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This mock test of Mechanical Engineering (ME) : Mock Test 6 For GATE for GATE helps you for every GATE entrance exam.
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QUESTION: 1

**Question 1 to 5 carry One Mark each**

**Q.**

**Even as the --------- else where in the world are struggling, to come out of recession, Indian consumers are splurging on consumer goods and to ----- this growth, companies are investing heavily in various sectors.**

Solution:

QUESTION: 2

In the olympic games, the flags of six nations were flown on the masts in the following way. T he flag of

America was to the left of Indian tricolor and to the right of the flag of france. T he flag of australia was on

the right of the indian flag but was to the left of the flag of japan, which was to the left of the flag of china.

Find the two flags which are in the centre.

Solution:

India and Australia

[France – America – India –Aus. –Japan – China]

QUESTION: 3

From the given equilateral triangle below, A, B and C run along. T he sides in clockwise direction and stop

aft er coming sides. Which of the following statements is true?

Solution:

A is the S–W of B

QUESTION: 4

In the following questions, a sent ence has been given in direct/indirect speech.

Nitin said to me, “why don’t you come with us? why do you want to be so unsocial.

Solution:

QUESTION: 5

**Direction (5) Spotting the error**

/In order to transfer **(A)**

/ branch licenses for one (B)

/ bank to anot her you require special approval from RBI **(C)**

/ No error **(D)**.

Solution:

QUESTION: 6

Question 6 to 10 carry Two Marks each

Q.

In an NGO, the daily average ages of 20 illiterate employee is decreased from Rs. 25 to Rs. 10. T hus the

average salary of all the literate (educated) and illiterate employees is decreased by Rs. 10 perday. T he

number of educated employees working in the NGO is :

Solution:

QUESTION: 7

**Common Data Question (7-8)**

The ratio of the percentage share of Dairy Milk to that of ot her is?

Solution:

QUESTION: 8

If in the next year, Crackle and Dairy Milk decided to join hands and increase their market share from their

combined existing share by 20%. What will be their combined sales if the mark size remains the same?

Solution:

QUESTION: 9

Simple interest on a certain amount is 9/16 of the principle. If the number represent ing the rate of intersest in percent and time in years be equal. T hen time, for when the principal is lent out is,

Solution:

QUESTION: 10

A boat sails across a river with a velocity of 10 km/hr. If resultant boat velocity is 14 km/hr, then what is the velocity of river water?

Solution:

QUESTION: 11

Question 11 to 35 carry One Mark each

Q.

If the probability for A to fail in an examination is .2 and that for B is .3 then the probability that either

A or B fails is

Solution:

QUESTION: 12

Eigen value of unit ary matrix are always

Solution:

T he eigen value of unit ary matrix are always of unit modulus.

*Answer can only contain numeric values

QUESTION: 13

If t hen the value of

______________

Solution:

*Answer can only contain numeric values

QUESTION: 14

A rigid wheel 1.25 diameter is to be provide with a t hin steel t yre. If the stress in the steel t yre is not

to exceed 140 N/mm^{2}, what is the int ernal diameter of the tyre? Take E = 2 × 10^{5} N/mm^{2} and

α = 1.2 × 10^{-5} per ^{o}C ________________

Solution:

QUESTION: 15

In case of solution of a two variable linear programming problem by graphical method one constraints line

comes parallel t o the objective function line which one of the following is correct?

Solution:

QUESTION: 16

If 'u' and 'v' the component of velocity in x-direction and y-direction respectively are given u = ax+by and

v = cx + dy then the condition to be satisfy is

Solution:

QUESTION: 17

T he two links OA and OB are connected by a pin joint at 'O'. If the link OA t urns with angular velocity

'ω_{1}' rad/s in the clockwise direction and th e link OB turns with angular velocity 'ω_{2}' rad/s is the

anticlockwise direction, then the rubbing velocity at the pin joint 'O' is

Where r = Radius of the pin at 'O'

Solution:

QUESTION: 18

According to Indian standard specifications, a grey cost iron designated by 'FG200' means that the

Solution:

*Answer can only contain numeric values

QUESTION: 19

T here is a slab having temperat ure at left and right faces 800 K and 600 K respectively and slab material

having conductivit y k = 20 W/mK at 0°C. Find the mean thermal conductivity for the slab given β = 0.01 per

unit kelvin _________________W/mK

Solution:

QUESTION: 20

The following sheet metal operat ion induces shear stresses in the part

Solution:

QUESTION: 21

Reduced pressure is

Solution:

QUESTION: 22

Steam coming out of the whistle of a pressure cooker is

Solution:

*Answer can only contain numeric values

QUESTION: 23

What should be the minimum length two a high strength steel rod of 12.5 mm diamet er so t hat one end

can be t wisted by 30^{o} with respect of the other end, without exceeding a shear stress of 270 N/mm^{2} given

modulus of rigidity G = 8 × 10^{4} N/mm^{2}

_________________ m

Solution:

QUESTION: 24

The linear programming is used for opt imization problems which satisfy the following conditions.

(1) Objective function expressed as a linear function of variable

(2) Resources are unlimited

(3) T he decision variable are interrelated and non-negative

Which of the statements is/are correct?

Solution:

*Answer can only contain numeric values

QUESTION: 25

Water flows up a conical pipe 450 mm diameter at the lower end and 250 mm diameter at 2.3 m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1 m/s,assuming a head loss in the pipe to be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper end

Solution:

QUESTION: 26

T he four bar mechanism shown in the given figure

Given OA = 3cm , AB = 5cm, BC = 6 cm and OC = 7cm is a

Solution:

QUESTION: 27

Ball bearing are usually made from

Solution:

QUESTION: 28

For a metallic wall at 200°C a metallic rod prot rudes to the ambient air. The temperat ure at the tip will be

minimum when the rod is made of

Solution:

QUESTION: 29

Blank holding is normally required in

Solution:

QUESTION: 30

When 'd' is the diameter of the molecules of a gas in a confined space, the collision frequency will be

proportional to

Solution:

T he collision frerquency is the number of collision experienced by the molecules of gas per second and is given by

Where v = average molecular velocity, d =

diameter of molecules, and N = number of

molecules per c.c.

*Answer can only contain numeric values

QUESTION: 31

A cant ilever beam of span 6m carries a point load of 100 kN at its free end and anot her point load 'W'

at the mid of its length. If the maximum bending moment is stated to be 900 kNm, the load 'W' will have

the value _______________________

Solution:

Maximum bending moment will occur at the fixed end.

QUESTION: 32

Free convection flow depends on

Solution:

QUESTION: 33

Straight turning operation was carried out at the same feed using tools

(1) 8 – 8 – 5 – 5 – 25 – 0 (ASA) and

(2) 8 – 8 – 5.5 – 7 – 30 – 0 (ASA).

Which tool will gives a better surface finish ?

Solution:

h_{1} < h_{2} (1 will give better surface finish)

*Answer can only contain numeric values

QUESTION: 34

A 150 mm long, 12 mm diameter rod is reduced to 11 mm diameter in a single pass straight turning. If the

spindle speed is 400 rpm and feed rat e is 200 mm/min, determine the material removal rate

____________________ mm^{3}/ min

Solution:

Mat erial removal rat e MRR = Vfd

Where,

QUESTION: 35

In the vander wall's equation

T he greater the value of constant equation

Solution:

T he vander wall's const ant (a) is a measure of the vander wall's force s of cohesion existing between the molecules of a give gas the greater the value the higher is the strength of the vander wall's forces, also the greater the value of 'a' the

grea ter is the case with whi ch a gas can be

liquefied.

*Answer can only contain numeric values

QUESTION: 36

**Question 36 to 65 carry Two Marks each**

**Q.**

A 60 mm diameter shaft transmitting a torque of 4 kNm is also subjected to an axial tension of 180 kN.

T he maximum tensile stress is

___________________

Solution:

Tensile stress due to axial tension

Shear stress at shaft surface due to torque

QUESTION: 37

The momentum correction factor is given by

Solution:

QUESTION: 38

Consider the following statements

1. In a kinematic inversion, the relative motions between links of the mechanism changes as different

links are made t h e frame by turns.

2. An ellipt ical trammel is a mechanism with three prismatic pairs and one revolute pair. Which of the

statements given above is/are correct?

Solution:

T hrough the process of inversion the relative motions between the various links is not changed in any manner but their absolute mot ions may be changed drastically.

Elliptical t rammels hav e t wo sliding pairs and two turning pairs. It is an instrum ent used for drawing ellipse.

*Answer can only contain numeric values

QUESTION: 39

A shaft rotat ing at constant speed is subjected to variable load. The bearings support ing the shaft are subjected to stationary equivalent radial load of 3kN for 10 percent of time, 2 kN for 20 per cent of time, 1 kN for 30 per cent of time and no load for remaining time of cycle. If the tot al life expected for the bearing is 20 × 10^{6} revolution at 95 per cent reliability, dynamic load rat ing of the ball bearing is

__________________ kN

Solution:

We know,

The equivalent radial load

QUESTION: 40

A plastic pipe (K = 0.5 W/mK) carries a fluid such that the convective heat transfer coefficient is 200 W/

m^{2}K. The average fluid temperat ure is 100°C. T he pipe has an inner diameter of 3 cm and outer diameter

4 cm. If the heat transfer rat e t hrough the pipe per unit length is 450 W/m, calculate the external pipe

temperat ure

Solution:

41.23 = 100 – T_{2}

T_{2} = 58.77 °C

*Answer can only contain numeric values

QUESTION: 41

A mild steel workpiece is being machined by two different tools 'A' and 'B' under identical machining conditions. The tool life equation for these tools are

Tool A VT^{0.31} = 43.3

Tool B VT^{0.43} = 89.5

Where V and T are in m/s, respectively. Determine the cutting speed above which tool B will give better tool

life

__________________ m/s

Solution:

At break-even speed V^{*} both tool gives the same tool life

QUESTION: 42

The net work input required for compressor with increase in clearance volume

Solution:

QUESTION: 43

If hot water and cold water are mixed, then the entropy of the system will be

Solution:

*Answer can only contain numeric values

QUESTION: 44

A solid shaft is subjected to a bending moment of 300 Nm and a twisting moment of 225 Nm. What should

be the diameter of the shaft with a factor of safety of 2 according to the maximum principal strain theory?

Take σ_{y} = 210 N/mm^{2} and μ = 0.25

______________

Solution:

M = 300 N.m

T = 225 N.m

With a factor of safety, the condition to be satisfied is

QUESTION: 45

Laminar flow takes place in the circular tube. At what distance form the boundary does the local velocity

equal to the average velocity ?

Solution:

QUESTION: 46

Consider the following statements

1. Corioli’s component of acceleration is a component of translatory acceleration.

2. If the relative motion between two links of a mechanism is pure sliding, then the relative instantaneous

centre for these two links does not exist.

Which of the statements given above is/are correct?

Solution:

Its unit is m/s^{2}. T herefore translatory acceleration (a^{t} = 2vω).

It does not exist at inf init y distance. Kennedy theorem says number of instantaneous centre =

n(n-1)/2

*Answer can only contain numeric values

QUESTION: 47

According to Von–Mises criterion, the shear yield stress of the material is 346.56 MPa t hen what will

be t he yield strength of this material in tension assume unidirectional loading _____________MPa

Solution:

Von – Mises criterion gives

*Answer can only contain numeric values

QUESTION: 48

Water flows a 20 mm I.D. at a rat e of 0.02 kg/s entering at 20°C. T he tube is wrapped from outside by an

elect ric heat ing element that produces a uniform flux of 18 K W/m2. If the exit tempe rat ure of water is

50°C, find the length of the pipe needed for this process. Given water propert ies at 35°C, ρ = 997 kg/m^{3}, C_{p}= 4180 J/kg-K, μ = 820 × 10^{–6} Ns/m^{2} and k = 0 .808 W/mK ___________________

Solution:

*Answer can only contain numeric values

QUESTION: 49

A tube is orthogonally machined in a lathe to reduce its length under the following conditions. Outside diameter of the tube 100 mm, inside diameter of the tube 96 mm, RPM of the workpiece 120, longitudinal feed 0.5 mm/ rev, cutting ratio 0.3, tangential force 800 N, axial force 600 N. The total power consumption

_______________W.

Solution:

*Answer can only contain numeric values

QUESTION: 50

100 cubic-meter o f air at 20°C and 60% RH (saturat ion pressure = 0.02384 bar) is heated per minute by

means of hot water spray supplied at 30°C. T he temperature of air coming out is 3 0°C and 50% R.H.

(saturat ion pressure = 0.04325 bar). T he heat added to the air will be, if atmospheric pressure is 1.033 bar

_____________kW

Solution:

QUESTION: 51

A bell coleman refrigeration cycle works between pressure limits of 1 bar and 5 bar. T he adiabatic efficiency of compression is 85% and expansion is 90%. Find out the tonnage capacity when the air flow rat e is 1 kg/sec. T he ambient temperat ure is 27°C and refrigerat or temperat ure is 0°C

Solution:

*Answer can only contain numeric values

QUESTION: 52

A 100 mm diameter safet y valve is to be designed to blow off at a gauge pressure of 1.2 N/mm^{2}. T he

valve is held in position by a 180 mm diameter close coiled compression helical spring whose init ial

compression is 25 mm. What is the number of turn required if the shear stress is not to exceed 80 N/

mm^{2} if G = 8.5 × 10^{4} N/mm^{2}

^{__________________}

Solution:

*Answer can only contain numeric values

QUESTION: 53

A pelton wheel 2.5 m diameter operates under the following conditions

Find the hydraulic efficiency _________________%

Solution:

QUESTION: 54

A cantilever beam is loaded as shown below

T he deflect ion of the free end will be

Solution:

*Answer can only contain numeric values

QUESTION: 55

A pipe carry water has a tapering section where the diameter changes from 10.0 cm at section 'A' to 8.0 cm

at section 'B'. T he flow is from 'A' to 'B' and the pressure and elevation at t hese section are as follow

Find the discharge in the pipe

_______________________ L/s.

Solution:

*Answer can only contain numeric values

QUESTION: 56

A thick walled cop per cylinder has an inside radius of 1 cm and an outside radius of 2 cm. T he inner and

outside surfaces are held at 310°C and 290°C respectively. Assume 'k' varie with temperature as k = 371.9

[1 – 9.25 × 10^{–5}(T – 150)] W/mK. Determine the heat lost per unit length

_______________ kW/m

Solution:

*Answer can only contain numeric values

QUESTION: 57

T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and

60 cm in diameter × 30 cm in height subjected to identical conditions of cooling

Solution:

*Answer can only contain numeric values

QUESTION: 58

In an experiment to determine the thermal conductivity of a long solid 2.5 cm diameter rod, its base is place

in a furnace with a large portion of it projecting in to the room air at 22°C. Aft er stea dy state condition

prevail, t he temp eratrue at two point s, 10 cm apar t are found to be 110°C and 85°C respectively. T he

convective heat t ransfer coefficient between the rod surface and the surrounding air is 28.4 W/m^{2}K.

Determine the t hermal conductivit y of the rod material _________________ W/mK

Solution:

QUESTION: 59

T he vapour compression Refrigerat ion cycle is represented as shown in figure below with state (1) being

the exit of the evaporator. T he coordinate system used in this figure is

Solution:

I f is (P - h ) di agram e be cause in v apo ur

compression cycle condenser and evaporation pro cess will work at con stant pressure, and throt tling process will work at isenthalpic process and in compression pressure and enthalpy both going to increase in diagrame

1 – 2 Compression process

2 – 3 Evaporation process (constant pressure)

3 – 4 T hrottling process (enthalpy constant )

4 – 1 Evaporat ion process.

QUESTION: 60

The atmospheric air at 760 mm of Hg. dry bulb temperat ure 15°C and wet bulb temperat ure 11°C enters a

heating coil whose temperature is 41°C. If the by-pass factor of the heating coil is 0.5. T hen what will be the

dry bulb temperat ure of air leaving the coil 2.

Solution:

If a sam ple o f un satur at ed air co nt aini ng superheated water vapor is cooled at constant pressur e. The partial pressure (P_{v} ) of each constituent remain constant untill the wate vapour reaches the saturat ed state as shown by point 'B'.

At this poin t 'B' the first drop of dew will be

formed and hence t he temperat ure at point B is called dew point temperature.

*Answer can only contain numeric values

QUESTION: 61

T he modulus pa rt of (1 + i)^{8} is ______________

Solution:

QUESTION: 62

If a vector The divergence of vector is

Solution:

*Answer can only contain numeric values

QUESTION: 63

Using Sim pson’s 1/3 rd rule with step size of .1, the value of is _______________.

Solution:

QUESTION: 64

The solution of the differential equation is

Solution:

QUESTION: 65

Find the v alue of λ and μ for which system of equations

x + λy + z = 3

x + 2y + 2z = μ

x + 5y + 3z = 9

has infinit e consistent solution.

Solution:

### Syllabus - Mechanical Engineering : ME, GATE

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