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QUESTION: 1

Choose the word or phrase which is nearest in meaning to the key word:

** Pilfer**

Solution:

QUESTION: 2

The following question comprises two words that have a certain relationship between them followed by four pairs of words. Select the pair that has same relationship as the original pair of words

Fox : Cunning

Solution:

QUESTION: 3

Replace the phrase printed in bold to make it grammatically correct?

A twenty-first-century economy "** cannot be held"** hostage by power cuts nor travel on nineteenth-century roads.

Solution:

QUESTION: 4

Improve the sentence with suitable options by replacing the underlined word.

He **" lay" **on the grass enjoying the sunshine.

Solution:

QUESTION: 5

- Fill in the blanks :

At times, we are all ______ to be mistaken.

Solution:

QUESTION: 6

There are two solutions of wine and water, the concentration of wine being 0.4 and 0.6 respectively. If five liters of the first solution be mixed with fifteen liters of the second, find the concentration of wine in the resultant solution.

Solution:

Resultant concentration of wine

QUESTION: 7

Rajiv bought some apples at the rate of 25 for Rs. 400 and an equal number at the rate of 30 for Rs. 270. He then sold all at the rate of 10 for Rs. 180. Find his profit/loss percentage

Solution:

Let Rajiv bought x apples of each kind.

Total cost price of Rajiv =

Total selling price of Rajiv =

SP > CP , Hence he makes profit;

Profit percentage =

QUESTION: 8

The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is -.

Solution:

QUESTION: 9

2 men and 3 boys can do a piece of work in 10 days, while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work ?

Solution:

Let work done by 1 man in 1 day = x units

Let work done by 1 boy in 1 day = y units

2 men and 1 boy can finish work

No. of days taken by 2 men and 1 boy = = 12.5 days

QUESTION: 10

In an exam, 60% of the candidates passed in Maths and 70% candidates passed in English and 10% of the candidates failed in both the subjects, 300 candidates passed in both the subjects. Find the total number of candidates appeared in the exam, if they took test in only two subjects that is Math and English.

Solution:

Let total number of students appear be X.

X = 750

QUESTION: 11

is equal to

Solution:

Thus 1^{∞} in determinant form occurs adding and subtracting 1

QUESTION: 12

A fair coin is tossed repeatedly. The probability of getting a result in the fifth toss different from those obtained in the first four tosses.

Solution:

Let E_{1} be the event that head occurs in fifth toss

E_{2 } be the event that first four heads and fifth tail

QUESTION: 13

Other Roots of the equation

if one root is same as one root of x^{2} + 10x + y = 0

Solution:

Given determinant on expansion reduces to the equation

? x^{3} – 67x+ 126 = 0 -------------(1)

? Given equation x^{2}+10x+ 9 has roots -9, -1

? {– 9 is also a root of (1)}

? So L.H.S of (1) is exactly divisible by x 9. On dividing x^{3} – 67x+ 126 by x+ 9 we get quotient x^{2} – 9x+ 14 Roots of x^{2}– 9x +14 which are 2 and 7 are also roots of (1)

QUESTION: 14

A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single event is

Solution:

P (A) = Probability that A speaks truth = 0.6

P(B) = Probability that B speaks the truth = 0.7

E_{1} : Both speaks truth

E_{2} : Both speak false

E : Both speaks the same thing

QUESTION: 15

While water passes through a given pipe at mean velocity V1. The flow is found to change from Laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from Laminar to turbulent is expected if the flow velocity is

Solution:

QUESTION: 16

A cylinder contains 0.12 m3 of air at 1 bar and 90^{0}c . It is compressed to 0.03 m^{3}, the final pressure being 6 bar. The index of compression will be

Solution:

n = 1.292

QUESTION: 17

The rpm of steel bar of 150 mm diameter which is turned at 50 m/min speed with carbide tool is.

Solution:

N = 106.1 rpm

QUESTION: 18

A nuclear fuel element is in the form of a solid sphere of 12.5 mm radius. It’s thermal conductivity is 24.2 W/mK. The heat generation rate is 50 × 10^{6} W/m^{3}. The heat generated is absorbed by a fluid at 200^{0}C . If the maximum temperature is limited to 360^{0}C , the convection coefficient (W/m^{2}K) required is

Solution:

Amount of heat generated = Heat convected

h = 1302.08 watt / m^{2} k

QUESTION: 19

Consider the PERT network shown below:

The desired completion date for the project if probability of finishing the project is 19% (Z(0.87) = 0.19) is.

Solution:

Critical path

A - B - D - F - G

Project time = 38

T_{S }= 35 Weeks

QUESTION: 20

In rolling process, roll diameter is 800 mm. The thickness of 60 mm strip is to be reduced to 40 mm in single pass. Coefficient of friction is

Solution:

m = 0.223

QUESTION: 21

A gas expands from an initial state where the pressure is 340 kPa and volume is 0.0425 m^{3} to a final pressure of 136 kPa. If the gas follows PV^{2} = c, then the work for the process (in kJ) will be.

Solution:

QUESTION: 22

An item is produced at the rate of 50 items per day. The demand occurs at the rate of 25 items per day. If the setup cost is Rs. 100 per setup and holding cost is Rs 0.01 per unit of item per day. The economic lot size is:

Solution:

= 1000 items

QUESTION: 23

In a pipe flow, the head loss due to friction is 6m. If the power transmitted through the pipe has to be maximum then the total head at the inlet will have to be maintained as.

Solution:

Head lost due to friction is 6 m. Power transmitted is maximum when the friction head is 1/3^{rd} of the supply head supply head is 18 m

QUESTION: 24

In a cutting operation, angle of approach is 75^{0} and feed is 0.32 mm/rev. The value of underformed chip thickness is.

Solution:

QUESTION: 25

Portion BC is semi-circular . If after several oscillation ball of mass 10 kg comes to rest. The bending moment at A when ball is at rest will be ? Take g = 9.81 m/s^{2}

Solution:

At rest, ball is at lower most potion of semi circle

BM at A = l0g × (10 2.5)

= 10 × 9.81 × 12.5

= 1226.25 N-m

QUESTION: 26

An orthogonal cutting operation is being carried out under following conditions. Cutting speed = 4m/s, depth of cut = 0.5 mm,Chip thickness = 0.6 mm,Chip velocity is:-

Solution:

Chip velocity, V_{C }= V × r

= 3.33 m/s

QUESTION: 27

A two stage compressor takes in air at 1.1 bars and discharges at 20 bars. For max efficiency, the intermediate pressure is.

Solution:

P_{2} = 4.7 bar

QUESTION: 28

In case of Partial bearing, the angle of contact between the bush and journal is

Solution:

QUESTION: 29

In a tool life test, doubling the cutting speed reduces the tool life to of the original. Taylor’s tool life index is.

Solution:

(4)^{n} = 2

n = 0.5

QUESTION: 30

A fluid jet is discharging from a 100 mm nozzle and the vena contracta formed has a diameter of 90 mm. If the coefficient of velocity is 0.95, then the coefficient of discharge for the nozzle is.

Solution:

QUESTION: 31

The purpose of helical grooves in a twist drill is to

1. Improve the stiffness

2. Save tool material

3. Provide space for chip removal

4. Provide rake angle for cutting edge

Select the correct choice given below

Solution:

QUESTION: 32

A heat engine receives heat from a source at 1200 K at a rate of 500 kW and rejects waste heat to a medium at 300 K. The power output of heat engine is 180 kW. The irreversibility rate associated is.

Solution:

Irreversibility Rate = Reversible power – useful Power

375 – 180

= 195 kW

QUESTION: 33

Consider the following statements about the v engine, when the angle between the cylinder center lines is 90^{0} .

1. The resultant unbalanced primary force is m r w^{2}

2. Primary unbalance force can be completely balanced by a mass placed at a suitable radius diametrically opposite to the crank

3. Secondary unbalanced force along the engine centre line is zero

4. Resultant secondary unbalance force is zero.

Which of the above statements is/are incorrect

Solution:

QUESTION: 34

When the annual demand of a product is 2400 units, the EOQ is 2000 units. If the annual demand is 4800 units, the EOQ will be:

Solution:

QUESTION: 35

A cantilever beam AB shown in the figure has an extension BCD attached to the free end. A force P acts at the end of the extension. What is the ratio of a/L, so that vertical deflection at point B is zero?

Solution:

QUESTION: 36

For an analytic function f (x iy) = u (x, y) iv (x, y), u is given by u = 4xy+ x. The expression for V considering K to be a constant

Solution:

Since f is analytic, it will satisfy Cauchy. Riemann equations

QUESTION: 37

Consider the differential equation with initial condition y (o) = 0. Taking step size of 0.1 the value of y at x = 0.1. Using fourth order Runge – kutta method

Solution:

= .34868

QUESTION: 38

Which condition of Rankine cycle has highest efficiency when operating between same pressure limits?

Solution:

The efficiency of ideal regenerative cycle is exactly equal to the corresponding Carnot cycle. Hence it is maximum.

QUESTION: 39

The inverse Laplace transform of

Solution:

QUESTION: 40

Find the natural frequency of vibration of the system

Solution:

QUESTION: 41

In Bell-Coleman refrigeration plant, air is drawn from cold chamber at pressure of 2 bar and 10^{0}C , then compressed to 10 bar and then cooled to 25^{0}C in cooler before expansion in exparder. Refrigeration effect per kg of air is ( g = 1.4, CP = 1.09 kJ/kg K)

Solution:

T_{1} = 283 K, T_{3} = 298 K

= 447.7 K

T_{4} = 188.3

R.E./kg = CP (T_{1} – T_{4})

= 95.55 kJ

QUESTION: 42

A closed tank containing water is partly filled with water and the air space above it is under pressure. A 5 c.m. hose connected to the tank discharges water to atmosphere on to the roof of a building 3 m above the level of water in the tank, if friction losses are 1.5 m of water, what air pressure must be maintained in the tank to deliver 15 L/s to the roof?

Solution:

V_{2} = 7.639 m/s

By applying Bernoulli equation to point 1and 2

QUESTION: 43

Calculate the elongation of copper bar of solid circular cross-section with tapered ends when it is stretched by axial loads of magnitude of 30 kN.

Diameter at cross section A, B, C and D are 0.5, 1, 1 and 0.5 cm respectively. Take E = 120 GPa

Solution:

= 1.59 × 10^{-4} m

Total elongation = (2 × 0.12732 0.15915) mn

= 0.4138 mm

QUESTION: 44

Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -180^{0}C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 25^{0}C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m^{0}C) is

Solution:

r_{1} = 0.5 m

r_{2} = 0.57 m

ti = - 180°C, t0 = 25°C

Boil off rate = 14 kg/hr

hfg = 210 kJ/kg

= 14 × 210 = 2940

Also L + 2r_{1} = 5

L = 4 m

Q_{cyl} = 644.69 watt

So, K = 0.0164 W /m^{0}C

QUESTION: 45

Brass billet is to be extruded from its initial diameter of 40 mm to final diameter of 20 mm. The extrusion constant is 200 MPa. Force required for extrusion is

Solution:

= 348237 N

= 0.348 MN

QUESTION: 46

An ideal reheat Rankine cycle operates between the pressure limits of 10 kPa and 8 MPa, with eheat occurring at 4 MPa. The temperature of steam at the inlet of both turbines is 500^{0} C, and the enthalpy of steam is 3185 kJ/kg at the exit of the high pressure turbine, and 2247 kJ/kg at the exit of the low pressure turbine. Disregarding the pump work, the efficiency of the cycle is.

Solution:

h_{1} = 339.5 kJ/kg

h_{3} = 3446 kJ/kg

h_{2} = 3185 kJ/kg3

h_{4} = 2247 kJ/kg

h_{5} = 191.81 = h6

w_{net} = w_{T} – w_{P} [ w_{P} = 0]

= (3399.5 – 3185) (3446 – 2247)

= 1413.5 kJ/kg = W_{T}

QUESTION: 47

The structure is carrying a horizontal load P at E. Legs AB and CD are vertical. The stress resultants in AB segment are

Solution:

QUESTION: 48

Find entropy change of air in a polytropic equation where pressure is doubled & volume becomes one third. (C_{p} = 1 kJ/kgK, C_{V}= 0.7 kJ/kgK)

Solution:

Tds = C_{V}dT PdV

= - 0.6134 kJ/kg

QUESTION: 49

Number of chlorine atoms in R – 12 are:-

Solution:

R – 012

R (m – 1) (n 1) p

m = 1, n = 0, p = 2

2m 2 = p q n

2(1) 2 = 2 q 0

q = 2

So, two chlorine atoms

QUESTION: 50

200 kW is transmitted by a single reduction gear. The pitch circle diameter of pinion is 200 mm and its speed 750 rpm. The teeth are of involute profile with pressure angle equal to 20^{0} .

The radial force acting on each wheel when transmitting the given power

Solution:

QUESTION: 51

In a engine working on otto cycle the temp. at the beginning and end of the compression are 50^{0}C and 373^{0}C . The compression ratio and air standard efficiency of the engine is.

Solution:

Compression ratio,

= 0.5 = 50 %

QUESTION: 52

In the production shop of a company the breakdown of the machine is found to follow poisson distribution with an average rate of 3 machines per hour. Break down time at one machine

costs 40 rupees per hour to the company. The company hires a repairman who demands rupees 20 per hour and will repair the broken down machines following the exponential distribution at the rate of 4 per hour. The total cost involved in hiring the repairman is

Solution:

λ = 3/hr

μ = 4/hr

Total waiting time in system for one machine is

= = 1 hour

The down time of 3 machines is

= 3 × 1 = 3 hour

Down time cost = 40 × 3 = Rs 120

Repairman cost = 3 × 20 = Rs 60

Total cost = 120 60 = Rs 180

QUESTION: 53

Figure shows the linear power characteristics, voltage and arc length is related to each other by a linear equation V = 20 2l. What is the value of current when arc length is 5 mm (l is in

mm).

Solution:

QUESTION: 54

If all the dimensions of a vertically subtended circular bar are doubled, then the maximum stress produced in it due to its own weight will

Solution:

Max. stress occurs at point where full weight acts.

Finally, stress = r × 2 L

Stress will be doubled

QUESTION: 55

Particle A makes a perfectly elastic collision with another particle B at rest. They fly apart in opposite direction with equal speeds. The ratio of their masses is

Solution:

m1 = mA, m2 = mB, u1 = u, u2 = 0, v1 =v, v2 = - v

By principle of conservation of linear momentum.

m_{1} u 0 = m_{1} V m_{2} (-v) = (m_{1} – m_{2}) v

By principle of conservation of K.E.

QUESTION: 56

A hole with 40 mm diameter and 50 mm depth is to be drilled in mild steel component. The cutting speed can be taken as 65 m/min and feed rate is 0.25 mm/rev. The time required to drill

the hole in minutes is [Take drill point angle118^{0} and over travel 3mm]

Solution:

T = 0.5026 min

QUESTION: 57

A flat steel bar with constant EI and length L it bent by couples applied at the ends so that the mid point deflection is δ(δ<<L). Then the value of applied couple M is?

Solution:

QUESTION: 58

The variation of saturation pressure with saturation temperature for a liquid is 0.1 bar/k. The specific volume of saturated vapour and dry saturated liquid at 400 K are 251m^{3}/kg and 0.001 m^{3}/kg . The latent heat of vaporization using clausius clapeyron equation is.

Solution:

h_{fg }= 1000kJ / kg

QUESTION: 59

A steel washer is of 46 mm outer diameter and 24 mm inner hole diameter and is 4 mm thick.Maximum shear stress is 40.5 N/mm2 and percentage reduction is 22.Work done (in Joules) will be

Solution:

Production of washer includes blanking of outer diameter and piercing of inner hole

QUESTION: 60

In a PERT network the expected time to finish one activity is 22 days and variance of the activity is 16 days. The ratio of pessimistic time to optimistic time if most likely time for finishing the activity is 23 days is

Solution:

QUESTION: 61

In beam ABCD, there is a roller support at B abd C as shown in the figure. If 200 kN load is applied at the indicant of BC. The shear force at the support A will be

Solution:

SF at A = 100 kN

QUESTION: 62

Which one of the following is not the correct statement about control volume?

Solution:

QUESTION: 63

Shaft is loaded with two point loads as shown

Transverse natural frequency if single load is applied is 100 Hz. Find the frequency if both loads are applied simultaneously

Solution:

QUESTION: 64

4800 kJ of heat is being transferred from constant temperature source at 800 K to another at 600 K when environment temperature is 200 K. The loss of available energy is.

Solution:

= 2 × 200

= 400 kJ

QUESTION: 65

In a certain double pipe heat exchanger hot water flow at a rate of 5000 kg/h. and gets cooled from 95^{0}C to 65^{0}C . At the same time,50000 kg/h of cooling water at 30^{0}C enters the heat exchanger. The flow conditions, are such that overall heat transfer coefficient remains constant at 2270^{ } W/m^{2}K. Assume two streams are in parallel flow and for both the streams C_{p} = 4.2 kJ/kg K. The effective heat transfer area is

Solution:

### Syllabus - Mechanical Engineering : ME, GATE 2022

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