SILVER OAK COLLEGE OF ENGINEERING & …socet.edu.in/socet/wp-content/uploads/2017/11/Question-Papers-ALL.pdfenroll. no. _____ silver oak college of engineering & technology aditya

Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY

BE - SEMESTER–I • MID SEMESTER-I EXAMINATION – WINTER 2017

SUBJECT: Communication Skills (2110002) (All BRANCH)

DATE: 03-10-2017 TIME: 10:00 am to 11:30 am TOTAL MARKS:40

Instructions: 1. Q. 1 is compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.

Q.1 (a) Give Answer with most suitable/correct option. [05]

(i) Feedback means …………… the receiver’s message.

(a) Encoding (b) Transmission of (c) Decoding (d) Ideation of

(ii) ………… is the study of communication done through the use of

time.

(a) Kinesics (b) Chronemics (c)Para-Linguistics (d) Proxemics

(iii) ………. has written the story the Romance of a Busy Broker.

(a) O’ Henry (b) Robert Frost (c) Nissim Ezekiel (d) Pushpa

(iv) There are total ……….. Vowel sound in English language.

(a) 05 (b) 20 (c) 24 (d) 26

(v) ……….. student has done fair in the exams.

(a) Each (b) All (c) Most (d) Many

(b) Explain barriers to effective communication with examples. [05]

Q.2 (a) Define the term ‘Communication’ and explain the process of

communication with a diagram. [06]

(b) Elaborate the ‘Kinesics’ with examples. [05]

(c) Why should the presenter know his/her ‘Audience’ and ‘Locale’

before delivering a presentation? [04]

OR

Q.2 (a) “Communication is the backbone of any organization”- Justify

the statement. [06]

(b) What is presentation? State the different strategies to make an

effective presentation. [05]

(c) Distinguish between General and Technical Communication. [04]

Q.3 (a) Discuss the central theme of the poem “The Road Not Taken”. [06]

(b) Keeping the use of irony in mind, discuss the appropriateness of

the title ‘The Eyes Are Not Hear’. [05]

(c) Explain the character of ‘Miss Pushpa’ with reference of poem

“Goodbye Party For Miss Pushpa T. S”. [04]

OR

Q.3 (a) Discuss the theme of the story “The Romance of a Busy Broker’. [06]

(b) What personal choices does the poem ‘The Road Not Taken’

remind you of? [05]

(c) Write a character sketch note on the Harvey Maxwell. [04]

Enroll. No. _____________



BE - SEMESTER–I• MID SEMESTER-I EXAMINATION – WINTER 2017

SUBJECT: Computer Programming and Utilizations (2110003)

(ME/AE/CH/CL/IT/EC)

DATE:05-10-2017 TIME:10:00 am to 11:30 am TOTAL MARKS:40

Instructions: 1.Q. 1 is compulsory.

2. Figures to the right indicate full marks. 3. Assume suitable data if required.


(i) What is Algorithm?

(a)Application code

(b)Type of programming language

(c)Step by step procedure for calculations

(d)None of the above

(ii) Which of the programming language is said to be machine

independent language?

(a)High Level Language

(b)Machine Level Language

(c)Assembly Level Language

(d)All of the above

(iii) Which of the following symbol is for AND operator?

(a) || (b) && (c) & (d) !

(iv) Which are not looping structures?

(a) For loop (b) Do...while loop (c) While loop (d) if…else

(v) Which of the following is ternary operator?

(a) ?? (b) :? (c) ?: (d) ::

(b) Explain Symbols of flowchart and explain it with suitable

examples.

[05]

Q.2 (a) Draw the Block Diagram of Computer Architecture and

explain each block with its functions. [06]

(b) Explain various operators used in C language. [05]

(c) Define following:

1. Application software 3. Compiler 2. Assembler 4. Operating system

[04]

OR

Q.2 (a) Explain structure of c program and list the features of C

language. [06]

(b) Explain basic data types of C. [05]

(c) Explain implicit type conversion and explicit type conversion

with example. [04]

Q.3 (a) Explain different types of loops in C with example. [06]

(b) Write a program to make simple calculator using switch..case

statement. [05]

(c) Write short notes on nested If-else statement. [04]

OR

Q.3 (a) Discuss general form of following decision — making statements with example.

1. IF 2.SWITCH 3. GOTO [06]

(b) Write a program for following Series:

13 + 23 + 33 + 43 … + n3. [05]

(c) Explain Else-If ladder with example. [04]

Enroll. No. _________________________


BE - SEMESTER - I • MID SEMESTER - I EXAMINATION - WINTER 2017

SUBJECT: ELEMENTS OF CIVIL ENGINEERING (2110004) [CL / ME / AE]

DATE : 09 Oct. 2017 TIME : 10:00 am to 11:30 am TOTAL MARKS : 40

Instructions: 1. Q. 1 is compulsory.

2. Figures to the right indicate full marks.

3. Assume suitable data if required.


(i) The Diagonal Scale is used to measure in how many units

(a) One (b) Two (c) Three (d) None of Above

(ii) Which of the following scale is the smallest one?

(a) 1cm = 5m (b) R.F=1

5000 (c) 1:10,000 (d) 1cm = 5km

(iii) In 20 m Metric Chain brass ring is provided at every______ and brass tally is

provided at every ______ length.

(a) 1m, 5m (b) 5m, 1m (c) 1m, 2m (d) 2m, 1m

(iv) Dead Load of RCC work is generally taken as _____

(a) 2400 kg/m3 (b) 200 gm/m (c) 2400 kg/m2 (d) 2400 N/m3

(v) A 1st class brick when immersed in cold water for 24 hours should not absorb

water more than______

(a) 1/10th (b) 1/6th (c) 1/4th (d) 1/5th

(b) Enlist different Branches of Civil Engineering and Briefly describe any two of

them.

[05]

Q.2 (a) What are the different Classifications of Surveying based on Instruments used. [06]

(b) What is Offsetting. Also, explain Optical Square in detail. [05]

(c) A 30 m chain was tested and found 80 cm too short before the start of work.

After measuring a distance of 2250 m, it was found 45 cm too long and after

measuring 1950 m; the chain was found 13 cm too long during testing at the

end of day’s work. Find Correct Distance measured during the day.

[04]

OR

Q.2 (a) What are the various Instruments used in Chaining. Describe them in brief [06]

(b) Explain Fundamental Principles of Surveying. [05]

(c) A 20 m chain was used in a Chain Survey to measure distance 555 m. Calculate

the true length of the line if

1. The length of chain was 20 m at start of the day and was 0.18 m too long at

the end of the day.

2. The length was measured with a 20 m chain and chain was 18 cm too long.

[04]

Q.3 (a) Classify Buildings based on Occupancy and Explain any six in short [06]

(b) What is Concrete ? Write about any three Types of Concrete. [05]

(c) What is Sand ? Short Note on Natural Source of Sand. [04]

OR

Q.3 (a) Define Brick. Discuss Types of Bricks. Also enlist Qualities of a Good Brick. [06]

(b) Enlist various Types of Foundation. Also write brief note on Shallow

Foundation with neat sketches.

[05]

(c) Differentiate between Load Bearing and Framed Structures. [04]

All The Best

Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING AND TECHNOLOGY BE - SEMESTER–I • MID SEMESTER-I EXAMINATION – WINTER 2017

SUBJECT: ELEMENTS OF ELECTRICAL ENGINEERING (2110005) (CE/IT/EC) DATE: 09/10/2017 TIME:10:00 am to 11:30 am TOTAL MARKS:40

Instructions:1. Q. 1 is compulsory. 2. Figures to the right indicate full marks.3. Assume suitable data if required.


(i) For a series resonance condition of a AC circuit current is

(a) minimum (b) maximum (c) zero (d) infinity

(ii) The Frequency of DC supply is (a)50 Hz (b)60 Hz(c) 0 Hz (d) 100 Hz

(iii) The unit of temperature coefficient of resistance

(a) Ω/°C (b) °C-1 (c) 1/ Ω°C (d) Unit less

(iv) The average value of sinusoidal wave over a half cycle

(a)1.11 (b)0.637 (c) 1.414 (d) 0

(v) Average power consumption in purely capacitive circuit is

(a)VrmsIrmscosØ (b) Zero (c)VIcosØ (d) maximum

(b) The following expressions represent the instantaneous values of currents of

three coils connected in parallel I1= 50 sin ωt, I2= 40 sin (ωt+60), I3= 60 sin (ωt-30) Find the expression for the resultant current when coils are connected in

parallel to give sum of currents.

[05]

Q.2 (a) With necessary diagram explain the method of transforming a delta connected network in to star network.

[06]

(b) State and explain Kirchhoff’s laws. [05]

(c) An inductive circuit of resistance 2 Ω and inductance of 0.01 H is connected to a 250 V, 50 Hz supply. What capacitance is required to be placed in series with this circuit to produce resonance? Also find out resonance frequency for 10µF capacitance for the above R and L value.

[04]

OR

Q.2 (a) Define Temperature co-efficient of resistance. Derive & obtain the expression t2 = 1 / (1/αt1 + (t2 - t1)) with usual notation.

[06]

(b) The Coil having a resistance R and inductance L is connected in parallel with capacitor C then explain the phenomena of electrical resonance for this circuit. Draw relevant vector diagram & define Q factor of the circuit.

[05]

(c) Explain series R-L-C circuit with necessary phasor diagram for any one from XL>XC and XL<XC.

[04]

Q.3 (a) Explain how ac sinusoidal emf is generated? Derive its equation of e = EmSin ωt.

[06]

(b) Explain the phenomena of electrical resonance in R–L–C series circuit connected to variable frequency supply. Draw relevant vector diagram & define Q factor of the circuit.

[05]

(c) Compare Series and Parallel Resonance. [04]

OR

Q.3 (a) Prove that current in purely capacitive circuit leads its voltage by 90° and average power consumption in pure capacitor is zero.

[06]

(b) Define the following: (1) Form Factor (2) Peak factor (3) Frequency (4) Cycle (5) Time Period

[05]

(c) Explain Analysis of purely Resistive Circuit with relevant phasor diagram [04]

Enroll. No. _____________




SUBJECT: ELEMENTS OF MECHANICAL ENGINEERING (2110006) (CE/IT/ME/EC/CL)

DATE: 27-10-2017 TIME: 02:00 pm to 03:30 pm TOTAL MARKS: 40




(i) Joule is the unit of

(a) Work (b) Power (c) Force (d) Pressure

(ii) In NH3-H2O vapor absorption refrigeration system, H2O acts

as:

(a) Refrigerant (b) Absorbent (c) Catalyst (d) None

(iii) Work is considered as negative when

(a) Work is done by the system (b)Work is done on the system

(c) always (d) Never

(iv) Power available at Engine output shaft is known as

(a) Brake Power (b) Indicated Power

(c) Mechanical Power (d) None

(v) Which one of the following is the low pressure boiler

(a) Cochran (b) Lancashire (c) Babcock & Wilcox (d) None

(b) Define Refrigerant, Refrigeration effect, Ton of refrigeration [05]

Q.2 (a) Differentiate between Petrol Engine and Diesel Engine. [06]

(b) Draw the neat sketch of typical IC engine with proper

nomenclature. [05]

(c) A gas is compressed from pressure of 1 bar and volume 0.9 m3 to

a pressure of 5 bar while its temperature remains constant. Find

out volume of gas after compression and work required in the

process.

[04]

OR

Q.2 (a) Explain working of 4 Stroke Diesel Engine [06]

(b) Differentiate between 4 Stroke IC Engine and 2 Stroke IC

Engine. [05]

(c) Give Boyle’s law & Charle’s law with mentioning their

equations. [04]

Q.3 (a) Draw the neat sketch of any one type of low pressure boiler and

give its Characteristics. [06]

(b) A six cylinder 4 stroke I.C. engine is to develop 90 kW indicated

power at 900 rpm. The stroke to bore ratio is 1.2, Assuming

mechanical efficiency is 81% and break mean effective pressure

of 6 bar. Determine the diameter and stroke of the engine.

[05]

(c) Give the functions of following:

1. Pressure Gauge

2. Safety Valve

3. Economizer

4. Water Level Indicator

[04]

OR

Q.3 (a) Explain with neat sketch working of vapor absorption

refrigeration system (VARS) [06]

(b)

A diesel engine developed 5 kW. It’s indicated thermal

efficiency is 30% and mechanical efficiency is 75%. Estimate the

fuel consumption of engine in kg/hr. Assume specific gravity of

diesel is 0.87 and C.V of fuel=4270kJ/kg.

[05]

(c) Derive the relation, PVᵞ= Constant [04]

Enroll. No. _________________________


BE - SEMESTER - I • MID SEMESTER - I EXAMINATION - WINTER 2017 SUBJECT: ENVIRONMENTAL STUDIES (2110007) (CE/IT/ME)

DATE: 04-10-2017 TIME: 10:00am -11:30am TOTAL MARKS: 40

Instructions: 1. Q.1 is compulsory.



(i) The outer soil crust of the earth is known as______

(a) Hydrosphere (b) Exosphere (c) Lithosphere (d) Mesosphere

(ii) Which ecosystem shows an inverted pyramid of biomass?

(a) Pond (b) Forest (c) Grass Land (d) Desert

(iii) During photosynthesis Autotrophs takes in______

(a) Oxygen (b) Carbon dioxide (c) Nitrogen (d) Sulphur

(iv) The deaths of infant per 1000 births, are known as______

(a)Birth rate (b) Mortality (c)Infant mortality rate (d)Total fertility rate

(v) Out of these which one is renewable source of energy?

(a) Natural gas (b) Wind energy (c) Nuclear power (d) Petroleum

(b) Define the following terms:

I. Ecology

II. Biogeochemical Cycle

III. Reforestation

IV. Population Density

V. Environmental Degradation

[05]

Q.2 (a) What is Ecological Pyramid? Explain Different types of Ecological Pyramids. [06]

(b) Write the Importance of Forests. [05]

(c) What is Urbanization? Discuss the Effects of Urbanization [04]

OR

Q.2 (a) Explain in detail with neat sketch:

1. Nitrogen Cycle 2. Oxygen Cycle [06]

(b) Differentiate between Renewable & Non Renewable Resources; Explain various

conservation measures of Natural resources. [05]

(c) Explain the Environmental Problems posed by Population Explosion. [04]

Q.3 (a) Why environmental education is important in engineering curriculum? What are the

objectives and guiding principles of environmental education? [06]

(b) Write a brief note on Sources of Water. [05]

(c) Explain in detail the Structure / Components of Ecosystem. [04]

OR

Q.3 (a) Define Environment. Explain the Components of Environment and their major

interaction. [06]

(b) Explain the Environmental Effects/ Impact of Agriculture. [05]

(c) Explain the important Theories of Population Growth. [04]

Enroll. No. _____________


BE - SEMESTER– I • MID SEMESTER-I EXAMINATION – WINTER 2017

SUBJECT: ENGINEERING PHYSICS (2110011) (CL-A,B,C/CE-A,B,C,D/ME-E/AE)

DATE: 04-10-2017 TIME: 10:00 AM to 11:30 AM TOTAL MARKS:40



Q.1 (a) Answer all 5 MCQs. [05]

(i) The frequency (f) of Infrasonic Wave is ________.

(a) f > 20 kHz (b) f < 20 kHz (c) f < 20 Hz (d) f > 20 Hz

(ii) The unit of loudness is ______.

(a) Phon (b) m/s (c) Ampere (d) O.W.U.

(iii) Superconductors are perfect __________materials.

(a)Paramagnetic (b)Diamagnetic (c)Ferromagnetic (d)Antiferromagnetic

(iv) The formula for critical current is __________.

(a) 2rHc (b) 2Hc (c) 4rHc (d) 2rHo

(v) The resistivity of Mercury drops to zero at ___ K.

(a) 4 K (b) 4.2K (c) 0 K (d) 77 K.

(b) (i) What is the resultant sound level when an 80 dB sound is added to 70 dB sound.

[03]

(ii) Mention the difference between Spontaneous and Stimulated Emission [02]

Q.2 (a) Describe seven factor affecting acoustics of any building and provide their

remedies as well. [07]

(b) Describe the principle and method of producing ultrasonic wave by magnetostriction method. Give merits and demerits of the method.

[05]

(c) The volume of a room is 1500 m3. The wall area of the room is 260 m2, the floor area is 140 m2 and the ceiling area is 140 m2. The average sound absorption coefficient for the wall is 0.03, for the ceiling it is 0.8 and for the floor it is 0.06. Calculate the average absorption coefficient and the reverberation time.

[03]

OR

Q.2 (a) Define Piezoelectricity. Explain in detail the Principle, Construction, Working, Advantage and Limitations of Piezoelectric Method for generation of Ultrasonic Waves.

[07]

(b) Write a short note on Types of Sound Absorbing materials. [05]

(c) A hall has a volume of 1,20,000 m3. It has a reverberation time of 1.55 sec. What is the average absorbing power of the surface if the total absorbing surface is 26,500 m2.

[03]

Q.3 (a) Write a short note on Nd:YAG laser clearly describing its Principle, Construction, Working and Applications. Draw figures as necessary.

[07]

(b) Explain in detail: (i) Josephson junction (ii) DC/AC Josephson Effect (iii) SQUID (iv) Cryotron.

[05]

(c) For mercury of mass number 202, the value is 0.50 and Tc is 4.2 K. Find the transition temperature for the isotope of mercury of mass number 200.

[03]

OR Q.3 (a) Define: Superconductivity and explain in brief all general properties of a

superconductor. [07]

(b) Differentiate Type I and II superconductors. Draw necessary diagram as well. [05]

(c) Calculate the critical current for a superconducting wire of lead having a diameter of 1 mm at 4.2 K. Critical temperature for lead is 7.18 K and Hc (0) = 6.5 x 104 A/m.

[03]

BEST OF LUCK TO ALL

Enroll. No. _____________




SUBJECT: ENGINEERING GRAPHICS (2110013) (CE/ME/AE/CL/CH)

DATE: 11-10-2017 TIME: 10:00 am to 11:45 am TOTAL MARKS: 40




(i) If line is parallel to HP and VP both then _____

(a) PL=TL (b) EL=TL

(c) PL=EL=TL (d) All of the above

(ii) The internal angle of regular pentagon is ___ degree.

(a) 72 (b) 108 (c) 120 (d) 150

(iii) If point A is above HP and on VP then point A is in ____ quadrant.

(a) 1st (b) 2nd (c) Either 1st or 2nd (d) None of the above

(iv) If a client of yours is having difficulty visualizing a design, what type

of drawing would be the easiest to understand for such client?

(a) Three views of orthographic (b) Two views of orthographic

(c) One view of orthographic (d) Isometric View

(v) The sequence for the direction of view or line of sight for any

orthographic projection drawn in third angle projection method is

(a) Observer>Plane>Object (b) Observer>Object>Plane

(c) Plane>Observer>Object (d) Plane>Object>Observer

Q.1 (b) Construct a curve of half convolution for given length of shortest

radius vector equal to 8 mm and the ratio of the lengths of successive

radius vectors equal to 7:5 for vectorial angle of 45º. Name the curve.

[05]

Q.2 (a) Construct an Archimedean spiral of one and half convolutions given

the greatest and shortest radii as 84mm and the 00 mm respectively. [06]

(b) The projectors of the ends of a line AB is 50 mm apart. The end A is

20 mm above HP and 30 mm in front of VP. The end B is 10 mm

below HP and 40 mm behind VP. Determine the true length of AB,

inclination with HP and VP. Also find its apparent angles.

[05]

(c) Construct a diagonal scale of RF = 1/36 showing Yard, Foot and

Inch and to measure up to 6 Yards. Show 4 Yard 1 feet 10 inches. [04]

OR

Q.2 (a) Draw an Archimedean spiral of 2/3 convolution. When maximum

and minimum radii being 60mm and 20mm respectively. [06]

(b) A line PQ 60mm long its end P on VP and end Q on HP. Line is

inclined to HP by 60º and VP by 30º and it is 20 mm away from the [05]

profile plane. Draw the projection of the line.

(c) Construct a scale of RF=1/60 to read yard and feet, and long enough

to measure up to 5 yards. Show 3 yards 3 feet on the scale. [04]

Q.3 (a) Draw front view and top view of the object shown in fig. 1 using first

angle projection system. [06]

(b) The front view of line AB, 90 mm long, measures 65 mm. Elevation

is inclined at 45° to XY line. Point A is 20 mm below HP and on VP.

Point B is in third quadrant. Draw the projections and find its

inclinations with HP and VP.

[05]

(c) Draw an involute of circle of 30 mm diameter for one turn. [04]

OR

Q.3 (a) Draw sectional front view along section P-Q of the object shown in

fig. 1 using third angle projection method. [06]

(b) A line AB 65 mm long appears to be 55 mm in plan and 45 mm in

elevation. It’s end A is 20 mm below H.P. and 40 mm behind V.P.

Draw projections of a line and find the true angle of inclinations of

line with H.P. and V.P.

[05]

(c) Construct an involute of square of 25 mm for one convolution. [04]

Fig. 1

Page 1 of 2

Enroll. No. _____________



SUBJECT: CALCULUS (2110014) (ALL BRANCH)

DATE: 10-10-2017 TIME:10:00 am to 11:45 am TOTAL MARKS:40




(i) limx→0

1−cos 𝑥

𝑥2 = ______

(a) 1

2 (b)0 (c)∞ (d)

−1

2

(ii) If

),(

),(

r

yxJ

&

),(

),(

yx

rJ

then the value of JJ is

(a)0 (b)-1 (c)1 (d) always JJ

(iii) A Stationary point (𝑎, 𝑏) is said to be Maximum if at (𝑎, 𝑏)____

(a) 02 srt ,𝑟 > 0 (b) 02 srt ,𝑟 < 0 (c) 02 srt (d)None of these

(iv) For an Implicit function 𝑓(𝑥, 𝑦) = 𝑐, the value of

dx

dy=_____

(a)

y

x

f

f (b)

x

y

f

f (c)

y

x

f

f (d) -

x

y

f

f

(v) For the function 3

122 yxu then the value of yx yuxu is

(a) -2u (b)

3

2u

(c)

9

u (d)

3

2u

(b) State Euler’s theorem for Homogeneous function & for

yx

yxu

331tan

Show that (1) x∂u

∂x+ y

𝜕𝑢

𝜕𝑦= 𝑠𝑖𝑛2𝑢 ,

(2) 𝑥2 𝜕2𝑢

𝜕𝑥2+ 2𝑥𝑦

𝜕2𝑢

𝜕𝑥 𝜕𝑦+ 𝑦2 𝜕2𝑢

𝜕𝑦2= 2𝑠𝑖𝑛𝑢 𝑐𝑜𝑠3𝑢

[05]

Page 2 of 2

Q.2 (a) (1) If , where , ,

Prove that [04]

(2) Find

dt

dw , if zxyw

where tytx sin,cos & tz .

[02]

(b) (1) Find

0limx

(𝑎𝑥+𝑏𝑥+𝑐𝑥

3)

1

3𝑥 [03]

(2) Find the equation of the Tangent plane to the

Surface 7432 2 xxyxz at (1, -1, 2). [02]

(c)

If )3log( 333 xyzzyxu show that 2

2

)(

9

zyxu

zyx

[04]

OR

Q.2 (a) (1)Let Show that

xy

u

yx

u

22

[04]

(2) Evaluate [02]

(b) (1) Using partial differentiation find 𝑑𝑦

𝑑𝑥 for . [03]

(2) Find the linearization of

f(x, y) =

x2

16+

y2

9+ 3 𝑎t point (-4, 3 ).

[02]

(c)

If xyzeu 3 show that xyzezyxxyz

zyx

u 32223

27273

[04]

Q.3 (a) (1) Find the maxima & minima of the function

4333),( 2223 yxxyxyxf . [04]

(2) For , find

[02]

(b) (1) Expand ex sin y in powers of x and y at the origin up to 3rd degree terms. [03]

(2) Show that

)0,0(),(limyx

x2−y2

x2+y2 does not exists.

[02]

(c) Find the minimum value of

32 yzx subject to the condition

2x + y + 3z = a , Using Lagrange’s method of undetermined multipliers. [04]

OR

Q.3 (a) (1) Find the maxima & minima of the function

xyxxyxyxf 7215153),( 2223 [04]

(2) Check the Continuity at origin for

)0,0(),(;0

)0,0(),(;),( 22

yx

yxyx

xy

yxf [02]

(b) (1) Expand 32 xyxy in powers of )2(&)1( yx using Taylor’s expansion. [03]

(2) Find

∂(u,v)

∂(x,y) when u = x2 – y2, v = 2xy.

[02]

(c) A rectangular box open at the top is to have a volume of 32 cubic. Find the

dimensions of the box requiring least materials for its construction. [04]

Documents

SILVER OAK COLLEGE OF ENGINEERING & …socet.edu.in/socet/wp-content/uploads/2017/11/Question-Papers-ALL.pdfenroll. no. _____ silver oak college of engineering & technology aditya