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This mock test of Past Year Paper - Mechanical Engineering GATE : 2020 (Session - 2) for GATE helps you for every GATE entrance exam.
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QUESTION: 1

The recent measures to improve the output would ______ the level of production to our satisfaction.

Solution:

QUESTION: 2

It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

Solution:

52 men can do in 10 days.

Since 12 men were sent out Remaining men left = 52 – 12 = 40

We know M_{1}D_{1} = M_{2}D_{2}

52 × 12 = 40 × x

Total number of days taken = 13 days 3 days more than the original estimate.

QUESTION: 3

An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below: (the product of X and Y linearly varies with Z )

Then, which of the following statements is FALSE?

Solution:

QUESTION: 4

While I agree ________ his proposal this time, I do not often agree ______ him.

Solution:

Agree with - a person,

Agree to - an idea, proposal

QUESTION: 5

Select the word that fits the analogy:

White : Whitening : : Light : ________.

Solution:

QUESTION: 6

There are five levels {P, Q , R, S, T ) in a linear supply chain before a product reaches customers, as shown in the figure.

At each of the five levels, the price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the paid (in rupees) by the customers?

Solution:

120 at each level increased 25% price paid by customer

QUESTION: 7

In one of the greatest innings ever seen in 142 years of Test history. Ben Stokes upped the tempo in a five-and-a-half hour long stay of 219 balls including 11 fours and 8 sixes that saw him finish on a 135 not out as England squared the five-match series.Based on their connotations in the given passage, which one of the following meanings DOES NOT match?

Solution:

QUESTION: 8

The two pie-charts given below show the data of total students and only girls registered in different streams in a university. If the total number of students registered in the university is 5000, and the total number of the registered girls is 1500; then, the ratio of boys enrolled in Arts to the girls enrolled in Management is __________.

Solution:

QUESTION: 9

Climate change and resilience deal with two aspects - reduction of sources of nonrenewable energy resources and reducing vulnerability of climate change aspects. The terms 'mitigation' and 'adaptation' are used to refer to these aspects, respectively.

Which of the following assertions is best supported by the above information?

Solution:

QUESTION: 10

Find the missing element in the following figure:

Solution:

This is the log i.e. (n = 4)

5 + 4 = 9

t = 20, x = 24

20 + 4 = 24

Similarly, h =8

Case - 1: 8 + 4 = 12(l)

? + 4 = 8

?= 4 (d)

QUESTION: 11

For an air-standard Diesel cycle,

Solution:

QUESTION: 12

The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is

Solution:

They are:

1. Double crank mechanism

2. Crank-rocker mechanism

3. Double rocker mechanism

*Answer can only contain numeric values

QUESTION: 13

If a reversed Carnot cycle operates between the temperature limits of 27°C and –3°C, then the ratio of the COP of a refrigerator to that of a heat pump (COP of refrigerator/ COP of heat pump) based on the cycle is __________ (round off to 2 decimal places).

Solution:

T_{H} = 27°C = 300 K

T_{L} = –3°C = 270 K

*Answer can only contain numeric values

QUESTION: 14

A machine member is subjected to fluctuating stress σ = σ_{0}cos(8πt). The endurance limit of the material is 350 MPa. If the factor of safety used in the design is 3.5 then the maximum allowable value of σ_{0} is __________ MPa (round off to 2 decimal places).

Solution:

Fluctuating stress,

σ = σ_{o}cos(8πt)

σ_{max} = σ_{o}

σmin =–σ_{o}

σ_{e} = 350 MPa

FOS = 3.5

From strength criteria,

σ_{o} ≤ 100 MPa

QUESTION: 15

The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is

Solution:

QUESTION: 16

In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?

Solution:

QUESTION: 17

A matrix P is decomposed into its symmetric part S and skew symmetric part V. If

then matrix P is

Solution:

*Answer can only contain numeric values

QUESTION: 18

In a furnace, the inner and outer sides of the brick wall (k_{1} = 2.5 W/mK) are maintained at 1100°C and 700°C respectively as shown in figure.

The brick wall is covered by an insulating material of thermal conductivity k_{2}. The thickness of the insulation is 1/4th of the thickness of the brick wall. The outer surface of the insulation is at 200°C. The heat flux through the composite walls is 2500 W/m^{2}.

The value of k_{2} is ________ W/mK (round off to 2 decimal places).

Solution:

Given,

Assuming steady state, one-dimensional conduction heat transfer through composite slab,

**Thermal circuit:
⇒
⇒
⇒ **k

QUESTION: 19

Which of the following conditions is used lo determine the stable equilibrium of all partially submerged floating bodies?

Solution:

Metacentre must be higher level than the centre of gravity.

QUESTION: 20

In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is

Solution:

P_{vap} + ρ_{Hg}gh = P_{atm}

(P_{vap})= P_{atm} – ρ_{Hg}gh

For gauge pressure P_{atm} = 0 (P_{vap})_{gauge} =–ρ_{Hg}gh

So, –ve gauge pressure.

QUESTION: 21

A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.

If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

Solution:

For pure rolling

V_{P} = V = (PR )ω_{ } ...(i)

V_{Q }=2V = (QR)ω ...(ii)

Divide by (ii) to (i),

PR + QR =2r

PR + 2(PR)= 2r

From equation (i),

QUESTION: 22

The sum of two normally distributed random variables X and Y is

Solution:

X_{1} ∼ N (μ_{1}, σ_{1})

and X_{2} ∼ N (μ_{2}, σ_{2})

then

Always normally distributed.

QUESTION: 23

The solution of which additionally satisfies = 0 in the

Laplace s-domain is

Solution:

y ′′ – y =1

y (0) = 1

y ′(0) = 1

L {y ′′ – y }= L {1}

s^{2}Y (s) − sy (0)− y ′(0) − y (s) = 1/s

QUESTION: 24

Let then, I may also be expressed as

Solution:

Change on rules,

QUESTION: 25

A closed vessel contains pure water, in thermal equilibrium with its vapour at 25°C (Stage #1), as shown.

The vessel in this stage is then kept inside an isothermal oven which is having an atmosphere of hot air maintained at 80°C. The vessel exchanges heat with the oven atmosphere and attains a new thermal equilibrium (Stage #2). If the Valve A is now opened inside the oven, what will happen immediately after opening the valve?

Solution:

Initially when water and water vapour mixture is at 25°C then the maximum vapour pressure that can be at 25°C in the saturation pressure of vapour at 25°C.

The saturation press at 25°C is very less than 1 atm (101.3 kPa). It is around 3.17 kPa.

Now when this vessel will be kept in oven at 80°C then at 80°C the saturation pressure of water is still less than 1 atm. It is around 47.2 kPa.

The vapour pressure will reach 1 atm when temperature is 100°C. Hence at 80°C also the pressure will be the than 1 atm 80 when valve is opened air will enter the valve.

*Answer can only contain numeric values

QUESTION: 26

Let I be a 100 dimensional identity matrix and E be the set of its distinct (no value appears more than once in E) real eigenvalues. The number of elements in E is ______.

Solution:

I_{100}

Eigen values of I →

Set of distributed eigen value E = {1} Number of elements in E = 1

*Answer can only contain numeric values

QUESTION: 27

A bolt head has to be made at the end of a rod of diameter d = 12 mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is 40 mm.

To avoid buckling of the rod, a closed forging operation has to be performed with a maximum die diameter of ________ mm.

Solution:

If l > 3d then

Die dia = 1.5d

= 1.5(12)

= 18 mm

QUESTION: 28

The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are h_{1} and h_{3} respectively. The enthalpy at the stator outlet (or, rotor inlet) is h_{2}.The condition (h_{2} – h_{1}) = (h_{3} – h_{2}) indicates that the degree of reaction of this stage is

Solution:

As enthalpy across stator and rotor is equal it is 50% reaction stage.

QUESTION: 29

The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below.

P: Maximum Waviness Height (mm);

Q: Maximum Roughness Height (mm);

R: Minimum Roughness Height (mm);

S: Maximum Waviness Width (mm);

T: Maximum Roughness Width (mm);

U: Roughness Width (mm);

The correct match between the specifications and the symbols (I to VI) is:

Solution:

I-R, II-Q, III-P, IV-S, V-U, VI-T

QUESTION: 30

The equation of motion of a spring-mass-damper system is given by

The damping factor for the system is

Solution:

Comparing with standard equation:

2ξω_{n} =3

2ξ × 3 = 3

QUESTION: 31

Which one of the following statements about a phase diagram is INCORRECT?

Solution:

*Answer can only contain numeric values

QUESTION: 32

Consider the following network of activities, with each activity named A–L, illustrated in the nodes of the network

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.

Solution:

Time along path A-B-C-F-I-J-K = 42 hours

Time along path A-B-C-E-H-L = 31 hours

Time along path A-B-C-D-G-H-L = 40 hours

Slack for L = 42 – 40 = 2 hours

*Answer can only contain numeric values

QUESTION: 33

A beam of negligible mass is hinged at support P and has a roller support Q as shown in the figure.

A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is __________ N.

Solution:

1200 × 5 – R_{Q} × 4 = 0

QUESTION: 34

Two plates, each of 6 mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affected zone

1. Arc welding

2. MIG welding

3. Laser beam welding

4. Submerged arc welding

Solution:

Processes with low rate of heat input (slow heating) tend to produce high total heat constant within the metal, slow cooling rates, and large heat-affected zones. high heat input process, have low total heats, fast cooling rates and small heat affected zones.

QUESTION: 35

An attempt is made to pull a roller of weight W over a curb (step) by applying a horizontal force F as shown in the figure.

The coefficient of static friction between the roller and the ground (including the edge of the step) is μ. Identify the correct free body diagram (FBD) of the roller when the roller is just about to climb over the step.

Solution:

Weigh = W

**Note:
(i) **When the cylinder is about to make out of the curb, it will loose its contact at point A, only contact will be at it B.

*Answer can only contain numeric values

QUESTION: 36

Moist air at 105 kPa, 30°C and 80% relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at 100 kPa and 15°C. The saturation pressure of water at 30°C and 15°C are 4.24 kPa and 1.7 kPa respectively.

Molecular weight of water is 18 g/mol and that of air is 28.94 g/mol. The mass of water condensing out from the duct is ______ g/kg of dry air (round off to 2 decimal places).

Solution:

P_{t1} = 105 kPa, DBT_{1} = 30°C, φ_{1} = 0.8 P_{t2} = 100 kPa, DBT_{2} = 15°C, φ_{2} = 1 P_{vs1} = 4.24 kPa

Pvs2 = 1.7 kPa

M_{water} = 18 g/mol.

M_{air} = 28.94 g/mol.

∴ P_{v1} = 3.392

∴

= 20.76 gv/kgd.a

∴ P_{v2} = 1.7

∴

Mass of water condensing = ω_{1 }– ω_{2} = 20.76 – 10.75

= 10.01 g/kgd.a

QUESTION: 37

The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth

If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed ω_{S} and ω_{R}, respectively, then the angular speed of the arm AB is

Solution:

r_{s} + 2r_{P} = r_{R}

⇒ T_{S} + 2T_{P} = T_{R }(T_{P} = T_{S})

3T_{P} = T_{R}

⇒ 3T_{P} = T_{R}

y + x = ω_{S}

Substract by,

QUESTION: 38

The forecast for the monthly demand of a product is given in the table below.

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is

Solution:

F_{t} = F_{t – 1} + α(D_{t – 1} – F_{t – 1})

For 2nd month F_{t} = 31.8, for 1^{st} month

F_{t} _{– 1} = 32 and D_{t – 1} = 30

31.8 = 32 + α(30 – 32)

2α = 32 – 31.8

α = 0.1

*Answer can only contain numeric values

QUESTION: 39

The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure.

The mean turning moment is 2000 Nm. The average engine speed is 1000 rpm. For fluctuation in the speed to be within ±2% of the average speed, the mass moment of inertia of the flywheel is _________ kgm^{2}.

Solution:

N = 1000 rpm

*Answer can only contain numeric values

QUESTION: 40

A rigid block of mass m_{1} = 10 kg having velocity v_{0} = 2 m/s strikes a stationary block of mass m_{2 }= 30 kg after travelling 1 m along a frictionless horizontal surface as shown in the figure.

The two masses stick together and jointly move by a distance of 0.25 m further along the same frictionless surface, before they touch the mass-less buffer that is connected to the rigid vertical wall by means of a linear spring having a spring constant k = 10^{5} N/m.

The maximum deflection of the spring is _________ cm (round off to 2 decimal places).

Solution:

Collision Theory

Conservation of momentum,

m_{1} × v_{0} + m_{2} × 0 = (m_{1} + m_{2}) × v

10 × 2 = (10 + 30)v

20 = 40v

v = 0.5 m/s

Now,

10 = 10^{5} × x^{2}

⇒

QUESTION: 41

A cantilever of length l, and flexural rigidity EI , stiffened by a spring of stiffness k, is loaded by transverse force P, as shown

The transverse deflection under the load is

Solution:

Δ_{beam} = Δ_{spring}

∴

∴

*Answer can only contain numeric values

QUESTION: 42

There are two identical shaping machines S_{1} and S_{2}. In machine S_{1}, the width of the workpiece is increased by 10% and the feed is decreased by 10%, with respect to that of S_{1}. If all other conditions remain the same then the ratio of total time per pass in S_{1} and S_{2} will be __________ (roundoff to one decimal place).

Solution:

*Answer can only contain numeric values

QUESTION: 43

Bars of 250 mm length and 25 mm diameter are to be turned on a lathe with a feed of 0.2 mm/rev. Each regrinding of the tool costs Rs. 20. The time required for each tool change is 1 min. Tool life equation is given as VT^{0.2} = 24 (where cutting speed V is in m/min and tool life T is in min). The optimum tool cost per piece for maximum production rate is Rs. ________ (round off to 2 decimal places).

Solution:

Optimum tool life (T_{o}) = = 4 min

V = πDN

⇒ 18.19 = π × 0.025 × N

⇒ N = 231.6 rpm

Maching time per piece

Number of tool needed per piece work

∴ The optimum tool cost per piece

*Answer can only contain numeric values

QUESTION: 44

A point P on a CNC controlled XY -stage is moved to another point ‘Q’ using the coordinate system shown in the figure below and rapid positioning command (G00).

A pair of stepping motors with maximum speed of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screw, each with a uniform pitch of 0.5 mm. The time needed to position the point ‘P’ to the point ‘Q’ is _______ minutes. (round off to 2 decimal places).

Solution:

N = 800 rpm, P = 0.5 mm/rev

V = N × P = rev/min × mm/rev = 400 mm/min

There are two stepper motor so both will work till 0.75 min then y axis motor will stop then only x axis motor will run for 0.75 more, so total time will be 1.5 min.

*Answer can only contain numeric values

QUESTION: 45

The spectral distribution of radiation from a black body at T_{1} = 3000 K has a maximum at wavelength λ_{max}. The body cools down to a temperature T_{2}. If the wavelength corresponding to the maximum of the spectral distribution at T_{2} is 1.2 times of the original wavelength λmax, then the temperature T_{2} is ________ K (round off to the nearest integer).

Solution:

From Wien’s Displacement law,

λ_{m}T = constant ⇒ λm_{1}T_{1} = λ_{m2}T_{2}

λ_{m1} × 3000 = 1.2 λ_{m1} × T_{2}

*Answer can only contain numeric values

QUESTION: 46

Consider a flow through a nozzle, as shown in the figure below:

The air flow is steady, incompressible and inviscid. The density of air is 1.23 kg/m^{3}.

The pressure difference (p_{1} – p_{atm}) is _______ kPa (round off to the nearest integer).

Solution:

A_{1}V_{1} = A_{2}V_{2}

0.2 × V_{1} = 0.02 × 50

Applying BE

(∵ z_{1} = z_{2})

QUESTION: 47

The function f (z ) of complex variable z = x + iy , where i = −1 , is given as f (z ) = (x^{3} – 3xy^{2}) + iv (x, y ). For this function to be analytic, v (x, y ) should be

Solution:

f (z)= u + iv

u = x^{3} – 3 xy^{2}, v = v (x, y )

For f (z ) to be Analytical,

ux =3x^{2} – 3y^{2} = v_{y}

uy =–6 xy = –v_{x}

v_{x} =6 xy by integrating w.r.t x ⇒ v = 3x_{2}y + C_{1}

vy =3x^{2} – 3y^{2} by integrating w.r.t y ⇒ v = 3x^{2}y – y^{3} + C_{2}

v =(3x^{2}y – y^{3}) + constant (C_{1} = –y^{3})

*Answer can only contain numeric values

QUESTION: 48

A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as 1000 kg/m^{3}, and the acceleration due to gravity as 10 m/s^{2}, the natural frequency of small oscillations of the ball, normal to the water surface is _________ radians/s (roundoff to 2 decimal places).

Solution:

Given data:

R = 20 cm = 0.20 m

ρ = 1000 kg/m^{3}

g = 10 m/s^{2}

mg =

*Answer can only contain numeric values

QUESTION: 49

A steel spur pinion has a module (m) of 1.25 mm, 20 teeth and 20° pressure angle.

The pinion rotates at 1200 rpm and transmits power to a 60 teeth gear. The face width (F ) is 50 mm, Lewis form factor Y = 0.322 and a dynamic factor K_{v} = 1.26. The bending stress (σ) induced in a tooth can be calculated by using the Lewis formula given below.

If the maximum bending stress experienced by the pinion is 400 MPa. the power transmitted is __________ kW (round off to one decimal place),

Lewis formula: where W^{t} is the tangential load acting on the pinion.

Solution:

F_{t} × c_{v}s = bmy [σ_{b}]max

c_{v} =1.26

F_{t} × 1.26 × 1 = 50 × 1.25 × 0.322 × 400

F_{t} = 6388.88 N

*Answer can only contain numeric values

QUESTION: 50

Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.

The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300 cm^{2}. Heat is now added and the piston moves slowly from its initial position until it reaches the stops. The spring constant of the linear spring is 12.5 N/mm. Considering the air inside the cylinder as the system, the work interaction is ________ J. (round off to the nearest integer).

Solution:

P_{0} = 100 kPa, P_{1} = 105 kPa, K = 12.5 N/mm = 12.5 kN/m

A = 300 cm^{2} = 300 × 10–4 m^{2}

x = 8 cm = 8 × 10^{–2} m

1-2 constant pressure

W_{1-2} = P_{1} × A × x = 105 × 300 × 10^{–4} × 8 × 10^{–2}

= 0.252 kJ = 252 J

P_{2} = 105 kPa

P_{3} × A = P_{2}A + Kx

W_{2-3} = 0.2919 kJ = 291.9 J

∴

W_{total} = W_{1-2} + W_{2-3} = 0.5439 kJ = 543.91 ≈ 544 J

**Alternate Solution:**

Total work = Workdone because of 105 kPa pressure + Workdone against spring which is equal to energy stored in spring

= 0.504 + 0.04

= 0.544 kJ = 544 J

*Answer can only contain numeric values

QUESTION: 51

Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from 15 to 21. Take ratio of specific heats = 1.3 and cut-off ratio of the cycle r_{c} = 2.

The difference between the new and the old efficiency values, in percentage,

(round off to one decimal place).

Solution:

η_{d}, _{r=21} – η_{d}, _{r=15} =4.8%

QUESTION: 52

Two rollers of diameters D_{1} (in mm) and D_{2} (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights H_{1} (in mm) and H_{2} (in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.

Which one of the following is the correct relationship to evaluate the angle α as shown in the figure?

Solution:

*Answer can only contain numeric values

QUESTION: 53

A fair coin is tossed 20 times. The probability that 'head' will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).

Solution:

Fair coin tossed 20 times

First 10 times probability that head will appear exactly 4 times

P [4 heads in 10 tosses] ⋅ P [4 tails in 10 tosses]

*Answer can only contain numeric values

QUESTION: 54

For the integral the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________. (round off to one decimal place).

Solution:

**True Value**

=4π + 4 = 16.566

By trapezoidal rule, (single step)

h = π/2

Approx.

Absolute error = ⎥ True value – Approximate value⎥

= ⎥ 16.566 – 15.707⎥ = 0.859

Absolute percentage error =

QUESTION: 55

A helical spring has spring constant k. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes

Solution:

k_{(spring)} =

k_{new} =

Hence, k_{new} = k

*Answer can only contain numeric values

QUESTION: 56

A cylindrical bar with 200 mm diameter is being turned with a tool having geometry 0° - 9° - 7° - 8° - 15° - 30° - 0.05 inch (Coordinate system, ASA) resulting in a cutting force F_{c1}. If the tool geometry is changed to 0° - 9° - 7° - 8° - 15° - 0° - 0.05 inch (Coordinate system. ASA) and all other parameters remain unchanged, the cutting force changes to F_{c2}. Specific cutting energy (in J/mm^{3}) is U_{c} = U_{0} (t_{1})^{–0.4}, where U_{0} is the specific energy coefficient, and t_{1} is the uncut thickness in mm. The value of percentage change in cutting force F_{c2}. i.e., x 100 , is _______ (round off to one decimal place).

Solution:

C_{s1} = 30°

∴ λ_{1} = 90 – 30 = 60°

Cs_{2} =0°

∴ λ_{2} = 90 – 0 = 90°

We know that specific energy consumption

∴ F_{c} = U_{0}(fsinλ)^{−0.4}× 1000fd

∴ F_{c} ∝ (sin λ)^{–0.4}

∴

QUESTION: 57

The directional derivative f (x, y, z) = xyz at point (–1, 1, 3) in the direction of vector is

Solution:

f = xyz

Directional derivative of f in direction of

*Answer can only contain numeric values

QUESTION: 58

A mould cavity of 1200 cm^{3} volume has to be filled through a sprue of 10 cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is 2 cm^{2}.

Consider acceleration due to gravity as 9.81 m/s2. Neglecting frictional losses due to molten metal flow, the time taken to fill the mould cavity is _______ seconds (round off to 2 decimal places).

Solution:

Volume of mould cavity (V ) = 1200 cm^{3} Height of sprue (h_{s}) = 10 cm Area of sprue at the bottom (A_{s}) = 2 cm^{2}

g = 9.81 m/s^{2}

Sprue is feed a horizontal runner: Filling time required (t_{f}) = ?

By assuming top gate, A_{g} = A_{s} = A_{3} = 2 cm^{2}

t_{f} = 4.28 s

QUESTION: 59

One kg of air in a closed system undergoes an irreversible process from an initial state of p_{1} = 1 bar (absolute) and T_{1} = 27°C, to a final state of p_{2} = 3 bar (absolute) and T2 = 127°C. If the gas constant of air is 287 J/kgK and the ratio of the specific heats γ = 1.4, then the change in the specific entropy (in J/kgK) of the air in the process is

Solution:

P_{1 }= 1 bar, P_{2} = 1 bar, T1 = 300 K, T_{2 }= 400 K,

*Answer can only contain numeric values

QUESTION: 60

Uniaxial compression test data for a solid metal bar of length 1 m is shown in the figure.

The bar material has a linear elastic response from O to P followed by a non-linear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is _______ mm (round off to one decimal place).

Solution:

For both end pin,

*Answer can only contain numeric values

QUESTION: 61

Water (density 1000 kg/m^{3}) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section A are V_{A} = 3.2 m/s, p_{A} =186 kPa and z_{A} = 24.5 m respectively, and those at section B are V_{B} = 3.2 m/s, p_{B} = 260 kPa and z_{B} = 9.1 m, respectively. If acceleration due to gravity is 10 m/s^{2} then the head lost due to friction is _________ m (round off to one decimal place).

Solution:

Energy at ‘A’ head =

= 18.6 + 0.512 + 24.5 = 43.612

Energy at ‘b’ head =

= 26 + 0.512 + 9.1 = 35.612

E_{A} > E_{B}, so flow from ‘A’ to ‘B’

Heat loss = E_{A }– E_{B} = 43.612 – 35.612 = 8 m of water head

*Answer can only contain numeric values

QUESTION: 62

In a steam power plant, superheated steam at 10 MPa and 500°C, is expanded isentropically in a turbine until it becomes a saturated vapour. It is then reheated at constant pressure to 500°C. The steam is next expanded isentropically in another turbine until it reaches the condenser pressure of 20 kPa. Relevant properties of steam are given in the following two tables. The work done by both the turbines together is ______ kJ/kg (roundoff to the nearest integer).

Solution:

Given data: h_{1} = 3373.6 kJ/kg, h_{3} = 3478.4 kJ/kg, h_{2} = 2778.1 kJ/kg, s_{1} = s_{2} (as from table)

s_{3} = s_{4}

s_{3} = 7.7621 = 0.8319 + x + (7.9085 – 0.8319)

x_{4} = 0.9793

h_{4} = h_{f} + x_{4} × (h_{g} – h_{f}) = 2560.91 kJ/kg

W_{T} =(h_{1} – h_{2}) + (h_{3} – h_{4}) = 1512.95 kJ/kg

*Answer can only contain numeric values

QUESTION: 63

Water flows through a tube of 3 cm internal diameter and length 20 m, The outside surface of the tube is heated electrically so that it is subjected to uniform heat flux circumferentially and axially. The mean inlet and exit temperatures of the water are 10°C and 70°C, respectively. The mass flow rate of the water is 720 kg/h. Disregard the thermal resistance of the tube wall. The internal heat transfer coefficient is 1697 W/m^{2}K. Take specific heat C_{p} of water as 4.179 kJ/kgK. The inner surface temperature at the exit section of the tube is __________ °C (round off to one decimal place).

Solution:

h = 1697 W/m^{2}K

From energy balance equation,

Heat flux × Area of HT =

q ′′ × πDL =

q ′′ = 26604.34 W/m^{2}

Applying Newton’s law of cooling at exit

T_{tube} at exit = 85.67°C

QUESTION: 64

A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure

The material of the cylinder has Young's modulus E, Poisson's ratio ν, and coefficient of thermal expansion α. What is the minimum rise in temperature ΔT of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere?

Solution:

Since cylinder is open at both end.

∴ σ_{L} =0

For no leakage, εL_{Pr} = ε_{Ltemp
}

*Answer can only contain numeric values

QUESTION: 65

For a single item inventory system, the demand is continuous, which is 10000 per year.

The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.

As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year.

Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).

Solution:

Given data: D = 10000 items/year, C_{o} = Rs. 300/order,

C_{h} = Rs. 4/unit/year, Cb = Rs. 25/unit/year,

For minimum tool cost,

Quantity ordered, Q =

Q = 1319.09 unit

Now, for minimum cost, optimum units backordered

(Q – S) × C_{h} =(S) × C_{b}

S (C_{b} + C_{h})= Q × C_{h}

Maximum inventory in the system, Q_{max} = Q – S

= 1319.09 – 181.94

= 1137.15 unit

≈ 1137 units

**Alternate:**

Maximum inventory in system =

### CBSE Past Year Paper Session (2018), Math Class 12

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