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QUESTION: 1

Assumptions:

I. Flats are available in the court area

II. Some people will respond to the advertisement

III. It is a practice to give such an advertisement

Solution:

QUESTION: 2

DIRE

Solution:

QUESTION: 3

The famous playwright has been in the sick bed from the last one week

Solution:

QUESTION: 4

He always _________ you in his letters

Solution:

QUESTION: 5

His health ____________ under the pressure of work.

Solution:

QUESTION: 6

A, B and C shoots to hit a target. If A hits the target 4 times in 5 trials, B hits in 3 times in 4 trials and C hits it 2 times in 3 trials. What is the probability that the target is hit by at least 2 persons?

Solution:
Probability that A hits the target = 4/5

Probability that B hits the target = 3/4

Probability that C hits the target = 2/3

P (at least 2) = P(2) + P(3)

Probability that B hits the target = 3/4

Probability that C hits the target = 2/3

P (at least 2) = P(2) + P(3)

QUESTION: 7

Two liquids are mixed in the ratio 4:3 and the mixture is sold at Rs 20 with a profit of %. If the first liquid is costlier than the second by Rs 7. Find the sum of costs of both the liquids.

Solution:
Profit= %

CP= =15 Rs

Cost of 1 unit of liquid 1 = x+7

Cost of 1 unit of liquid 2 = x

CP= =15 Rs

Cost of 1 unit of liquid 1 = x+7

Cost of 1 unit of liquid 2 = x

QUESTION: 8

Henry and Ford worked together to complete a task in 10 days. Had Henry worked with half of his efficiency and Ford at 5 times of his efficiency it would have taken them to finish the job in 50% of the scheduled time. In how many days can Ford complete the job working alone?

Solution:
Let henry’s one day work be x

Let ford’s one day work be y

Hence, Ford can complete the job working alone in 30 days

Let ford’s one day work be y

Hence, Ford can complete the job working alone in 30 days

QUESTION: 9

A new flag is to be designed with six vertical stripes using some or all of the colours- yellow, green, blue and red. Then the number of ways this can be done such that no two adjacent stripes have the same colour out is:

Solution:
There are 6 stripes. The stripe can be coloured in 4ways, in 3, in 3 and so on.Thus, total number of ways = 4×3×3×3×3×3=12×81

QUESTION: 10

Find the value of

Solution:

=y

=3y

y(y-3) = 0

y = 3

=y

=3y

y(y-3) = 0

y = 3

QUESTION: 11

Identify the incorrect statement

Solution:

QUESTION: 12

The divergence of the field at (1, 2, 1) is

Solution:

QUESTION: 13

The argument of the complex number is

Solution:

Complex number is lying in second quadrant hence argument is

Complex number is lying in second quadrant hence argument is

QUESTION: 14

The velocity ratio in case of an inclined plane inclined at angle θ to the horizontal and weight being pulled up the inclined plane by vertical effort is

Solution:

QUESTION: 15

During non-flow reversible process, a gas enclosed in piston cylinder assembly expands from 3 to 6 P = -3v+15 where, P is in bar, V is volume in Determine the work interaction.

Solution:

QUESTION: 16

Solution:

QUESTION: 17

Surface is at and is exposed to surroundings at and convicts and radiates heat to the surroundings. The convection co-efficient is 80 K.The radiation factor is one. If the heat is conducted to the surface through a solid of conductivity 12 W then the temperature gradient at the surface of the solid is

Solution:
Heat conducted + heat radiated = heat conducted considering 1,

QUESTION: 18

Air at 1100 K & 101.32 kPa is passing through a converging nozzle and leaves it at 300K. Determine velocity of air at nozzle exit. Nozzle is horizontal. Inlet velocity of air can be ignored. = 1 kJ/kg K

Solution:
S.F.E.E.

QUESTION: 19

In an NC machine, the tool is programmed to move along a circular arc from to taking the center of the arc O[15, 20]. The tool path command followed by the tool is

Solution:

QUESTION: 20

During a certain reversible process, for a closed system, the entropy of system increases by 4 kJ/K. If the process occurs at a constant temperature of 500 K, the heat input to the system will be

Solution:
500(4)=2000 kJ

QUESTION: 21

The polar modulus for a hollow shaft of outer diameter (*D*) and inner diameter (*d*) is

Solution:

QUESTION: 22

The men's department of a large store employs one tailor for customer fittings. The number of customers requiring fitting appears to follow a Poisson distribution with a mean arrival rate is 24 per hour. Customers fitting time follows an exponential distribution with a mean of 2 minute. The time (minute) a customer is expected to spend in the fitting row is………….

Solution:

QUESTION: 23

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: 24

Which of the following is incorrectly matched?

Solution:

QUESTION: 25

When an ideal gas expands, its temperature

Solution:

QUESTION: 26

A steel rod 12 mm is diameter and 60 mm long, with an insulated end,is to be used as a spine. It is exposed to surroundings with a temperature of 60°C and a heat transfer coefficient of 55 W/m2°C. The temperature at the base of fin is 95°C. The fin efficiency is

Solution:
For insulated end

QUESTION: 27

In a certain cooling dehumidification operation, 360 kg/h of air (DBT 35°C & RH 50%) is blown over a cooling coil having apparatus dew point of 5°C, assuming a bypass factor 15% determine outlet conditions of air

Solution:

QUESTION: 28

If amplitude of vibration reduces to 0.25 of its initial value after five oscillations. The longitudinal decrement will be:

Solution:

QUESTION: 29

In ECM, the material removal rate will be higher for metal with:

Solution:

QUESTION: 30

Which of the following statement is correct? In case of clutches, the uniform pressure theory

Solution:

QUESTION: 31

Consider the I-section of a beam shown below:

If the shear stress at the level of junction in flange is 5 what will be shear stress in web at the level of junction?

If the shear stress at the level of junction in flange is 5 what will be shear stress in web at the level of junction?

Solution:

QUESTION: 32

In fusion welding process, which of the following holds good within the heat affected zone.

Solution:

QUESTION: 33

For the internal expanding shoe brake shown in the figure. Which shoe is self energizing?

Solution:

In the leading shoe friction forces are helping the applied force F i.e. the moment produced by the friction forces about the hingeare in the same direction as produced by force F about Therefore leading shoe is self energizing. However in case of trailing shoe moments produced by friction forces about are opposing the moment produced by F about and therefore trailing shoe is not self energizing.However, if the direction of rotation is changed then leading shoe will

In the leading shoe friction forces are helping the applied force F i.e. the moment produced by the friction forces about the hingeare in the same direction as produced by force F about Therefore leading shoe is self energizing. However in case of trailing shoe moments produced by friction forces about are opposing the moment produced by F about and therefore trailing shoe is not self energizing.However, if the direction of rotation is changed then leading shoe will

QUESTION: 34

A simple pendulum of length 5m with a bob of mass 1 kg, is in simple harmonicmotion. As it passes through its mean position, the bob has a speed of 5m/s. The net force on the bob at the mean position is:-

Solution:

QUESTION: 35

A helical gear made of plain carbon steel has face width 10 times the normal module. If number of teeth on pinion and gear are 20 and 60 respectively, then what will be the wear strength of helical gear? (Assume m_{n} = 5, BHN = 200 & Ψ = 24^{o})

Solution:

QUESTION: 36

The particular solution of the differential equation is

Solution:

QUESTION: 37

There are 200 individuals with a skin disorder, 120 had been exposed to the chemical c_{1}, 50 to chemical c_{2}, and 30 to both chemicals c_{1} and c_{2}. find the number of individuals exposed to chemical c_{2} but not chemical c_{1}

Solution:

Let U= set of individuals suffering from the skin disorder

A= set of individuals exposed to the chemical c_{1}

B= set of individual exposed to the chemical c_{2}

Then n(u)=200, n(A)=120, n(B)=50 and n(A∩B)=30

Similarly, B=(B−A)∪(A∩B)

∴n(B)=n(B−A)+n(A∩B)

∵n(B−A)∩(A∩B)=φ

∴n(B−A)=n(B)−n(A∩B)

=50−30=20

Hence, 20 individuals exposed to chemical c_{2} but not to chemical c_{1}

QUESTION: 38

Which of the following is not a solution of the differential equation

Solution:

Thus differential equation is

D (D - 1)y – 2Dy +2y = 0

Therefore, D = 1, 2

Roots are real and distinct

From this general solution we cannot get 1/x

Thus differential equation is

D (D - 1)y – 2Dy +2y = 0

Therefore, D = 1, 2

Roots are real and distinct

From this general solution we cannot get 1/x

QUESTION: 39

Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected of

people free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?

people free of HIV, 99% of the test are judged HIV –ve but 1% are diagnosed as showing HIV +ve. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV +ve. What is the probability that the person actually has HIV?

Solution:

QUESTION: 40

In the given figure below, the slope at point P will be:

Solution:

QUESTION: 41

In a laminar boundary layer, the velocity distribution can be assumed to be given, in usual notation asWhich of the following is the correct expression for the displacement thickness for this boundary layer?

Solution:

QUESTION: 42

In a reduction gear shown in the figure, the input S has 24 teeth. P & C constitute a compound planet having 30 and 18 teeth respectively. Considering same pitch for all the gears and A to be fixed, the ratio of speeds of gear S to gear D is:

Solution:

QUESTION: 43

The dimension of null space of the matrix

Solution:
No. of columns = 3

determinant of matrix is zero = rank = 2

Dimension of null space

= No. of columns - rank

= 3 – 2 = 1

Hint ? Refer Rank Nullity theorem

determinant of matrix is zero = rank = 2

Dimension of null space

= No. of columns - rank

= 3 – 2 = 1

Hint ? Refer Rank Nullity theorem

QUESTION: 44

The equation is to be solved using Newton – Raphson method with intial guess 1.8500 the value obtained after one iteration step

Solution:

= 1.8556

= 1.8556

QUESTION: 45

In spot pulsed laser welding of aluminum plates (density = 2700 specific heat =896J/kg, melting temperature = 933K, latent heat of melting is 380 kJ/kg) at a temperature of Pulse with energy of 0.5 J is focused on to area of 0.05 mm2. If the entire energy is coupled into the material. What will be depth of weld assuming crosssection area of weld as circular and uniform throughout depth and only heat conduction in direction of penetration?

Solution:
Let depth = d

Volume of weld = Ad

d = 3.84 mm

Volume of weld = Ad

d = 3.84 mm

QUESTION: 46

A block slides down an inclined plane of with an acceleration The kinetic friction coefficient is:-

Solution:

QUESTION: 47

A pelton wheel is required to develop 6 MW when working under a head of 300m. It rotates with a speed of 550rpm. Assuming jet ratio as 10 and overall efficiency as 85%. The diameter of wheel and number of jets respectively are:[ (coefficient of velocity of jet)= 0.98 and (coefficient of peripheral velocity)= 0.46]

Solution:
Velocity of jet,

Tangential [Peripheral] velocity of wheel,

Tangential [Peripheral] velocity of wheel,

QUESTION: 48

Historical data on the sales of cars of company for the year 2000 to 2006 is given below

Projection of the forecast for the year 2007 is

Projection of the forecast for the year 2007 is

Solution:

For 2007, x = 4

y = 10416.7

For 2007, x = 4

y = 10416.7

QUESTION: 49

A hole of 60mm diameter is pierced in a steel sheet of 4mm thickness without shear on the tool. Shear strength of steel is 600 and penetration is 25%. The expected percentage load reduction if a shear of 1mm is provided on the punch is:

Solution:

50% load reduction

50% load reduction

QUESTION: 50

Two masses are placed on the opposite side of the shaft axis in the same axial plane as shown in the figure. The masses to be added at locations. A and D respectively at radius 40mm which will produce complete static and dynamic balance

Solution:

Since the given configuration is already in static balance, therefore for dynamic balancing,

QUESTION: 51

A balloon of 20 cm diameter is filled with air at 1.2 bar and 35°C. It is heated to 500°C,as a result its diameter increases to 25 cm. During heating process, pressure varies linearly with diameter rising to maximum value of 1.5 bar. Estimate heat transfer to balloon, if energy change in air where is change in temperature in Kelvin.

Solution:

= 1860 + 543.4

= 2403.4 J

= 1860 + 543.4

= 2403.4 J

QUESTION: 52

A cube shaped solid 20 cm side having a density of 2500 kg/m3 and specific heat of 0.52 kJ/kg K has a uniform heat generation rate of 100 kJ/m3s If heat is received over it’s surfaces at 240 W, the time rate of temperature change of the solid (in °C/sec) is ----

Solution:
The energy equation yields,

Heat transfer + heat generated = heat stored

Heat stored = volume × density × specific heat × temperature rise

Heat transfer + heat generated = heat stored

Heat stored = volume × density × specific heat × temperature rise

QUESTION: 53

A thin cylindrical pressure vessel 5.5m in diameter is made of 16mm steel plates. The longitudinal joint is a double riveted lap joint with no staggering between the rows. The rivets are 20mm nominal diameter with a pitch of 75mm. Allowable stress are 140 MPa in tension, 110 MPa in shear and 240 MPa in bearing. The efficiency of joint and safe pressure inside the vessel will be

Solution:
Strength of the rivets pitch in shear,

= 6.91 kN

(n = 2, because rivets in single shear and rows of rivets are two)

= 6.91 kN

(n = 2, because rivets in single shear and rows of rivets are two)

QUESTION: 54

An ideal sprue basin system has been modeled in the laboratories as shown. Consider the sprue design as parabolic when the vertex of this parabola passes through A. The mould cavity is of dimension For how many values of the above condition will be satisfied.

Solution:

d = 0.0252 m

r = 0.0126 m

Equation of parabola

This will give a cubic equation in x on solving, we get 3 real values of x

d = 0.0252 m

r = 0.0126 m

Equation of parabola

This will give a cubic equation in x on solving, we get 3 real values of x

QUESTION: 55

A gear box of machine is operating under steady state. Input shaft receives 46 kW from prime mover and transmits 30 kW to output shaft, the rest being lost to friction etc. Gear box surface is at an average temperature of 47°C and losses heat to surrounding at 27°C. Find the irreversibility involved.

Solution:
Heat loss due to friction = 46-30 = 16 kW

QUESTION: 56

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

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

Project time = 38

QUESTION: 57

A square plate hangs in water from one of its corners and its centroid lies at 8m from the free water surface. Find the total pressure force on the top half of the plate

Solution:

QUESTION: 58

Degree of freedom of the given linkage is

Solution:

F = 3[8-1]-2[10]

F = 21-20

F = 1

F = 3[8-1]-2[10]

F = 21-20

F = 1

QUESTION: 59

A round plate of diameter 500 mm has to be faced on both sides to reduce its thickness from 30mm to 20mm. Maximum depth of cut allowed is 3mm. If the crossfeed is 0.05 cm/rev and cutting velocity is 785 m/min, the machining time will be:

Solution:

QUESTION: 60

An engine working on OTTO cycle have compression ratio of 5. The maximum and minimum pressure during the cycle are 40 bar and 1 bar respectively. The mean effective pressure of the cycle will be:

Solution:

QUESTION: 61

A hollow shaft having outer diameter equal to 3 times the inner diameter. It transmits 40 kW power at 2500 RPM. If the maximum permissible shear stress is 32 MPa, then outer diameter is

Solution:

P = 40 kW

N = 2500 rpm

P = 40 kW

N = 2500 rpm

QUESTION: 62

In a certain machining operation with cutting speed of 50m/min, tool life of 45 min was observed; when the cutting speed was increased to 100m/min, tool life decreased to 10 min. The cutting speed for maximum productivity if tool change time is 2 minutes is:

Solution:

QUESTION: 63

An air refrigerator of 10 ton capacity operates in Bell Coleman cycle between pressure limits of 1 bar and 4 bar. Air at inlet of compressor is at 1 bar and 253 K. Air at exit of cooler is at 313 K. After air is cooled to 290 K at constant pressure in cooler, it is allowed to expand isentropically to 1 bar in expansion cylinder where temperature limit of cycle. Cold air is then sent to cold chamber to extract heat (Refrigerating effect) determine COP of refrigerator.

Solution:

QUESTION: 64

A power plant cycle with entropy at various points is shown in figure below. All other processes in the steady flow cycle are adiabatic.

Power plant cycle is

Power plant cycle is

Solution:
Heat transferred in the boiler/kg of fluid

Heat transferred from the condenser per kg of fluid

Hence the cycle will be irreversible

Heat transferred from the condenser per kg of fluid

Hence the cycle will be irreversible

QUESTION: 65

A rigid beam ABCD is hinged at D and supported by 2 springs at A and B as shown in the given figure. The beam carries a vertical load P at C. The stiffness of spring at A is 2k and that at B is 3k. The ratio of forces of spring B to that of spring A is:

Solution:

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

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