2, length = 1m, Young‟s moduls = 100 GPa) from a height H of 10mm as shown (Figure is not to scale). If g = 10m/s2, the maximum compression of the elastic bar is _______ mm.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 28

Given that
m = 100kg, g = 10 m sec2 , E = 100GPa
H = 10mm, L = 1m 100mm,
A = 100mm2
From the given figure, we can say that this is case of Impact loading, We know that, stress due to Impact load is

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 29

One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at constant volume, cn = 1000J/kg.K) at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100kJ of work is done on the system by a stirrer. The increase in entropy of the system is _________ J/K.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 29

Given that m = 1kg, R = 400 kJ/kgK, CV = 1000 J/kgK
P1 = 1 bar, T1 = 300 K

Since the gas is contained in a sealed rigid cylinder, and given that adiabatic process is done to the system, means no heat is transferred from/to the system, Q = 0 And we know from first law of thermo dynamics,

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 30

The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 30

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 31

For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 31

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 32

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100 rpm. Let the number of teeth on the sun, planet and outer gears to be 50, 25, and 100, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ____________.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 32

TS = 50
TP=25
TR=100

N x y 100            ...(1)
NR = y (50/100) x = 0
y = 0.5x                ... (2)
x+ 0.5x = 10
x = 100/1.5 = 66.66rpm

y 33.34 rpm

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 33

Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30°C and the relative humidity is 55%. Given that the saturation pressure of water at 30°C is 4246 Pa, the mass of water vapor per kg of dry air is _____________ grams.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 33

Total pressure p=100kpa

temperature t=30 degree c

relative humidity

*Answer can only contain numeric values
Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 34

Following data refers to the jobs (P, Q, R, S) which have arrived at a machine for scheduling. The shortest possible average flow time is ___________ days.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 34

For shortest avg. flow time SPT rule is used

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 35

Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ____________.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 35

Let x1 = No. of units of P
x2 = No. of units of Q

So, for maximum profit, No. of units of P produced is 15 units.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 36

Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below:
--------------------------------
N60  G01  X 30  Y  55  Z – 5 F 50
N70  G02  X 50  Y  35  R 20
N80  G01  Z 5
--------------------------------
The coordinates of the centre of the circular arc are :

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 36

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 37

Two black surfaces, AB and BC, of lengths 5m and 6m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor F12=0.5, T1=800K, T2=600K, Tsurrounding=300K and Stefan Boltzmann constant, 
s = ´ the heat transfer rate from Surface 2 to the surrounding environment is ____________ kW.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 37

Given that two black surfaces `AB` and `BC`
Length of AB = 5m, BC = 6 m
And temperature of
Surface `1` (TBC = T1 ) = 800°K
Temperature of surface `2`(TAB = T2 = 600°K)
Temperature of surroundings (T3) = 300° K

Using resistance concept we can draw as follows Since surfaces are black and area of surrounding is large we can write

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 38

Consider the matrix 

Q. Which one of the following statements about P is INCORRECT? 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 38

P is an orthogonal matrix
(A) Is correct ⇒ Inverse of P is its transpose only
(B) and (C) both are correct
(D) is incorrect

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 39

The Pressure ratio across a gas turbine (for air, specific heat at constant pressure, pc = 1040J / kg. K and ratio of specific heats, γ = 1.4) is 10. If the inlet temperature to the turbine is 1200K and the isentropic efficiency is 0.9, the gas temperature at turbine exit is ______ K.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 39

CP = 1040 J/kg.K , r = 1.4
P2 / P1 =  10, T3 = 1200K

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 40

An initially stress-free massless elastic beam of length L and circular cross-section with diameter d (d << L) is held fixed between two walls as shown. The beam material has Young‟s modulus E and coefficient of thermal expansion a .

If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 40

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 41


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 41

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 42

A 10 mm deep cylindrical cup with diameter of 15mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto 2 decimal points accuracy) of the blank is _________ mm.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 42

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 43

A machine element has an ultimate strength (σu) of 600 N/mm2, and endurance limit (sen) of 250 N/mm2. The fatigue curve for the element on log-log plot is shown below. If the element is to be designed for a finite of 10000 cycles, the maximum amplitude of a completely reversed operating stress is _________ N/mm2.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 43

σu = 600MPa
σen = 50MPa
N = 10000 cycle

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 44

A sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/s. Assume acceleration due to gravity as 9.8 m/s2 and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is  ________________m/s


*Answer can only contain numeric values
Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 45

Air contains 79% N2 and 21% O2 on a molar basis. Methane (CH4) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N2 in the products is ________________


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 45

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 46

P(0,3), Q(0.5, 4), and R (1,5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson‟s rule within limits x = 0 and x =1 for the curve. The difference between the two results will be.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 46

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 47

Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107 W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 47

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 48

Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 48

 

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 49

A block of length 200mm is machined by a slab milling cutter 34mm in diameter. The depth of cut and table feed are set at 2mm and 18mm/minute, respectively. Considering the approach and the over travel of the cutter to be same, the minimum estimated machining time per pass is _____________ minutes.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 49

Milling Time 

Where, D = Dia of cutter (mm), d = depth of cut (mm)
L = length f = feed (mm/ min)

*Answer can only contain numeric values
Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 50

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm2. Its elastic modulus varies along its length as given by E(x) = 100e-x GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 50

P = 10kN = 10 *103 N, A = 100mm2

Total change in the length of the bar 

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 51

Consider steady flow of an incompressible fluid through two long and straight pipes of diameters d1 and d2 arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, f = K(Re)- n where K and n are known positive constants and Re is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe 1 to that in pipe 2, 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 51

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 52

The velocity profile inside the boundary layer for flow over a flat plate is given as    is the free stream velocity and d is the local boundary layer thickness. If d * is the local displacement thickness, the value of 

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 52

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 53

For a steady flow, the velocity field is   The magnitude of the 
acceleration of a particle at (1, -1) is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 53

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Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 54

Two cutting tools with tool life equations given below are being compared: Tool 1: VT0.1=150 Tool 2: VT0.3=300 Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ________ m/minute.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 54

At Breakeven point
T1 = T2

*Answer can only contain numeric values
Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 55

A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains, εxx = 0.001, εyy = 0.002, γxy = 0.003. The deformed length of the elongated diagonal, up to three decimal places, is _________ units.


Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 55

εxx = 0.001, εyy = 0.002
rxy = 0.003
Length of the diagonal (PR) 

To find the diagonal (PR) strain, the direction of the plane angle from the +ve x-axis will from `R` towards `P`
 εθ= ?

Where θ = 180 + tan -1 (3 / 4) 216.87°

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 56

A right – angled cone (with base radius 5cm and height 12cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.

By what angle (in radians) about P does the cone travel?

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 56

Circumference of base circle = length of arc QR
(2πr) Rθ (R = Slant height of the Cone = 13 cm) 

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 57

In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000,8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 57

All the values put either in ascending or descending order first.
Now number of observations equal to 100 [even]
The median of these values = Avg of two middle most observations.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 58

As the two speakers became increasingly agitated, the debate became __________.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 58

Lukewarm means mild; other options like poetic and forgiving are not suitable here. Hence heated is the correct answer.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 59

P,Q, and R talk about S‟s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one Car. Only one of P, Q and R is right the number cars owned by S is.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 59

P States that S has atleast 3 cars, i.e., >3
Q believes that S has less than 3 cars, i.e., < 3
R indicates that S has atleast one car>1
P`s and Q`s statements are exactly opposite in nature and R`s statement is proportional to P`s statement.

From the given data, only one person statement is right as it mean that two persons statements are wrong, i.e., P and R wrong when S has zero cars.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 60

He was one of my best __________ and I felt his loss _________.

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 60

You may have thought that A is correct option .Well that’s how we learn new things the negative marks way

The phrase “one of” implies that you are describing a single (singular) thing out of many (plural) things. So the correct statements is “one of my best friends,”.

After “one of” always use plural countable noun like – “One of the students”.  It is quite logical and straight forward- When we say one of, we assume that there are more than two.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 61

Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, “There is no way you are good enough to play for your country." James replied, “Maybe not, but at least I am the best player in my own family.” Which one of the following can be inferred from this conversation?

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 62

“Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that `A stronger instance than this of European prejudice with relation to this country has never come under my observations‟ had no effect on his superiors.” According to this paragraph, which of the statements below is most accurate?

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 63

The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8(in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 litre of milk is plotted as a function of time, at two different temperatures, 25°C and 37°C Consider the following statements based on the data shown above:


(i) The growth in bacterial population stops earlier at 37°C as compared to 25°C
(ii) The time taken for curd formation at 25°C is twice the time taken at 37°C


Q. Which one of the following options is correct?

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 63

From the graph, Statement (i) is correct,
The time taken for curd formation @25° C= 120 min,
the time taken for curd formation @ 37°C= 80 min, hence (ii) is incorrect.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 64

Let S1 be the plane figure consisting of the points (x,y) given by the inequalities  and   Let S2 be the plane figure given by the inequalities x - y > - 2, y > 1, and  x < 3 Let S be the union of S1 and S2. The area of S is.

Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 65

What is the sum of the missing digits in the subtraction problem below?

Detailed Solution for Mechanical Engineering - ME 2017 GATE Paper MCQ Quiz - Question 65

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