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QUESTION: 1

Statement: All bags are cakes. All lamps are cakes.

Conclusions:

I. Some lamps are bags.

II. No lamp is bag.

Deduce which of the above conclusion logically follows statements:

Solution:

Conclusion I and II are complementary. So either conclusion I or conclusion II follows the statement.

QUESTION: 2

Man does not live by __________ alone.

Solution:

Man does not live by bread alone.

QUESTION: 3

Extreme focus on syllabus and studying for tests has become such a dominant concern of Indian students that they close their minds to anything ___________ to the requirements of the exam.

Solution:

Extraneous – irrelevant or unrelated to the subject being dealt with

QUESTION: 4

Select the pair that best expresses a relationship similar to that expressed in the pair:

LIGHT : BLIND

Solution:

A deaf person doesn't hear well, irrespective of any language. Tongue is not necessary to produce sound. Every voice doesn't produce vibration. But..... if a person doesn't speak anything, he is considered to be dumb. Hence, a is correct.

QUESTION: 5

If + = , then:

Solution:

Log(a/b) + log(b/a) =log(a+b)

loga- logb+logb-loga=log(a+b)

0=log(a+b)

exp(0)=a+b

1=a+b

QUESTION: 6

In an exam, the average was found to be 50 marks. After deducting computational errors the marks of the 100 candidates had to be changed from 90 to 60 each and average came down to 45 marks. Total number of candidates who took the exam was:

Solution:

Let number of candidates be n

50 × n – 100 × 30 = 45 × n

n = 600

QUESTION: 7

A solid 4cm cube of wood is coated with red paint on all the six sides. Then the cube is cut into smaller 1cm cubes. How many of these 1cm cubes have no colour on any side?

Solution:

Number of cubes with 3 faces red = 8

Number of cubes with 2 faces red = 24

Number of cubes with 1 face red = 24

Number of cubes with no face red = 64-(24+24+8) = 8

QUESTION: 8

One of the warmest winters on record has put consumers in the mood to spend money. Spending is to be the strongest in thirteen years. During the month of February, sales of existing single family homes hit an annual record rate of 4.75 million. This paragraph best supports the statement that:

Solution:

This is clearly the best answer because the paragraph directly states that warm weather affects consumers inclination to spend. It furthers states that the sales of single-family homes was at an all-time high. There is no support for choice a or c. Choice b is wrong because even though there were high sales for a particular February, this does not mean that sales are not higher in other months. Choice d presents a misleading figure of 4 million. The paragraph states that the record of 4.75 million was at an annual, not a monthly, rate.

QUESTION: 9

The age of father is 4 times more than the age of his son Amit. After 8 years, he would be 3 times older than Amit. After further 8 years, how many times will he be older than Amit?

Solution:

Let Amit’s age be n years

Age of his father = (4n+n) = 5n years

After 8 years:

Amit’s age = n+8

Father’s age =

3(n+8) = 5n+8

3n+24 = 5n+8

16 = 2n

n = 8 years

After further 8 years:

Amit’s age = 24 years

Father’s age = 5n+16 = 56 years

So father is 2.33 times older than Amit

QUESTION: 10

Pipe A, B and C are kept open and fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will C alone take to fill the tank?

Solution:

A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.

A and B together can fill 1/*t* of the tank in a minute. A alone can fill 1/3*t* of the tank in a minute. So, in a minute, B can fill 1*/t* - 1/3*t* = 2/3*t*. Or, B takes 3*t*/2 minutes to fill an entire tank.

To fill one-third the tank, B will take *t*/2 minutes. B is kept open for t - 10 minutes.

*t*/2 = t - 10, t = 20 minutes.

A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.

C, which is kept open for 8 minutes also fills one-third the tank. Or, C alone can fill the tank in 24 minutes.

QUESTION: 11

Which one of the following matrix is not diagonalizable:

Solution:

has 2 repeated eigen values 1 and 1. There is only one linearly independent eigen vector corresponding to eigen value =1

QUESTION: 12

A bus arrives every 10 minutes at a bus stop. Assuming waiting time X for bus is uniformly distributed, the probability that a person has to wait for the bus for more than 7 minutes is:

Solution:

P (7< <10) = = 0.3

Hint p.d.f is f(x) =

QUESTION: 13

If two concurrent forces A and B acting on a point are 200 N and 300 N. What is the magnitude of resultant force, if it makes an angle of 50^{o} with each force?

Solution:

θ = 50°

force A = 200 N

force B = 300 N

**Formula:** Resultant force = √A^{2} + B^{2} + 2 AB cos 50^{o}

**Solution:** Resultant force = √A^{2} + B^{2} + 2 AB cos 50^{0} = √200^{2} + 300^{2} + 2 x 200 x 300

**= 455.12 N**

QUESTION: 14

The function f(x) =|5x - 3| is:

Solution:

f(x) = |5x - 3|

f(x) is everywhere continuous but not differentiable at the corner point

QUESTION: 15

A random variable is uniformly distributed over the interval [0, 6]. The value of E (x +1) is:

Solution:

Since X is uniformly distributed over [0, 6]

Its pdf is

E(X+1) = - (x+1) f(x)dx

=(x+1)dx = 4

QUESTION: 16

Which of the following statement is correct about the matrix A given as

A =

Solution:

A =

Characteristic equation is =0

=0

=0

QUESTION: 17

Characteristic equation has no negative real root.The laplace transform of the function shown in figure is

Solution:

=

QUESTION: 18

An Autocollimator is used to:

Solution:

An autocollimator is an optical instrument that is used to measure small angles with very high sensitivity. As such, the autocollimator has a wide variety of applications including precision alignment, detection of angular movement, verification of angle standards, and angular monitoring over long periods.

QUESTION: 19

A customer order of 50 parts is to be processed through a plant. Raw material and tooling are supplied by the customer. The total time for processing the parts is 100 hr.Direct labour cost is $10/hr. The factory overhead rate is 250% and the corporate overhead rate is 600%. The cost in $ of the job is…………

Solution:

The direct labour cost for the job is = 100 × 10 = $ 1000

The allocated factory overhead charge, at 250% of direct labour is = 1000 × 2.5 = $2500

The allocated corporate overhead charge = 1000 × 6 = $ 6000

Total cost = $ 9500

QUESTION: 20

Mathematics allows us to expand our consciousness. Mathematics tells us about economic trends, patterns of disease, and the growth of populations. Math is good at exposing the truth, but it can also perpetuate misunderstandings and untruths. Figures have the power to mislead people.

This paragraph best supports the statement that:

Solution:

QUESTION: 21

The defect in a sand casting which occurs due to low pouring temperature of the liquid metal is:

Solution:

Mis run is a defect which occurs due to the low pouring temperature of the liquid metal

QUESTION: 22

When stress is repeated in nature, stress ratio and Amplitude ratio respectively will be:

Solution:

QUESTION: 23

The following stream function will represents/ satisfy:

Solution:

satisfies Laplace equation as shown below:

=(2??-2) (-2?? 2)=0

Hence, it is irrotational flow and satisfies equation of continuity

QUESTION: 24

The initial feasible solution by Vogel's approximate method is given by

To perform optimal test, the (infinitesimally value) should be introduced at:

Solution:

Note: Number of basic cell = m + n - 1 (Non-degenerate problem)

Number of basic cell < m + n - 1 (Degenerate problem) 6 < 3 + 5 - 1

(So, it is degenerate problem)

To obtain optimal solution, we need to convert the degenerate problem into nondegenerate

problem. So, we need to allocate E, to the least cost cell which shouldn’t form

a closed loop.

QUESTION: 25

There is a smooth curved track which terminates in a horizontal part. A spring of spring constant 500 N/m is attached at one end to a wedge fixed rigidly with horizontal part. A 50g mass is released from rest at a height of 5m on the curved track. Maximum compression of the spring is

Solution:

QUESTION: 26

The tool of an NC machine has to move along a circular arc from point to Absolute dimensions are used and dimensioning is in metric units. Feed and spindal speed are selected as 200 mm/min and 1000 rpm respectively. The head of the NC tool path commands for the above mentioned operation is:

Solution:

G71 – Dimensioning in metric units

G90 – Absolute dimensions

G94 – Feed rate mm/min

QUESTION: 27

The ratio of tension on the tight side after n blocks on the brake and tension on the slack side in case of a band and block brake (where is the angle subtended by each block at the center of drum & n is the number of blocks) is:

Solution:

QUESTION: 28

Heat is supplied to air taken in a cylinder and enclosed by a frictionless piston held under a constant load. Expansion of gas will be:

Solution:

Isobaric process is a constant pressure process....so the pressure is given to the cylinder in the constant loading and the volume changes....then the option A is rght

QUESTION: 29

A ductile metal bar is subjected to pure shear test and its yield strength was found to be 230,the maximum permissible shear stress on that metal will be:

Solution:

Shear strength = 230/2 = 115 N/mm^{2.}When ductile metal bar is subjected to pure shear test, maximum permissible shear stress is 115 N/mm^{2}

QUESTION: 30

Curved lines on psychrometric chart indicates:

Solution:

Inclined lines shows enthalpy and wbt

Horizontal lines shows specific humidity and dpt

Curved lines shows relative humidity

QUESTION: 31

In a 4 cylinder 4 stroke in-line IC engine the angle between two successive cranks should be

But this rule is violated for cranks 2 and 3 (i.e. inner cranks) and the angle is made This is done to achieve:

Solution:

QUESTION: 32

An engine working on otto cycle consumes 16 litres of gasoline per hour and develops 50 kW. The specific gravity of gasoline is 0.75 and its calorific value is 44000 KJ/kg. The thermal efficiency of the engine (in %) will be:

Solution:

QUESTION: 33

If a shaft is subjected to pure torsion, it will fail along the plane:

Solution:

If shaft is subjected to pure torsion it will fail along^{ }45^{o }to longitudinal axis in brittle material and 90^{o} to longitudinal axis in ductile material.

QUESTION: 34

A triangular plate of base ‘a’ is kept in contact with a square plate of edge ‘a’. The density of the material and thickness are same everywhere. The center of mass of composite system will be

Centre of mass of composite system will be:

Solution:

For same thickness and density, mass of square plate is twice the mass of triangular plate. So, C.M. lies inside square plate.

QUESTION: 35

An air standard Brayton cycle operating between the temperature limits of 300K and 1500K. For maximum work output, what will be the pressure ratio and thermal efficiency (in %) of the cycle respectively.

Solution:

QUESTION: 36

Consider the differential equation

with y(o) = 1

This equation is to be solved using fourth order Runge – Kutta method. The value of y(0.1) taking step size of 0.1:

Solution:

f (x,y) =

QUESTION: 37

The value of ∫_{c}dz/(z^{2} + 9) where c is a curve in counterclockwise sense given by |z+3i| = 2

Solution:

Curve is z - (-3i) = 2

f(z) = its poles are z = Pole Z = -3i is inside the curve c.

Residue at z = -3i =

Using Residue theorem

QUESTION: 38

The system of linear simultaneous equations:

x+2y+3z = 6

x+3y+5z = 9

2x+5y+az = b

has no solution for values of a and b:

Solution:

For no solution rank (A)rank (C) we know rank (A) rank (C)

For a = 8 using we conclude rank (A) = 2

So rank (C) must be 3, which is possible only when b15 because otherwise rank (C)

will be also become 2 making consistent system.

QUESTION: 39

The square roots of -i are:

Solution:

Adding to generalize the argument,

Using Demoiver’s theorem

For K = 0

For K = 1

QUESTION: 40

A refrigerator operates in a standard vapour compression cycle using F-12 as refrigerant. Its condenser operates at 1 bar and evaporator operates at 1.5 bar.Evaporator absorbs 1.25 kW of energy as heat producing a wet, saturated vapour of F-12, which is then charged to compressor that compress it to a dry, saturated vapour,determine flow rate of refrigerant

Solution:

QUESTION: 41

Two people weighing W each are sitting on a plank of length L floating on water at L/3 from either end. Neglecting the weight of the plank, the bending moment and shear at the center of plank is:

Solution:

QUESTION: 42

A soldering operation was work sampled over two days (16 hours) during which an employee soldered 108 joints, actual working time was 90% of total time and the performance rating was estimated to be 120 percent. If the contract provides allowance of 20 percent of the total time available, the standard time for the operation would be:

Solution:

Total time = 16 × 60 minutes

Actual time =

Normal Time = 864 × 1.2 = 1036.8 minutes

Standard time = Normal time + Allowance

Standard time

= = 1296 minute

Standard time per joint

==12 minute

QUESTION: 43

A single pass rolling operation on a 28mm thick plate reduces the thickness to 24mm. The width of the plate is 150mm and the average flow stress for the plate material is 300 MPa For a roller radius of 250mm and rotational speed of 12rpm, the power required for the rolling operation in (kW) is closest to:

Solution:

QUESTION: 44

The form factor of a speed gear tooth depend upon the-

(1) Number of teeth

(2) Pressure angle

(3) Addendum modification co-efficient

(4) Circular pitch

Which of the above statements are correct?

Solution:

For stub teeth addendum modification coefficient is 0.8 ( Add = 0.8m) while for full

depth involute addendum modification coefficients is 1 ( Addendum = 1m).

Therefore form factor also depends upon addendum modification coefficient in addition to pressure angle.

QUESTION: 45

Air enters an adiabatic diffuser of aircraft of 0.1 bar with velocity 90 kmph at temperature It reaches a pressure of 0.2 bar at diffuser outlet and then enters the compressor.If temperature at outlet of compressor isdetermine temperature of air at compressor inlet.

Solution:

S.F.E.E. for diffuser

QUESTION: 46

In an orthogonal cutting process, the rake angle is and width of cut is 10mm. The cutting velocity is 2.5 m/s and undeformed chip thickness is 200 If the steel chips of 13.36 grams are obtained with a total length of 50 mm, the slip plane angle is:Take density = 7830

Solution:

For Chip thickness

Weight = density × volume

QUESTION: 47

In a two dimensional stress analysis, the state of stress at a point is shown in the figure below:

The magnitude of are respectively:

Solution:

QUESTION: 48

Determine the temperature rise due to water falling through height of 100m. Change in internal energy of water is related to temperature change

Solution:

Internal energy and hence temperature of water increases due to loss of potential energy which is converted into its internal energy.

QUESTION: 49

The average heat transfer co-efficient on a thin hot vertical plate suspended in still air can be determined from observations of the change in plate temperature with time as it cools Assume the plate temperature to be uniform at any instant of time and radiation heat exchange with the surrounding is negligible. The ambient temperature is the plate has a total surface area of and a mass of 4 kg. The specific heat of the plate material is 2.5 kJ/kg K. The convective heat transfer co-efficient in at the instant when the plate temperature is and the change is plate temperature with time. is:

Solution:

Here negative sign shows that plate temperature decreases with the time.

From the given condition,

Heat transfer by convection to the plate = Rate of change of Internal energy,

QUESTION: 50

A rectangular link AB made of steel is used to support a load W through a rod CD as shown in the figure. If the link AB is 30mm wide, determine its thickness for a factor of safety 2.5.The ultimate strength of steel may be assumed to be 450 MPa.

Solution:

Draw Free body diagram

Taking net moment about C = 0

Tensile along link AB = 31.75 kN

t = 5.88 mm

QUESTION: 51

While removing material from iron (atomic weight 56, valency 2 and density 7.8 g/cc) by ECM, MRR of 2cc/min is desired. The current in ampere required is:

Solution:

QUESTION: 52

In the given figure, a disc has mass m and its radius is R. What will be natural frequency of system?

Solution:

When disc is twisted clockwise through angle ?, then

QUESTION: 53

A hydraulic model of a spillway is constructed with a scale 1:16. If the prototype discharge is 2048 cumecs, then the corresponding discharge for which the model should be tested is:

Solution:

Q = A×V

Spillway model obeys Froude’s Law

QUESTION: 54

What is work interaction during the process of filling up of an evacuated bottle with 1 of air from atmosphere when its stop cock is opened? (Atm pressure is 1 bar)

Solution:

QUESTION: 55

A long rod 12 mm square section, made of low carbon steel protrudes in to air at from a furnace wall at The convective heat transfer coefficient is estimated at 22 The conductivity of the material is 51.9 W/mK. The location (mm) from the wall where the temperature will be is:

Solution:

Long fin model will suit the problem situation.

QUESTION: 56

Two plates are welded together as shown in figure with 8mm fillet welds. Safe stress in shear is 75 MPa. The lengths so that the welds are equally stressed in shear are

Solution:

The total length (l ) of the weld required to withstand the load of 120 KN is given by

QUESTION: 57

Water is to be pumped out of a deep well under a total head of 95m. A number of identical pumps of design speed 1000 rpm and specific speed 90 rpm, with rated capacity of 150 liters/sec are available. How many pumps are required?

Solution:

Since total head required to be developed is more than head developed by each pump, so pumps should be connected in series.

QUESTION: 58

The diameter of the shaft is 100mm and length is 1m. One end of shaft is fixed and other has a disc of mass 500kg at a radius of gyration of 450mm. The modulus of rigidity for the shaft material is 80 The value of natural frequency of torsional vibration is shaft:

Solution:

QUESTION: 59

For a production system annual consumption is 20,000 units.Past lead time are 15, 20, 18, 12, 22, and 27 days. If there are 330 working days in a year, then reorder level is:

Solution:

Safety stock = Maximum demand during lead time – Average demand during lead time

= (Maximum lead time - Average lead time)R

QUESTION: 60

A steel rod of 1 cm diameter and 1m length has initial tensile stress Calculate the work done in raising this stress to Young’s modulus of steel is

Solution:

QUESTION: 61

A solid sphere of diameter 0.18 m generates at a rate of 7 × 106 W/ m^{3}.Heat generated is convected over the outer surface to a fluid at 160°C with h = 140 W/m^{2}K KMaterial =30 W/mK. Maximum temperature in the material (in ^{o}C) is:

Solution:

QUESTION: 62

The upper arms of Porter governor are pivoted on the axis of rotation, their lengths being 30 cm. The lower arms are pivoted on the sleeve at a distance of 3 cm from the axis and their lengths being 27 cm. Mass of each bull is 6 Kg and sleeve mass is 50 Kg.The radius of rotation for a particular equilibrium speed is 17 cm. The effort for 1% speed change is:

Solution:

QUESTION: 63

In a sand casting process,a sprue of 10mm base diameter and 250 mm height leads to a runner which fills a cubical mould cavity of 100 mm size.Volume flow rate (in mm^{3}/s) is:

Solution:

QUESTION: 64

In a sand casting process,a sprue of 10mm base diameter and 250 mm height leads to a runner which fills a cubical mould cavity of 100 mm size.Mould filling time (in seconds) is:

Solution:

QUESTION: 65

The stream function for a 2-D flow is given by The resultant velocity at a point P(2,3) is:

Solution:

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

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