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QUESTION: 1

Direction

Q. No. 1 - 5 Carry One Mark Each

Q. A right –angled cone (with base radius 5 cm and height 12 cm), 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?

Solution:

According to the given information about the figure, the new shape is as follows

QUESTION: 2

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

Solution:

Put all the values either in ascending or descending order first. Now number of observations equal to 100 which is even

The median of these values = Avg of two middle most observations. i.e 50th and 51st observation

QUESTION: 3

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

Solution:

QUESTION: 4

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 of cars owned by S is

Solution:

QUESTION: 5

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

Solution:

QUESTION: 6

Directions

Q. No. 6- 10 Carry Two Marks Each

Q.

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?

Solution:

QUESTION: 7

“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?

Solution:

QUESTION: 8

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

Which one of the following options is correct?

Solution:

QUESTION: 9

Let S_{1} be the plane figure consisting of the points (x,y) given by the inequalities |x - 1|≤2 and |y+2|≤ 3. Let S_{2} be the plane figure given by the inequalities x - y ≥ -2, y ≥1, and x ≤3 Let S be the union of S_{1} and S_{2}. The area of S is.

Solution:

QUESTION: 10

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

Solution:

*Answer can only contain numeric values

QUESTION: 11

Directions

Q. No. 1 to 25 Carry One Mark Each

Q. 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.

Solution:

QUESTION: 12

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

Solution:

u(x,y) = f(x-cy)

*Answer can only contain numeric values

QUESTION: 13

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 at t = 5s is______m.

Solution:

QUESTION: 14

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

is given by

Solution:

QUESTION: 15

The differential equation with the two boundary conditions

Solution:

*Answer can only contain numeric values

QUESTION: 16

Metricthread 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 _________

Solution:

*Answer can only contain numeric values

QUESTION: 17

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.

Solution:

C_{v}= 2.5R_{v} where (R_{v}= 8.314J/moLK)

ΔT=100K

ΔH=?

ΔH=C_{p}ΔT

∴ C_{p }-C_{v} = R_{v}

QUESTION: 18

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

Solution:

QUESTION: 19

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

Solution:

*Answer can only contain numeric values

QUESTION: 20

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 ___________.

Solution:

QUESTION: 21

Which one of the following is NOT a rotating machine?

Solution:

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

QUESTION: 22

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

Solution:

*Answer can only contain numeric values

QUESTION: 23

Water (density = 1000 kg/m^{3}) 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_____

Solution:

Power = w Q h_{L} (Power is required to overcome losses, h_{L})

QUESTION: 24

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?

Solution:

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

QUESTION: 25

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

Solution:

QUESTION: 26

The product of eigenvalues of the matrix P is

Solution:

From the property of eigenvalues Product of eigenvalues = |P|

= 2

QUESTION: 27

Solution:

QUESTION: 28

The value of

Solution:

QUESTION: 29

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

Solution:

By doubling welding speed, Area reduces by 50%

*Answer can only contain numeric values

QUESTION: 30

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

Solution:

The Probabilities corresponding to the outcomes are given below:

QUESTION: 31

Consider the two dimensional velocity field given by

where a_{1},b_{1},a_{2} & b_{2} are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?

Solution:

QUESTION: 32

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

Solution:

*Answer can only contain numeric values

QUESTION: 33

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.

Solution:

*Answer can only contain numeric values

QUESTION: 34

In a metal forming operation when the material has just started yielding, the principal stresses are σ_{1} = +180 MPa, σ_{2} = -100 MPa, σ_{3} = 0. Following Von Mises criterion, the yield stress is ________ MPa.

Solution:

As per Von-Mises criteria

QUESTION: 35

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

Solution:

QUESTION: 36

Directions

Q. No. 36 to 65 Carry Two Marks Each

Q.

A parametric curve defined by x = cos (πu/2), y= sin (πu/2)

in the range 0≤ u ≤1 is rotated

about the X – axis by 360 degrees. Area of the surface generated is.

Solution:

QUESTION: 37

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 µm ) is

Solution:

QUESTION: 38

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 systems is.

Solution:

Max moment of inertia of Rod.

*Answer can only contain numeric values

QUESTION: 39

A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm^{2}, 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.

Solution:

Given that

m = 100kg, g =10 m /sec^{2} , E= 100GPa H=10mm, L =1m= 100mm, A =100mm^{2}

From the given figure, we can say that this is case of Impact loading, We know that, stress due to Impact load is

*Answer can only contain numeric values

QUESTION: 40

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.

Solution:

Given that m = 1kg, R = 400 kJ/kgK, CV = 1000 J/kgK 11

P_{1} = 1 bar, T_{1}= 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,

*Answer can only contain numeric values

QUESTION: 41

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.

Solution:

*Answer can only contain numeric values

QUESTION: 42

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100rpm. 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 _________.

Solution:

T_{s= }50 , T_{p}= 25, T_{R}=100

*Answer can only contain numeric values

QUESTION: 43

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.

Solution:

*Answer can only contain numeric values

QUESTION: 44

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.

Solution:

*Answer can only contain numeric values

QUESTION: 45

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 ____________.

Solution:

Let x_{1 }= No. of units of P

x_{2}= No. of units of Q

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

QUESTION: 46

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 :

Solution:

Centre of circular arc is (30, 35)

*Answer can only contain numeric values

QUESTION: 47

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 F_{12}=0.5, T_{1}=800K, T_{2}=600K, Tsurrounding=300K and Stefan Boltzmann constant, σ = 5.67 x 10^{-8} W / ( m_{2}K_{4} ) , the heat transfer rate from Surface 2 to the surrounding environment is ____________ kW.

Solution:

Given that two black surfaces 'AB' and 'BC' Length of AB = 5m, BC = 6 m And temperature of Surface '1' ( T_{BC} = T_{1}) = 800^{o }K

Temperature of surface '2' (T_{AB }= T_{2 }= 600^{o} K )

Temperature of surroundings ( T_{3} ) = 300^{o }K

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

QUESTION: 48

Consider the matrix.

Which one of the following statements about P is INCORRECT?

Solution:

∴ P is an orthogonal matrxi

∴ (A) Is correct ⇒ Inverse of P is its transpose only

∴ (B) and (C) both are correct

∴ (D) is incorrect

*Answer can only contain numeric values

QUESTION: 49

The Pressure ratio across a gas turbine (for air, specific heat at constant pressure, c_{p} = 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.

Solution:

C_{p} = 1040J/KgK ,r = 1.4

P_{2}/P_{1} = 10, T_{3 }= 1200K

QUESTION: 50

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 α.

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

Solution:

*Answer can only contain numeric values

QUESTION: 51

For the vector

is ———

Solution:

for any vector V

*Answer can only contain numeric values

QUESTION: 52

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.

Solution:

*Answer can only contain numeric values

QUESTION: 53

A machine element has an ultimate strength (σ_{u}) of 600 N/mm^{2}, and endurance limit ( σ_{en} ) of 250 N/mm^{2}. 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/mm^{2}.

Solution:

σ_{u} = 600MPa

σ_{en} = 250MPa

N = 10000 cycles

σ_{max} = 386.19MPa

*Answer can only contain numeric values

QUESTION: 54

A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s^{2} 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.

Solution:

Apply Bernoulli's between (1) and (2)

*Answer can only contain numeric values

QUESTION: 55

Air contains 79% N_{2 }and 21% O_{2} on a molar basis. Methane (CH_{4}) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N_{2} in the products is ________________

Solution:

QUESTION: 56

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.

Solution:

*Answer can only contain numeric values

QUESTION: 57

Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×10^{7} W/m^{3}. 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.

Solution:

Given that, heat is generated uniformly i.e.,

g = 4x10^{7} W/m^{3}Diameter at the rod (d) = 10 mm

Thermal conductivity of the rod (K) = 25 W/mK

W.K.T for steady state, with internal heat generation, the conduction equation will be,

The above equation will become

QUESTION: 58

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.

Solution:

QUESTION: 59

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.

Solution:

*Answer can only contain numeric values

QUESTION: 60

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100mm^{2}. 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.

Solution:

Given that

P=10kN =10x10^{3}N , A = 100mm^{2}

QUESTION: 61

Consider steady flow of an incompressible fluid through two long and straight pipes of diameters d_{1} and d_{2} 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,

is given by

Solution:

QUESTION: 62

The velocity profile inside the boundary layer for flow over a flat plate is given as

where U_{∝} is the free stream velocity and d is the local boundary layer thickness. If δ^{*} is the local displacement thickness, the value of

Solution:

QUESTION: 63

For a steady flow, the velocity field is

The magnitude of the

acceleration of a particle at (1, -1) is

Solution:

*Answer can only contain numeric values

QUESTION: 64

Two cutting tools with tool life equations given below are being compared:

Tool 1: VT^{0.1}=150

Tool 2: VT^{0.3}= 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.

Solution:

At Breakeven point

T_{1}=T_{2}

*Answer can only contain numeric values

QUESTION: 65

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,ε_{xx} =0.001 , ε_{yy }=0.002, γ_{xy }=0.003. The deformed length of the elongated diagonal, up to three decimal places, is _________ units.

Solution:

Given that

ε_{xy} = 0.001, ε_{xy }= 0.002, γ_{xy} = 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'

ε_{θ} = ?

### MCQ: Mechanical Engineering, GATE

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