-S b

Cc \ \A. I ) 5-evn TIT

Bharatiya Vidya Bhavan's

Sardar Patel College of Engineering (A Government Aided Autonomous Institute)

Munshi Nagar, Andheri (West), Mumbai — 400058. Final Exam (November 2017)

2017-18 (Odd Semester) Q. P. Code: Duration: Three Hours Program: U.G. (B. Tech. Civil) Course Code : 1-1S301

ck,s+eY- 1 e

Max. Marks: 100 Class: S. 1'. (Civil), Sem: III (Value Added Audit course) Name of the Course: Economics for Engineers

Instructions:

• Solve any FIVE questions. • Answer to all sub questions should be grouped together.

• Figure to right indicates full marks.

• Assume suitable data wherever necessary and state it clearly.

• Each question carries 20 marks

Course

No. Question

Max. Description Marks

Outcome Number

Module No.

Q.1 (a) State both the laws of production. Explain in detail "Law of variable proportion"

10 CO-04 (a) IV

(b) Explain Isoquants and Isocost lines in detail 10 CO-04 (b) IV

Q.2 (a) What is the meaning of Engineering Economics? Describe

principles of Engineering Economics in brief? Whats is the Nature & Scope of Engineering Economics?

10 CO-01 (a) I

(b) State the basic economic problems? Differentiate between Micro & Macro Ecomonics? 10 CO-01 (b) 1

Q.3 (a) in details

Explain cash flow diagram, Simple interest & Compound interest 10 CO-05 (a) V

(b) What are the different types of Costs? Also discuss in detail "Elements of Costs"

10 CO-05 (b) V

Q.4 (a)

Suppose a seller of a textile cloth wants to lower the price of its clotg from Rs.150 per meter to Rs.142.5 per meter .If its present sales are 2000 meters per month. And further if it estimated that its elasticity of demand for the product equals 0.7. Show:

a) Whether or not his total revenue will increase as a result of his decision to lower the price.

b) Calculate the exact magnitude of its total revenue.

10 CO-03 (c) III

(b) If price of coffee rises from Rs. 45 per packet to Rs.55 per packet and as a result the consumer's demand for tea increases from 600 packets to 800 packets. Find out the CED for coffee.

10 CO-03 (d) III

1,50,000 Direct labour 150,000

60,000 Administrative 75,000 4,65,000 12

C0-06 (a) i VI

20,000 Sales

Selling overheads

25,000 20,000

20

CO-06 (b) VI

Particulars Raw material

. Work ion ro Finished oods

31.12.2008 60,000 24,000 34,000

31.112009 50,000 18,000 55,000

Particulars Purchase of materials

Factory overheads Distribution overheads Chargeable expenses

Carriage Inward

productive wages I Admin. Overheads

t Sales Selling Overhead

7

Amount

4,23,000

43,000

6,000 45,000

8,000 80,000 24,000 7,20,000

16,000

********************************

What is Demand? Classify demand in detail. What is Law of

10

CO- 02 (a)

Demand, explain in detail Q.5 (a)

6

Suppose a market consists of 3 consumers A, B,& C whose individual demand functions are given below:

a) 50 — 0.25 QA

b) P= 40— 2.00 QB

c) 35— 0.50 Qc

i) Find out the market demand function

ii) If market supply function is, Qs ----- 401-3.5 P, determine

equilibrium price & quantity.

What is "Cross Elasticity of demand"? Explain in details

From the following particulars given below, prepare a cost sheet:

(b) 10

CO-02 (b)

lii

. CO-02(b)

Direct material Factor Overheads

(b) Distribution Overheads Direct Expenses

From the following data, prepare a Cost Sheet as on 31.12.2009

Bharatiya Vidya Bhavan's

Sardar Patel College of Engineering (A Government Aided Autonomous Institute)

Munshi Nagar, Andheri (West), Mumbai 400058. End Semester Exam, November-2017

Max. Marks: 100 Class: S.Y.B.Tech. Semester: III Name of the Course: Surveying-I

Instructions: 1. Question No 1 is compulsory. 2. Attempt any four questions out of remaining six. 3. Draw neat diagrams 4. Assume suitable data if necessary

Q. P. Code: Duration: 3 hour Program: Civil

Course Code : BTC- 202

Plots 1 c-r- fi 1 e

Question No

Maximum Marks

Course Outcome Number

Mod. No.

(a) Derive an expression for the radius of zero circle, when 06 C.0.1 5 the wheel is outside the pivot and tracing point.

Q1 (b) Explain two peg method in Theodolite survey. 05 C.0.3 6 (c) Explain construction and working of optical square. 05 C.0.1 1 (d) Discuss the term balancing of sight in Levelling. 04 C.0.3 3 (a) Derive an expression for the Sensitivity of bubble tube. 10 C.0.1 3 Also discuss the factors affecting the same. (b) The following readings were observed from a 06 C.0.1 5 planimeter: initial reading = 9.874, final reading = 3.467,

Q2 the zero crossed the index thrice in the clockwise direction. The anchor point was kept inside the areas and the constant were M— 100.5 cm2 and C-30. Find the area of the plan. (c) What are the primary divisions of surveying? 04 C.O. 1 1

(a) A closed traverse PQRSTP was run using prismatic 10 C.0.2 2 compass to collect field details. Detect local attraction at all the stations and find the correct included angles. Also

Q3 eliminate the local attraction by applying suitable corrections and find corrected bearings.

Line PQ QR RS ST TP T

F.B. 144° 202°00' 246°30' 336° 55°30'

B.B. 323°30' 20°30' 66°30' 157° 232°30' 10 C.O. 3 (b) Explain with neat sketch characteristics of contours.

40 60 3.91 5.10

180 200 4.32 3.77

corrections required during (a) Discuss the various

C.0.1 1 6 10

C.0.2 3

Si. No.

B.S. I.S. F.S. Rise Fall R.L. Remark

i 2.150 250.000 B.M.1

1.645 9 I 0.500 MN

2.345

4 7 1.965 ?

5 2.050 1.825 0.400

6 9 MI 251.500 B.M .2

1.690 0.120

2.865 2.100

9 7 251.250 B.M.3

(b) What are the fundamental lines of Theodolite? Explain the desired relationship between them. (a) Explain Two point problems in plane table survey.

(b) Discuss the procedure for measurement of deflection

using Theodolite. (c) The offset taken from a survey line to a boundary are given below. Find the area by Trapezoidal rule and

Simpson's rule.

linear measurements. (b) Explain the difficulties in chaining and ranging works?

(c) During a Theodolite survey the following details were •

Line AB BC CD DE EA

Length 145m 76m 65m ? ?

Bearing 1350 12' 85° 12' 288° 37' 24° 46' 234° 18'

Q6

Chainage (m) Offset (m) Chainage (m) Offset (m)

0 20 3.80 140 5.20

3.20 160 5.90

4.6 80 100 I 120

4.40 3.81

05

05 C.0.3

05 C.0.3

C.0.3 5

1

1

Calculate the lengths of line DE and EA?

Write short notes on any four (i) Difficulties in levelling (ii) Variation in magnetic declination

(iii) Graphical method of contour interpolation

(iv) Sources of error in Theodolite survey (v) Corrections to linear measurements (vi)Orientation of Plane Table [Q7

L-) • I C.-- r) 1r

(a) The following is the page of a level field book. Fill in the 12 missing readings. Also apply usual checks.

is-). --1-- r •

08 C.0.1 6

10 C.0.1 7

05 C.0.1

Q4

Q5

C.0.3 C.0.1 C.0.2 C.0.1 C.0.3 C.0.3

5 5 5 5

5

3 2 3 6 1 7

e—, it 4,

l',/dA'1):0;$Pi

I (06)

(04)

S .Y B c-re,-1) Sc t‘ki

ion; .3

111.

4.S+c/v

Max. Marks: 100

Class: S.Y. B. Teel.

Coarse.: Engineering

CogAseri 3TC 204

InstrucOoos:

Solve any five sr os .Draw neat sketetwsi ASSIIII».0 Stijl:able data ifile•-..:essory and

0 Figure wa right ithr.catc, maximum matlis ur

Od13.1e, r,./ O. of q tts

91 Answer the followino

(a)

jlaj,..iireihs... chara9yep.5 •ry

Define/Explain the .1:01

OR

• ath,‘ti

...

(05)

(0i) CO1

CO2

.. There are two stress strain curves provided b-low tssity theca alto either brittle or ductile material, Further name the numbers or:,liphabets in the figure

St! ess

8

(05)

2 1

i

Strr -

. f(c.'•/ F...ulain cen--Irilie3 awl di,-..--,.•„ ,-...4- •,";.•,,e advaptapes of ceramics

(d) ..............•............. „,...- ,. ' . - -.:.:........- ,, - ...a.....•. _______.............,......

.. ..............

Classify rocks. Exrlain (Yi.aarving of stones in short

Answer the followip eqijeortS

(a) What are , -oroRerties of vood ounciing mortae?

(b) Exp!ain dressing/finishing of store. and enlist various types of dressing ov;thd 413 clone,-,yah PNptarlatioi, crazy tour.

„.

05) CO1

r M.3

CO2 M2

CO1 M3 (05) Describe how the compounds o.!. clinker affect the properties of cement. I-(d) (05) CO2 M4 ,

Describe in short the process of manufacture of clay tiles. L

1 oft

Q3 ..•

Ammer the following Qnestioos • . . • . . ___.... (a)

FTO. _

1 Q4 r"- L,. I Answer the following C,itestions , _

(a)! D • ' 1

,

escribe with flow diagrams the wet r.wocess of Plamifacturina of cement. I (4r'.0

, , , ,, - -I-- ! (06) 1 CO2 M..5

are the consg,rtuents of .t.1,1,,,,..,;',. StaIC. thC: `i-LIIICOOPq i 4 each of inerh

(c) I •,

1 06) 1 ooz i m5 I DISCUSS the properties and ores or c„opper and Aluminium,

r (07\ CO2 1

• (05) Col M5

- COI M5

(07)

(4) CO2 l'1,17

(5) COI M3

_1 (04) CO1

(07) COI

(O5) col M3

(04) COZ m7

(04) CO1 m7

• State the conditions under which you will suggest use quick...setting

• cement and low heat Portland-coractit, .

CO' •

C0.1.

M3

2

(b) (05) Enumerate types et roo 1 tc u Y TWO. , • Enlist and Explain the selection criteria for building matetials, (05) COI

(d) CO2 Enumerate varims tests cla bricks with slandard limits for any 5 tests. (05)

Q5

(08) (a)CO2

Explain different types of Ge,iynthelic maf,s'via!s used civil engineering

construction works.

Answer the Move-ing.QueNtiot:s

(b) What are the different fOrms of bitumen and discuss their uses?

(C) Write short note on AsCu Treatment

Q6-7 .Answer the followingQuttsti(ms

1---(1)T-111 *** --t—

(c) Discuss the various properties of concrete.

(d) E,xplain with nog sketch Batt-e:n )loard,

(a) Explain the differences between cast iron, wrought bon and low carbon I

Q7 ThAnswer 14 he, following Questions

State the qualities you will consider in selecting timber for construction (a)

/-L 1)) +1 How lime is classified according,to IS: 71.2 ocifications?

(e)—i Wrte short note on Sound insu/ating materials.

(d) I Describe in brief different 1.7,./nes of adhesives.

2 efl_

, r3H BharatiYa Vidya Bhavan's

Sardar Patel College of Engineering (A Government Aided Autonomous Institute)

Munshi Nagar, Andheri (West), Mumbai — 400058. END SEMESTER Examination

November 2017

3

—4 1(a)

If A =

—299 —300

300 301 prove that A1011

f ex) =

7I < X < 0

0 < x < it

—z1 —6 7

2

Maximum Marks: 100 Class: S.Y.B.Tech

Semester: III

Name of the Course: Eng,ineering, Mathematics III

Duration: 3 hour Program:Civil Engineering Course Code : BTC201

ttss-kr )-e Instructions:

• Attempt any FOUR questions out of remaining SIX questions.

• Question number.l is compulsory.

• Answers to all sub questions should be grouped together.

96 1.1 M*' —

Prove that the following function is analytic

r(z). ct)Sh z 3 (a)

5 5

6 4 7

A=

Prove that yin t +sin31 , 37r

ict 4

o x2

Find hall range cosine series using ParseVal1 s identity deduce

7E4 ill,

2(a)

((

(b)

(c)

region 1 x 2 and 2

1'1nd the etgen values 8 —6 2

y 3 tinder the mapping w =ez

and eigen vectors ot the matrix.

Find the image and draw a rough sketch o1 the mapping ol the

2

(b)

(c) Obtain the Fouvier series for

Find Laplace transforms of j ( ) = sin7

2

5

— (1) 0 c —b

ShoW that the matrix A = —c 0 a

b —a 0

Hamilton's theorem ( d 1— cos2t

dt t

satisfies Cayley-

6

8

4

1

7

1 (c)

Find L

4 (a) Find the Fourier series for f (x) =

0 —7c < x 0

x 0<x<71

6 2 4

6 1 1

(b) Find the Laplace transforms of f(t), where

<t <1

0, t >1

If f (z) is a regular function of z, prove that 3

(c) ( a2 a2

V(4 12 12

=411t(z)l . 8 5

+ , 2 xa uY 1

5 (a) I - s2 + b2 6 1 2

Evaluate: , log }

2 , - S ± a

(b) Find non — singular matrices P, Q so that PAQ is a normal 6 4 6

form where _ 2 1 —3 —6

A = 3 —3 1 2

_ 1 1 1 2

(c) Find the Fourier sine series for the function 8 2 4

f(x) = e" for 0 < x < 7C where a is constant _ 2

6(a Fvaluate: I, 1-

, s` + 2s + 3 6 1

t(s2 + 2s + 2)(s2 + 2s + 5)

For what values or x, and 1.t the linear equations. 6 4 6

())

2x +2y+2z =13

3x + 4y + Xz = have

i)No solution

ii) A unique solution

iii)infinite number of solutions _____

8 3 5

6 2

1 2

6 4

(c)

7(a) I

(b)

Find the analytic function f (z) = u + iv such that

u — v = ex (cos y — sin y) Obtain complex form of the Fourier series of the. function the

0 < x < 0 f

1 0 < x < 7C

Evaluate: El {log (1 +

Solve y"-3y 1+ 2y = 4e2t

Given y(0) = —3

y'(0)=5

(c)

CcL C'i0 sem Bharatiya Vidya Bhavan's

Sardar Patel College of Engreerin (A Government Aided Autonomous Institute)

Munshi Nagar, Andheri (West), Mumbai - 400058

END SEMESTER EXAMINATION

November 2017 •

Program: S.Y.B.Tech (Civil)

Course code: BTC203

Course Name: Strength of Materials

Date: 20-11-2017

Duration: 3 hours

Maximum Marks: 100

Instructions: Semester: III Attempt any FIVE questions out of SEVEN questions.

otS VcA,- )-cs Attempt any one from Q3 (a) and Q6(c).

Figures to the right indicate full marks. Assume suitable data wherever required and state it clearly.

Question

Maximum Course Module No. Marks Outcome No.

Number

-Nc a) Analyse the beam ABCDE and draw the axial 15

01 03

force, shear force and bending moment diagrams. Also determine the maximum moment for beam AE.

30

1 1 tT\ m

b) State the assumptions made in Simple Theory of • Bending.

05 02 04

_

1- -I a) A cylindrical shell of internal diameter 250 mm is 10 J 02 01 6mrn thick and is 3m long. When filled with fluid at an internal pressure p), there was change in its internal volume by 10000mm3. Determine the fluid pressure 'p', circumferential stress and longitudinal stress induced in the shell. Also find the changes in its length and internal diameter.

LiTake 11 ',- 2x I 07'\l/rnm ), 1/m- 0.31 L 1

0 1

b) I Determine the expression for total elongation of uniformly tapering circular section of diameters 'd,' and 'd,' respectively subjected to an axial load cp,

c)

With the help of neat sketches, explain what is ' meant by the term 'Shear Centre'. Also state its

importance.

1(4 Al

a) A member ABCD is subjected to loads Pi, P2, P3

and P, as shown in fig 2.below. Calculate the force P2, necessary for equilibrium if P,=50kN, P3=500kN and P4=200kN. Determine the total elongation of member assuming modulus of elasticity as 2.1x1. 01\1/mm2. Given: Lengths: 1(A13)=. 1500mm, 1(BC)= 500rnm, 1(CD)— I 000mm. Areas: Ar(AB) 700inm2, A.r(BC) —3000mm2, Ar(CD) 1300min2

I SD Cm SD C.rri

700 1^n Y171-

Fig 2.

P1 o o

bOOh

*— P2 P3

06

04

02

01

01

06

a) A composite bar made up of aluminium and steel 08 02 01 is held between two supports as shown in fig 1. below. The bars are stress free at a temperature of 50°C. What will be the stresses in the two bars when the temperature is 25°C if:

(i) The supports are non-yielding (ii) The supports come nearer to each other

by 0.15mm. It can be assumed that the change in temperature is uniform all along the length of the bar. [Take E. 210GPa, E,, = 74GPa, a,---- 12x10'/°C, = 24x10°/°C]

?Ot rcro 600 rorr) )I•

64-ee4.

Fig 1. OR

J 08 02 01

02-

1-Q4.

-"B .1.)) I At a point in a strained material, the state of stress 12

is as shown in fig 3.below. Calculate the noth.:1,1 stress, shear stress and principal stresses along the plane AB inclined at 300 with the major stress by analytical method. Also verify the results

! graphically by Mohr's circle. 400MPa

00 tiPa

800MPa

tgo ompo

tbotipaj Fig.3

OOMPat,

02 02

a) formula for a circular shaft subjected to equal and opposite torque, 'T'. Also state the assumptions made in deriving this formula.

b) A cantilever of rectangular cross section is 150mm wide and 300mm deep and carries a UM, & a point load as shown in fig 4. Find the deflection and slope at the free end. [Take E-----10000N/mmi

A 100x100x15mm angle section as shown in fig 5. 12 is used as a simply supported beam over a span of 3.5m. It carries a load 600N along the line YG, where 'G' is the centroid of the section. Calculate:

i) Stresses at the points P, Q and R of the mid section of the beam.

ii) Position of neutral axis [Take IF, =200GPai

With usual notations, derive the torsion 02 06

07

02 04

10

10 03

100 mm

03

b) I Locate the shear centre for the channel section 08 02 ' 06 shown in fis46.

Fig 6. Igo >Y1

08 02 05 I

06 03 07

Find the maximum and minimum stress intensities at the base of a uniform circular chimney, having external and internal diameters as 7m and 4m. The height of the chimney is 30m and is subjected to a wind pressure of 2 kN/m2. The density of the masonry may be taken as 21 kN/m3.

b) A steel beam of cross section 200mm x 400mm which is simply supported at its ends is loaded as shown in fig 7. Find the slope at each ends (A & 13) and deflections at points C and D. [Take E-200GPal

t 6olc,A

C

Fig 7. Derive the bending eTlation,

OR c) Draw the stress-strain curve for mild steel and

indicate and explain the following terms in detail: (i) elastic limit (ii) yield stress (iii) ultimate stress (iv) breaking point (!) strain hardening_re_gion.

06 02 04

06 02 01

A cantilever cast iron bracket of span 6m and cross 07 section as shown in fig 8. supports a UM of 4001/m throughout the span. Sketch the shear stress variation at the mid span of the beam.

01&02 04-

6.1-

' A simply supported beam of span 8m and cross section as shown in fig 9.is subjected to UDL of ‘w'kNim over the whole span. If the tensile and compressive stress is not to exceed lOOMPa and 150MPa respectively, calculate what is the maximum intensity of UDL 'w', the beam can carry. 1Sb Mtn

inr,1

.2 Om

g o rah)

2,0 tnn

.3do-rom Fig 9.

/#4' 00 mire)

S jet4

asirran

25rtyry-74'

07 01&02 04

A solid circular shaft has to transmit a power of 06

02

06 200 kW at 120 rpm. If the shear stress is not to exceed 50 N/mm2 and the twist in length of 4m does not exceed 1", find the suitable diameter of the shaft.

I [Take Modulus of rigidity, G — 80x103 N/mml

06-

Lo9 [11

C;yi Bharatiya Vidya 13havan's

Sardar Patel College of Engineering (A Government Aided Autonomous Institute)

Munshi Nagar, Andheri (West) lVlumbai 4M058.

End Semester Examinations (Civil Engineering)

November 2017

Q. P Code: Duration: Three Flours Program: U.G. (B, Tech. Civil)

Course Code : BTC205 A• c

N Lix. Marks: 100 lay;: S. E (Civil), Semester; 111

Name or the Course: Engineering Geology

Instructions: 1, Attempt /try Five questions

A I I questions carry equal marks r

to each question to be started on the fresh page 1ssume suitable data if necessary and mention it clearly,

I >ra\A, neat diagrams.

. Clive the name of the mineral One set of cleavage, black colour, pearly lustre Cherry red streak, metallic lustre, botroidal Form

II

H. 'Define the rolHviini, terms

Aquiler Aquiluge Aquitard

i\'. 8ortilifJ,

v. Anhedral Di iw d'i•ctgratits of the follo\v"1112,

Yardang ii,Sei I Dune

Porphyritic texture Translational landslide

Rock Cycle

Draw 1 diag,rain of the different stages of the ox bow hike formation and 10

explain hie process of the same.

What :ire t he \\,,,,ps, i i

which mechan i ca l \\. e ,, n her i n

)raw the internal ,-;tyncture of' the 1-',arth and explain the various layers. 10

H . I )r:t' d umrau is of diff(Iviit kinds of dunes and explain how wind \:\ orks ts a 0

eatheinw, uncut

5

2 x 5

can take place'' 10

•r-TeciL, )(is 4. a. How can folds be classified according to the orientation of the axial plane? JO

b. What are the different types of forces that act on a gravity dam? If the dam is to 10 be constructed on an antiform fold, then which part of the fold is most suitable

for construction of the dam?

5. a. Describe the different types of normal faults with suitable diagrams. 10

b. How can faults be recognized in the field? 10

6. Write short notes on the following. 5 x 4

1. Barchan Dune Porphyritic texture Sorting and packing

iv. Factors of metamorphosis

7, Describe the formation of the Himalayas on the principles of Plate Tectonic 20.

theory.

***** 4:*******4: ,!; nt ,t, ****;14

2

.o)

g c v Bharatiya Vidya Bhavan's

Sardar Patel College of Engineering (A Government Aided Autonomous Institute)

Munshi Nagar, Andheri (West), Mumbai - 400058. End Semester EXAM

Max. Marks: 100 Class: B.Tech Semester: III Name of the Course: Building Construction

Instructions:

Q. P. Code: Duration: 3 Hrs

Program: Civil Engineering Course Code : BTC 206

q31-cir- cr-I' I C'

1. Q.1 is compulsory & solve any four remaining six. 2. Illustrate answer with neat sketches wherever required.

3. Make suitable assumptions where necessary and state them clearly.

4. Use Drawing sheet for only question no.3

Questio n No

Max. Marks

Course Outcome Number

Module no,

Q.1

Write a short note on following points (Any four) a) Grease Trap in Plumbing b) Underpinning c) Brick Flooring d) Framed & Panelled doors e) Brick Stone Composite Masonry 1) Basic components of building

20 1,2,3, 1-7

Q.2

A) Compare Brick Masonry Vs. stone masonry and Explain defects in brick masonry (any four points each)

Also draw & explain English bond for one & half brick thick

wall.

10

01 02

03

B) Explain following types of Masonry in details 1) Square Rubble Masonry 2) Polygonal Rubble masonry

06

C) Explain shortly method of Plastering 04

04

01

Q.3

A) Draw a neat sketch of following types of doors, 1) Battened, ledged, framed & braced door 2) Louvered Door

B) Draw a neat sketch of following types of windows, 1)' Pivoted Window 2) Double Hung Window

04

C) Design a dog-legged stair for residential building having staircase hall inside dimension is 2.00 M X 4.60 M. the height of floor is 3.30 M & roof consists of R.C.C. Slab of 12 CM thickness. Draw a plan & sectional elevation which is passing through stair.

12

Q.4 A) Write a short note on: Sloping Roof 08 01 04 B) Write a short note on following types of floorings 08

Q.6

Q.7

01

02

02

08

04

08

02 08

04

10

cv \ • Se kfr1 atr

1) Mud & Murum Flooring 2) Stone flooring

C) What factors to be considered while selecting type of flooring?

(any four) A) Explain fire protection systems provided in building to resist

fire load with sketch (any two) Also explain fire resisting properties of common building

materials. (any four)

Q.5 B) Compare steel formwork Vs. Timber Formwork (any four

points) Also explain any two method of scaffolding.

C) Explain sound insulation methods for various condition of

source. A) Explain the piping systems in plumbing services for a Building with a neat sketches & details. B) What is Damp Proofing?

Explain its causes & effects over building structures. (any two)

Also explain how DPC should be provided with sketches.

C) Explain shortly the reasons responsible for water leakage in

building. (any four) A) What do you understand by "Green Building"? Also explain advantages of Green Building. (any five)

B) Explain the all criteria's given by LEED's rating agency for certifying green building.

03

03

10 01

04

08

_110 SY me3\ ckyo -nr

Bharatiya Vidya Bhavan's

Sardar Patel College of Engineering (A Goverment Aided Autonomous Institute)

Munshi Nagar, Andheri (West), Mumbai - 400058. END SEMESTER Examination

November 2017

Maximum Marks: 100 Class: S.Y.B.Tech Semester: III Name of the Course: Engineering Mathematics III

Instructions:

Duration: 3 hour Program:Civil Engineering Course Code : BTC201

ovs4-ev

• Attempt any FOUR questions out of remaining SIX questions. • Question number.' is compulsory. • Answers to all sub questions should be grouped together.

Q Marks , CO Module

No.

1(a) If A =1

(2 3

--.3 -4) oo prove that Al =I

(-299 -300 \

300 301 .

7

(b) Find Laplace transforms of f (t) = sin' t 5 1 1

(c) Obtain the

f (x) =

Fourier series for

11 2x + _n<x<0

7t

, 2x i.,

1 - — U<X<7t 7E

5 2 4

(d) Find the image and draw a rough sketch of the mapping of the region 1 5_ x 5_ 2 and 2 5_ y 5.. 3 under the mapping w = ez

5 3 5

2 (a) Find

A =

_ the eigen values 8 -6 21

-6 7 -4]

and eigen vectors of the matrix. 6 4 7

(b) isin 2t + sin 3t 3ir Prove that dt . — 6 2

tet 4

(c) If f (x) = x 0<x<2

Find half range cosine series using Parseval's identity deduce

le 1 1 1 ' -7 4- -7 -4- -7 + 96 1 34 54

3 (a) Prove that the following function is analytic

Azy.,- cosh z 6

-(b)

Show that the matrix A =

Hamilton'stheorem

- 0 c —b-

—c 0 a

b —a 0 -

. ,

satisfies Cayley-

6 4 7

(c) Find L

r d

Ldt

11—cos2tN

j

8 1 1

t )

4(a) —n<x5_.0 1 6 2 4 Find the Fourier series for f (x) = {0

Lx 0<x__ TC

(b) Find the Laplace transforms of f(t), where 6 1 1

t2,0<t <1

f (t) 0, t > 1

If f (z) is a regular function of z, prove that

(c) ( a2 a 2\ 2 1 2 8

fl (z) "If c (z) • —T —T ax aY i

5 (a) s2 Evaluate: L4 log

+b 2 } 1

S2

+ a2

(b) Find non — singular matrices P, Q so that PAQ is a normal 6 4

form where

2 1 —3 —6

A= 3 —3 1 2

1 1 1 2 -

(c) Find the Fourier sine series for the function

f (x) = e for 0 < x < a where a is constant

6(a) L-1

s2 +2s+3Evaluate:

(s2 + 2s + 2)(s2 + 2s ± 5)

For what values of X and IA the linear equations. 6 4

(b) x+2y+z=8

2x + 2y + 2z = 13

3x+4y+Xz=p, have

i)No solution ii) A unique solution iii)infinite number of solutions

s \i, .(c)

Find the analytic fun

u— v = ex (cos y —sin

7 (a) Obtain complex fori

f (x) = {0

1

-IL

0<

Solve y"-33/1+2y =

Given y(0) = —3

y'(0) = 5

' roil - —AV) )-- j - vr t

lion f (z) .-----; u +iv such that

y)

3 5

of the Fourier series of the function the

x ... 0

: < n

6 2 4

i\1 L -F -Tif S

6 1 2

4e2t 8 1 2

{Evaluate: L4 log (

(c)