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This mock test of GATE Mock Test Mechanical Engineering (ME) - 8 for GATE helps you for every GATE entrance exam.
This contains 65 Multiple Choice Questions for GATE GATE Mock Test Mechanical Engineering (ME) - 8 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in total from both as interest. The rate of interest per annum is.

Solution:

Let the rate % = R

According to the question,

100R + 120 R = 2200

QUESTION: 2

Amit rows a boat 9 kilometres in 2 hours down-stream and returns upstream in 6 hours. The speed of the boat (in kmph) is:

Solution:

Down-stream rate = 9/2 = 4.5 kmph

Upstream rate = 9/6 = 1.5 kmph

The speed of the boat = (4.5 – 1.5) kmph = 3 kmph

QUESTION: 3

The sentences given with blanks are to be filled with an appropriate word(s). Four alternatives are suggested for each question. For each question, choose the correct alternative and click the button corresponding to it.They abandoned their comrades ______the wolves.

Solution:

When something is left in between more than 2 things or persons, ‘among’ is used. There are a number of wolves in the sentence hence the correct answer is option D.

QUESTION: 4

In the following question, out of the four alternatives, select the word opposite in meaning to the given word.Turgid

Solution:

Turgid = swollen and distended or congested; pompous

Bloated = inflated

Humble = plain, simple

Puffy = inflated

Tumescent = swollen

Hence, humble is the correct answer.

QUESTION: 5

**Direction:** Read the information carefully and give the answer of the following questions:

Total number of children = 2000

If two-ninths of the children who play football are females, then the number of male football children is approximately what percent of the total number of children who play cricket?

Solution:

57.4% (If 2/9 th of children play football are female , then

male children = 1 - 2/9 = 7/9th of children play football;

Let's take z% of male football children equal to cricket children , then

=> z% of cricket children = 7/9 th of football;

=> z% of (23% of 2000) = 7/9 th of (17% of 2000);

=> z% of 23 = 7/9 th of 17

=> z = 7× 17 × 100 = **57.4%**;)

**Short-cut :**

Required percentage = (7/9)*17*100/ 23 = 57.4%

QUESTION: 6

**Direction:** Study the following information carefully and answer the given questions:

The following pie chart shows the percentage distribution of total number of Apples (Dry + Wet) sold in different days of a week :

The pie chart2 shows the percentage distribution of total number of Apples (Wet) sold in different days of a week.

Find the ratio of Apples (Dry + Wet) sold on Tuesday to that of the Apples (Wet) sold on Thursday?

Solution:

Required ratio = 13% of 7000: 23% of 4500 = 182:207

QUESTION: 7

**Directions:** In each of the questions below, some statements are given followed by some conclusions. You have to consider the statements to be true even if they seem to be at variance with commonly known facts. You have to decide which of the following conclusions logically follows from the given statements. Give answer.

**Statements:**

Some jacket is shirt.

Some shirts are trouser.

No shoes are t-shirt.

All trousers are shoes.

All pants are t-shirt.

**Conclusions:**

I. All shirts being t-shirt is a possibility.

II. Some shoes are trouser.

III. Some jackets are t-shirt.

IV. Some shirts being t-shirt is a possibility.

Solution:

QUESTION: 8

The question below consists of a set of labelled sentences. These sentences, when properly sequenced form a coherent paragraph. Select the most logical order of sentences from among the options.

P: July 1969 was to see a transformed Indira Gandhi.

Q: Quite a few people contributed with ideas.

R: She sounded the bugle through her historic ‘Note on Economic Policy and Programme’ that was

circulated among delegates at Bangalore on July 9, 1969.

S: But the pivot was P.N.Haksar who gave shape, structure and substance with the help of some of his

colleagues in the Prime Minister’s Secretariat.

Solution:

P is clearly the first sentence as it introduces the main person of the paragraph, i.e. Indira Gandhi. The pronoun ‘she’ in R refers to Indira Gandhi mention in P. Thus, R forms the second statement. Now, in the sentence R, ‘delegates’ is mentioned which says about the people, who are given in the sentence Q. So, sentence Q must follow R. Thus, the sequence after rearrangement is PRQS and option A is the correct answer.

QUESTION: 9

**Direction:** Which of the following is the MOST SIMILAR in meaning to the given word?

__Remnant__

Solution:

‘Remnant’ means ‘remainder’ which is same as ‘residue’.

QUESTION: 10

**Direction:** Study the following information carefully and answer the given questions.

Seven people, P, Q, R, S, T, W and X sitting in a straight line facing north, not necessarily in the same order. R sits at one of the extreme ends of the line. T has as many people sitting on his right, as on his left. S sits third to the left of X. Q sits on the immediate left of W. Q does not sit at any of the extreme ends of the line.

If all the people are made to sit in alphabetical order from right to left, the positions of how many people will remain unchanged?

Solution:

Hence, only Q's position will remain unchanged.

*Answer can only contain numeric values

QUESTION: 11

A wooden block (relative density = 0.65) floats above surface of a liquid of relative density of 1.35, contained in a tank. The volume fraction of metallic piece lies above the liquid surface is

Solution:

Let V be total volume of wooden block and V’ is the volume that lies immersed in the liquid.

Using principle of floatation,

Weight of wooden block = weight of the liquid displaced by the immersed portion of the wooden block

So, the volume fraction of wooden block below the liquid surface = 1 – 0.4815 = 0.5185

QUESTION: 12

Match the following lists and choose the correct answer using the codes given below

Solution:

QUESTION: 13

In a 1:36 scale model test of a spillway, discharge of flow over the model is 6 m^{3}/s. If the velocity of flow over model was found to be 5 knots, then the velocity of flow over prototype in m/s will be

Solution:

Q_{m} = 6 m^{3}/s, V_{m} = 5 knots = 5 × 0.515 =2.575 m/s Using dimensional analysis

QUESTION: 14

A cylindrical pipe is made up of copper having E=120 Gpa and A=110 mm2. This cylindrical tube is covered with an aluminum tube having E=70 Gpa and A=70 mm2. If the two assembly are in parallel and is loaded with a force of 70 KN. Find the deflection of the whole assembly under this loading. Given length of the tube is 500 mm.

Solution:

QUESTION: 15

A bar of uniformly tapering section with 75 mm and 150 mm diameter, is held between two parallel end supports 6 m apart. If the length of the bar is 5.998 m, then stress induced in the bar for a temperature change of 30^{o}C will be (Take coefficient of thermal expansion =12×10^{-6} per ^{o}C and E = 2×10^{5} N/mm^{2})

Solution:

Expansion of bar due to temperature only,

ΔL = αtL = 12 x 10^{-6} x 30 x 5.5 = 1.98 x 10^{-3} m

Since (6 – 5.998 = 0.002 m) of expansion is allowed, but expansion in bar due to temperature change is 0.00198 m, which is less than 0.002 m. Hence there will not be any stress inside the bar.

*Answer can only contain numeric values

QUESTION: 16

A spherical body of diameter 750mm of initial temperature 25℃ is immersed in the fluid at temperature 400℃. Thermo physical properties of the body are k=22W/m-K, c=400 J/kg and ρ=9000kg/m^{3} (Regular notations used). Determine the time (in seconds) when the temperature will become 390℃, given the convective heat transfer coefficient between body and fluid is 300W/m^{2}.

Solution:

QUESTION: 17

Which of the following statement is correct regarding transportation

Solution:

• North-West corner method gives initial feasible solution

• Hungarian method is used to solve transportation problem

QUESTION: 18

Consider a project given below

The variance for the project will be

Solution:

From the network, we can see that critical path is A – C – E (1 – 2 – 4 – 6).

Now variance of the project is

QUESTION: 19

Guest’s theory of failure is best suited for

Solution:

Maximum shear stress theory is given by Guest. According to this theory,

Since the shear stress at yield point in a simple tension test is equal to one-half the yield stress in tension, therefore the equation may be written as

This theory is mostly used for designing members of ductile materials.

QUESTION: 20

In automobiles, the brakes used in hand braking systems are usually

Solution:

In automobiles, the brakes used in hand braking systems are usually externally contracting brakes.

QUESTION: 21

In AJM process nozzle tip distance changes with MRR

Solution:

*Answer can only contain numeric values

QUESTION: 22

A 50mm thick strip rolled to 30mm thickness in 3 passes with equal reduction in each pass by using rolls of 600mm diameter, what is the minimum coefficient of friction required for rolling operation________.

Solution:

*Answer can only contain numeric values

QUESTION: 23

A rectangular hole of size 50mm x 60mm is to be made on a 8 mm thick sheet having ultimate tensile strength and sheer strength of 500MPa & 300MPa respectively the punching force required (in KN) is__________.

Solution:

QUESTION: 24

Which of the following is not related to soldering operation:

Solution:

Soldering operation is a solid-liquid (heterogeneous) welding process.

QUESTION: 25

A metric thread of pitch 3mm and diameter 30mm, inspected for its pitch diameter using 2- wire method. The diameter of best size wire in mm is

Solution:

For metric thread included angle is taken 60^{0
}

QUESTION: 26

Hardenability of steel can be improved by adding which of the following element

Solution:

Molybdenum, Chromium, Nickel, Boron are used to increase hardenability.

QUESTION: 27

The value of sensitivity for an isochronous governor is

Solution:

Isochronous governor is that governor which has same speed for all position of sleeves and sensitivity equal to infinity. Therefore right option is (c).

QUESTION: 28

Match **list I** (terms) with **list II** (definition) and select the correct answer using the codes given below the lists:

**List I**

A) Base circle

B) Trace point

C) Pitch point

D) Prime circle

**List II**

I. Smallest circle that can be draw from the centre of cam and tangent to pitch curve

II. Smallest circle that can be draw from the centre of cam through the pitch points

III. Point on pitch curve having the maximum pressure angle

IV. Point on pitch curve having the minimum pressure angle

V. Smallest circle that can be draw to the cam profile

VI. Reference point on follower and used to generate pitch curve

**Codes:**

A B C D

Solution:

Base circle → smallest circle that can be draw to the cam profile

Trace point → Reference point on follower and used to generate pitch curve

Pitch point → Point on pitch curve having the maximum pressure angle

Prime circle → smallest circle that can be draw from the centre of cam and tangent to the pitch curve

*Answer can only contain numeric values

QUESTION: 29

A milk chilling unit can remove heat from the milk at the rate of 42 MJ/h. The rate of heat leakage into the milk from the surrounding is 4.2 MJ/h. The specific heat of milk above the freezing point is 4.2 kJ/kg K and below the freezing point is 2.1 kJ/kg K. The freezing point of milk is -2 ^{o}c and the latent heat is 100 kJ/kg. The time required (in min) for cooling a batch of 100 kg milk from 47 ^{o}c to -5 ^{o}c is

Solution:

Suppose the time required is t hrs then

The amount of heat removed

= heat removed to decrease the temperature from 47 ^{o}c to -2 ^{o}c + latent heat + heat removed to decrease the temperature from -2 ^{o}c to -5 ^{o}c

(42000 – 4200)t = 100 ×[4.2 × (47+2) + 100 + 2.1× (−2+5)]

t = 0.825 hr = **49.5 min**

*Answer can only contain numeric values

QUESTION: 30

A power plant operating on a closed Brayton cycle operates between pressure of 1 bar and 8 bar. Compression and Expansion both are isentropic. The heat absorbed by the coolant per kg kW output of air which is used to cool the air after expansion in turbine is_____

Solution:

Heat supplied per kg-kW output,

Heat supplied=2.23 kW

Hence, heat rejected = heat absorbed by the coolant= 1.23

QUESTION: 31

The matrix 3×3 matrix A is transformed to the diagonal matrix D = P^{-1}AP, where, P The possible Eigen vector of A is

Solution:

The model matrix P, which diagonalizes A is obtained by grouping the Eigen vectors of A into square matrix

So, the Eigen vectors of A are (-1,-2,1), (2,-1,0), (3,0,1).

Out of these options only option 2 is correct which can be the Eigen vector of A.

QUESTION: 32

The value of the integral evaluated around the closed curve |z-3| = 1 is

Solution:

The poles are determined as

z^{2} - 4z + 3 = 0

(z−3)(z−1) = 0

z = 3, 1

There is only one pole z =3 lies inside the given circle |z-3| =1

So, the value of integral

*Answer can only contain numeric values

QUESTION: 33

If 5 unbiased dice are thrown simultaneously, the probability of obtaining exactly two sixes is

Solution:

*Answer can only contain numeric values

QUESTION: 34

The velocity vector is given as The divergence of this velocity vector at (1,1,1)

Solution:

QUESTION: 35

The volume of solid bounded by the surface x = 0, y = 0 and x + y + z =4 and z = 0 is

Solution:

z varies as 0 to 4 – x – y

y varies as 0 to 4 – x

x varies as 0 to 4

Volume,

*Answer can only contain numeric values

QUESTION: 36

An airplane, travels through still air at 300 km/hr, is having two propellers of 2.5 m diameter. Take density of still air as 1.22 kg/m^{3}. The difference of pressure (in kPa) across a propeller, if discharge through each propeller is 480 m^{3}/s, will be

Solution:

Let V_{1} and V_{2} be velocities at upstream and downstream section.

So, theoretical efficiency,

*Answer can only contain numeric values

QUESTION: 37

Water of mass density 1000 kg/m^{3} is transported using a pipe of diameter 40 cm. Flow in the pipe is turbulent. If the flow velocity at the centre and that at a 5 cm distance from centre of pipe are 5 m/s and 4 m/s respectively, then the value of wall shear stress (in Pa) will be

Solution:

As we know, in pipe flow, maximum velocity occurs at the pipe centre.

*Answer can only contain numeric values

QUESTION: 38

A single acting reciprocating pump has a piston of 15 cm diameter and 22.5 cm stroke. The pump is required to deliver 0.29 m^{3} of water per minute at 75 rpm. If the suction and delivery heads are 3 m and 10 m respectively, then the percentage of slip of pump is

Solution:

For a single acting pump,

*Answer can only contain numeric values

QUESTION: 39

The tensile stress at the bottom edge of a cast iron beam shown in figure is 50 MPa when it is subjected to a bending moment. The value of stress (in MPa) at the top will be

Solution:

QUESTION: 40

Consider the beam in figure given below. The reaction at point C and rotation at point B will be (flexural rigidity of beam = EI)

Solution:

The moment at point B = 4Pa

In the cantilever beam ABC, the deflection at C due to moment 4Pa will be given as

The reaction at C will be upwards

Rotation at B due to moment

Rotation at B due to reaction at C

Rotation at B = rotation due to moment + rotation due to reaction

*Answer can only contain numeric values

QUESTION: 41

A thin cylindrical vessel of 3.2 m diameter and 5 m long is subjected to a circumferential tensile stress of 140 N/mm^{2} and axial tensile stress of 70 N/mm^{2}. If the volumetric strain of the vessel is 14×10^{-4}, then the Poisson’s ratio of the material will be (Neglect the compressive stress on the walls and take E = 2×10^{5} N/mm^{2})

Solution:

Axial strain,

Circumferential strain,

Now, the volumetric strain for cylindrical vessel

QUESTION: 42

A 5 mm diameter and 4 m length steel wire is submerged in a fluid at 60^{o}C. The conductivity and resistivity of wire is 20 W/m-deg and 70 micro-ohm-cm. If 600 amperes electric current passes through it and conductance at wire surface is 4 kW/m^{2}-deg, then maximum temperature of the wire is

Solution:

Given that, L = 4 m =400 cm, d = 5 mm = 0.5 cm

Electrical resistance,

Heat generated per unit volume,

Maximum temperature occurs at geometric centre line of the wire, and can be computed from the relation,

QUESTION: 43

In a certain heat exchanger, cold fluid enters at 40^{o}C and rate of the flow is 1650 kg/hr. The hot fluid is at a temperature of 130^{o}C and cold fluid leaves the heat exchanger at 90^{o}C. Specific heat of the cold fluid is 3.5 kJ/kg-K. If heat transfer area is 0.707 m^{2}, then the overall heat transfer coefficient is

Solution:

QUESTION: 44

Find the net value of heat flux between two parallel, infinite plates having emissivity of 0.75 and 0.7. The planes are maintained at 450 K and 500 K.

Solution:

The grey body factor is given by,

Since infinite long plates can see each other. So, F_{12} = 1 and A_{1} = A_{2 }So, the grey body factor will become

Now, the rate of heat interchange between the plates

And net heat flux,

*Answer can only contain numeric values

QUESTION: 45

A parallelepiped enclosure measures 3 m × 3.5 m with 4 m height. The bottom floor having 0.75 emissivity is maintained at 380 K and all other surfaces (emissivity = 0.8) are maintained at 505 K. The net radiation (in kW) to the floor will be

Solution:

As per the given data,

A_{1} = area of four walls and ceiling

QUESTION: 46

A hot plate of 40 cm × 40 cm maintained at 90^{o}C is exposed to ambient air at 30^{o}C. The appropriate correlation for the convective coefficient is

The properties of ambient air at 60^{o}C are given as

thermal conductivity = 0.028 W/m-deg, c_{p} = 1.008 kJ/kg-K,

mass density = 1.06 kg/m^{3}, kinematic viscosity = 18.97×10^{-6} m^{2}/s.

If the plate is kept vertical, the value of convective heat transfer coefficient will be

Solution:

All the properties are measured at mean temperature.

*Answer can only contain numeric values

QUESTION: 47

A ball pen manufacturer produces refill and barrel. The work department is capable of producing 20000 refills or 10000 barrels or any other combinations of these per week. The demand for refills and barrels is limited to 15000 and 8000 units per week respectively. The profit per unit from refill is 1 rs. And that from barrel is 3 rs. The maximum profit to the manufacturer in rupees will be

Solution:

Let x_{1} and x_{2} be number of refills and barrels respectively and Z denotes total profit earned.

**Formulation of problem:
**

From the above tableau, we can conclude that x

Second Iteration:

Since there is no negative Z

Refills = 4000, and barrels = 8000

The maximum profit is given by

*Answer can only contain numeric values

QUESTION: 48

Exponential smoothening method with smoothening index 0.4 is used to determine the forecast of certain product. The demand for August, September, October and November were 210, 220, 200 and 230 units respectively. Find the forecast for the month of December if the forecast of August was 250 units.

Solution:

*Answer can only contain numeric values

QUESTION: 49

A steel shaft of 75 mm diameter and 630 MPa ultimate tensile strength is subjected to a torque which varies from 1500 N-m to -950 N-m. Assume the yield stress for steel in reversed bending as 510 N/mm^{2}, surface finish factor as 0.87, size factor as 0.85 and fatigue stress concentration factor as 1. The factor of safety using Soderberg criteria will be

Solution:

*Answer can only contain numeric values

QUESTION: 50

Consider the following figure of welded joint. If the allowable shear stress is 105 MPa for static loading and value of static load P is 350 kN, then the length (in mm) of the bottom weld will be

Solution:

Given : x + y = 200 mm ; P = 200 kN = 200 × 103N ; ï€ = 75 MPa = 75 N/mm2

Let L_{1} = Length of weld at the top,

L_{2}= Length of weld at the bottom, and

L = Total length of the weld = L_{1} + L_{2
}

Since the thickness of the angle is 20 mm, therefore size of weld, s = 20 mm

We know that for a single parallel fillet weld, the maximum load (P),

*Answer can only contain numeric values

QUESTION: 51

A shaft of 300 mm diameter is carrying a load of 20 kN at 2000 rpm. A bearing of 450 mm length supporting the shaft. The absolute viscosity of lubricating oil is 0.011 kg/m-s at the operating temperature and diametral clearance of the bearing is 0.30 mm. The power loss in bearing due to friction will be

Solution:

Given : d = 300 mm = 0.3 m ; W = 20 kN = 20000 N ; N = 2000 r.p.m. ;

l = 450 mm; c = 0.30 mm ; Z = 0.011 kg/m-s

We know that, bearing pressur

*Answer can only contain numeric values

QUESTION: 52

A 150 mm diameter blind hole is to be drilled upto 60mm depth at a speed of 500 rpm and feed 0.2 mm per revolution, point angle of drill is 110^{0} . Machining time per hole (minute) __

Solution:

*Answer can only contain numeric values

QUESTION: 53

A cast steel slab of dimension 40 x 20 x 10 cm, is poured horizontally using side riser. The riser is cylindrical in shape with diameter and height both equal to 20 cm.Then the freezing ratio is___.

Solution:

*Answer can only contain numeric values

QUESTION: 54

The epicyclic gear arrangement with the compound planets 3-4 is shown in figure. The number of teeth on gears 2, 3, 4 and 5 are 60, 20, 30 and 20 respectively. The annular gear 2 is keyed to the propeller shaft X which rotates at 650 rad/s (CCW). The shaft Y is free to rotate with respect to gear 5 which is fixed and makes the same no. of revolution as the arm. If 100 kW power is supplied to gear 2 then the holding torque (in N-m) on gear 5 is (assume 100% efficiency throughout)

Solution:

Given, T_{2} = 60, T_{3} = 30, T_{4} = 30, T_{5} = 20,ω_{2} = 650 rad/s,

ω_{5 } = 0 rad/s, P =100 kW

First of all we need to find the angular velocity of arm 1.

Using algebraic method,

ω_{1} = 520 rad/s (CCW)

Since the shaft Y will make same no. of revolution as arms, so

Speed of shaft X = 520 rad/s (CCW)

Torque on driving shaft X or gear 2

Since 100 % efficiency throughout, so power available at gear 5 of shaft Y = 100 kW

Torque on driving shaft Y or gear 5

So, the holding torque on gear 5 = 192.3−153.84 = 38.46 N -m

QUESTION: 55

A homogeneous solid disc of mass M and radius r is connected to a spring (spring constant =K) at a point a above the centre of the disc on an inclined plane as shown in figure. The other end of the spring is fixed to the vertical wall. If the disc rolls without slipping then the natural frequency of the spring in rad/s is

Solution:

*Answer can only contain numeric values

QUESTION: 56

A two stage vapour compression plant with a direct contact heat exchanger uses R-12 as refrigerant. The evaporator and condenser temperature are -30^{0}C and 40^{0}C respectively. The condenser and evaporator pressure are 15.5 bars and 1.2 bars respectively. If the capacity of the plant is 25 tonnes of refrigeration then the COP of the plant is

Given data:

Solution:

Compression work = m_{1} (h_{2}−h_{1}) + m_{2} (h_{4}−h_{3})

Capacity of plant = 25 tonnes = (25×14000)/ (3600) = 97.22 kJ/s

m_{1} (h_{1}−h_{8}) = 97.22 (∵ h_{7} = h_{8})

m_{1} (1404.6−181.5) = 97.22

m_{1} = 0.08 kg/s

Also,

m_{1} (h_{2}−h_{7}) = m_{2} (h_{3}−h_{6})

0.08 × (1574.3−181.5) = m_{2} (1443.5−371.7) (∵ h_{5} = h_{6})

m_{2} = 0.104 kg/s

Compression work, W = 0.08 × (1574.3−1404.6) + 0.104 × (1628.1−1443.5)

W = 32.77 kW

So, COP = 97.22/32.77 = **2.97**

QUESTION: 57

A quantity of air initially at 1.5 bar, 27^{0}C brought to a final temperature of 127 ^{0}C by heat transfer from a thermal reservoir at 227 ^{0}C. The irreversibility is (take atmospheric temperature = 27 ^{0}C, atmospheric pressure = 1 bar, C_{p} = 1.005 kJ/kgK, C_{v} = 0.718 kJ/kgK)

Solution:

Given, T_{1} = 27^{0}C =300 K, T_{2} = 127^{0}C = 400 K, T = 227^{0}C = 500 K, T_{o} = 300 K

Entropy change of universe,

*Answer can only contain numeric values

QUESTION: 58

An unsaturated air enters in an insulated chamber at 32^{0}C where it flows over a long sheet of water and becomes cooled to 26^{0}C, which is adiabatic saturation temperature. The total pressure of the mixture remains constant at 100 kPa. The corresponding pressure to saturation temperature is 3.363 kPa. The humidity ratio at the entry of chamber is (in kg vap/kg dry air)

Given data: C_{p} of air = 1.005 kJ/kgK

At 32^{0}C, h_{v1} = 2559.9 kJ/kg,

At 26^{0}C, h_{fg2} = 2439.9 kJ/kg, h_{f2} = 109.1 kJ/kg

Solution:

Given, p =100 kPa, p_{s} = 3.363 kPa

Since the system is insulted and no work interaction, so using conservation of energy

m_{a1}h_{a1} + m_{v1}h_{v1} + (m_{v2}−m_{v1}) h_{f2} = m_{a2}h_{a2} + m_{2}h_{v2} (i)

m_{a} = mass of dry air (kg)

m_{v} = mass of water vapour (kg)

h_{a} = specific enthalpy of dry air (kJ/kg)

h_{f} = specific enthalpy of liquid water (kJ/kg)

h_{v} = specific enthalpy of water vapour in air (kJ/kg)

Divide the eq^{n} (i) by m_{a1,} we get

h_{a1} + W_{1} h_{w1} + (W_{2}− W_{1}) h_{f2} = h_{a2} + W_{2}h_{v2} (∵ m_{a1} = m_{a2}) (ii)

Where, W = specific humidity

Humidity ratio at exit,

(h_{a1} − h_{a2}) + W_{2} (h_{f2} − h_{v2}) = W_{1} (h_{f2}−h_{v1})

C_{p} (T_{2} – T_{1}) + W_{2} h_{fg2} = W_{1} (h_{v1}−h_{f2}) (∵ h_{v2} = h_{g2} and h_{fg2} = h_{g2} − h_{f2})

1.005 × (26−32) + 0.0216×2439.9 = W_{1} × (2559.9−109.1)

W_{1} = **0.019** **kg vap/kg dry air**

QUESTION: 59

A four stroke double acting petrol engine is used 90 kW brake power on a job. The engine used 40 kg/h of fuel under working condition and its mechanical efficiency is 75%. If the engine friction power reduces by 10 kW then the saving of fuel (in kg/h) is (assume, indicated thermal efficiency remain constant)

Solution:

Given, BP = 90 kW, m_{1}= 40 kg/h, η_{mech}= 0.75

Initial indicated power,

(IP)_{1} = 90/0.75 = 120 kW

Frictional power, FP =IP−BP = 30 kW

New frictional power, FP = 30−10 =20 kW

(IP)_{2} = BP + IP =90 + 20 =110 kW

According to question,

QUESTION: 60

The force in the member BD and CD respectively are

Solution:

Suppose R_{1}, R_{2} and R_{3} are the reactions at A and F as shown in figure.

R_{3} = 4 kN

R_{1} + R_{2} = 12

R_{1} × 8 = 12 × 4 + 4 × 6

R_{1} = 9 kN

R_{2} = 3 kN

cos θ_{ }= 6/7.21

sin θ = 4/7.21

**At joint A**

Resolving vertically,

T_{AB} = −9 kN (∵ considered tensile as positive)

**At joint B**

Resolve vertically,

T_{BC} cos θ + T_{AB} = 0

Resolve horizontally,

T_{BC} sin θ + T_{BD} = 0

T_{BD} = −10.815 × 4/7.21 = −6 kN **= 6 kN (compressive)**

QUESTION: 61

A ball of mass M strikes the floor with a speed of V m/s at an angle of incidence θ with the normal as shown in figure. The coefficient of restitution is e. The speed of the reflected ball and the angle of reflection of ball respectively are

Solution:

let the angle of reflection is α and the speed after collision is V_{2} m/s.

As there is no force parallel to the surface so,

V sin θ = V_{2} sin α (i)

In the vertical direction, the floor exerts a force on the ball.

As we know that

Velocity of separation = e (velocity of approach)

V_{2 }cos α= e V cos θ (ii)

From (i) and (ii)

QUESTION: 62

The function, f (x) =2 Inx, satisfies the Lagrange’s Mean Value Theorem in the interval x∈ [1, 5] then the value of x is

Solution:

According to Lagrange’s Mean Value Theorem, if the function f (x) is continuous in the interval x∈ [a, b] and f’(x) exist in the interval x∈ (a, b) then

QUESTION: 63

A function follows the following equation

The Laplace transform of f(t) is

Solution:

Taking Laplace transform on both the sides

QUESTION: 64

Consider the following differential equation

If y (2) = 1 then the value of y (2.2) using Runge- Kutta third order method is

Solution:

QUESTION: 65

An ideal gas of mass 0.5 kg has a pressure of 600 kPa, a temperature of 77^{0}C and a volume of 0.08 m^{3}. This gas undergoes an irreversible process to a final pressure of 600 kPa and final volume of 0.12 m^{3}, during which the heat addition and work done on gas are 2 kJ and 30 kJ respectively. The value of C_{v} of gas is

Solution:

Given, m =0.5 kg, p_{1} = p_{2} =600 kPa, T_{1} = 77^{0}C = 350 K, V_{1} = 0.08 m^{3}, V_{2} = 0.12 m^{3}, Q =2 kJ, W = −30 kJ

From ideal gas eq^{n},

p_{1}V_{1} = mRT_{1
}

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