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*Answer can only contain numeric values

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.

Solution:

QUESTION: 2

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

Solution:

*Answer can only contain numeric values

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.

Solution:

QUESTION: 4

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

Solution:

QUESTION: 5

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

Solution:

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 _________

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

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

Solution:

*Answer can only contain numeric values

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 ___________.

Solution:

QUESTION: 10

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.

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

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.

Solution:

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 _______

Solution:

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?

Solution:

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

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 C_{p} is

Solution:

QUESTION: 15

The product of Eigen values of the matrix P is

Solution:

We know that, product of eigen values of P = determinant of P

= 2 (3- 6) - 0 +1(8)

= -6 +8

= 2

QUESTION: 16

Match the processes with their characteristics.

Solution:

QUESTION: 17

Solution:

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

Solution:

By doubling welding speed, Area reduces by 50%

*Answer can only contain numeric values

QUESTION: 19

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: 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?

Solution:

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.

Solution:

*Answer can only contain numeric values

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.

Solution:

*Answer can only contain numeric values

QUESTION: 23

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:

QUESTION: 24

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

Solution:

**For mild, steel stress-strain curve is :
**

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.

Solution:

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

Solution:

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

Solution:

*Answer can only contain numeric values

QUESTION: 28

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/s^{2}, 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: 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.

Solution:

Given that m = 1kg, R = 400 kJ/kgK, C_{V} = 1000 J/kgK

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: 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.

Solution:

*Answer can only contain numeric values

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.

Solution:

*Answer can only contain numeric values

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 ____________.

Solution:

T_{S} = 50

T_{P}=25

T_{R}=100

N x y 100 ...(1)

N_{R = y (50/100) x = 0}

y = 0.5x ... (2)

x+ 0.5x = 10

x = 100/1.5 = 66.66rpm

y 33.34 rpm

*Answer can only contain numeric values

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.

Solution:

Total pressure p=100kpa

temperature t=30 degree c

relative humidity

*Answer can only contain numeric values

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.

Solution:

For shortest avg. flow time SPT rule is used

*Answer can only contain numeric values

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 ____________.

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: 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 :

Solution:

*Answer can only contain numeric values

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 F_{12}=0.5, T_{1}=800K, T_{2}=600K, T_{surrounding}=300K and Stefan Boltzmann constant,

s = ´ 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^{°}K

Temperature of surface `2`(T_{AB }= T_{2} = 600^{°}K)

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

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

QUESTION: 38

Consider the matrix

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

Solution:

P is an orthogonal matrix

(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: 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.

Solution:

C_{P} = 1040 J/kg.K , r = 1.4

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

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

Solution:

*Answer can only contain numeric values

QUESTION: 41

Solution:

*Answer can only contain numeric values

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.

Solution:

*Answer can only contain numeric values

QUESTION: 43

A machine element has an ultimate strength (σ_{u}) of 600 N/mm^{2}, and endurance limit (sen) 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} = 50MPa

N = 10000 cycle

*Answer can only contain numeric values

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/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:

*Answer can only contain numeric values

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 ________________

Solution:

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.

Solution:

*Answer can only contain numeric values

QUESTION: 47

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

Solution:

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.

Solution:

*Answer can only contain numeric values

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.

Solution:

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

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.

Solution:

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

Total change in the length of the bar

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,

Solution:

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

Solution:

QUESTION: 53

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: 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.

Solution:

At Breakeven point

T_{1} = T_{2}

*Answer can only contain numeric values

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, 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:

ε_{xx} = 0.001, ε_{yy} = 0.002

r_{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}= ?

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

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?

Solution:

Circumference of base circle = length of arc QR

(2πr) Rθ (R = Slant height of the Cone = 13 cm)

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

Solution:

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.

QUESTION: 58

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

Solution:

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

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.

Solution:

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.

QUESTION: 60

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

Solution:

**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.**

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?

Solution:

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?

Solution:

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?**

Solution:

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.

QUESTION: 64

Let S1 be the plane figure consisting of the points (x,y) given by the inequalities and 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: 65

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

Solution:

### MCQ: Mechanical Engineering, GATE

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