silver oak college of engineering & technology index...

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

INDEX PAGE

SEMESTER IV

Sr. No Subject Name Subject Code

1 Engineering Economics & Management 2140003 2 Advanced Surveying 2140601 3 Structural Analysis-I 2140603 4 Numerical & Statistical Methods 2140606 5 Building & Town Planning 2140607 6 Concrete Technology 2140608

(Note: Assignment of “Engineering Economics & Management” will be provided by respective subject faculty.)

CIVIL ENGINEERING DEPARTMENT

ACADEMIC YEAR 2017-2018


SUBJECT: ADVANCED SURVEYING (2140601)

SEMESTER IV

ASSIGNMENTS



Branch: Civil Semester: IV

Subject Name: Advanced Surveying Subject Code:2140601

Assignment No. 1 – Tachometric Survey

1. What is tachometry survey? Why tachometry survey is necessary to conduct? Give

its principle?

2. Differentiate between fixed hair method & movable hair method.

3. Explain the principle of stadia method & determine stadia contents.

4. Explain errors & precision in tachometry survey.

5. Compute the horizontal distance PA & R.L of point A for staff held vertically for

below observations taken by tacheometer. BM=100 m, K=100 & C=0

Inst. Station Staff Point Vertical Angle Staff Readings

P BM -60

1.360, 1.915, 2.470

A +50

1.065, 1.885, 2.705

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Activity/Task 1: Field project on Tachometry to be performed in groups.

A/Prof. Yamee Thakkar

Subject Co-ordinator

Lect. Anuj Bhatt

Subject Partner

Silver Oak College of Engineering & Technology Page 1

Silver Oak College of Engineering & Technology

Civil Engineering Department

Branch: Civil Semester:IV


Assignment No. 2 – Geodetic Surveying

1. What do you understand by geodetic surveying? Why geodetic surveying is carried out?

2. Explain principle triangulation.

3. Give classification of triangulation system.

4. What is base line? Which points will you consider during the selection of base line?

5. Enlist various points which are required for selection of station.

6. Explain orders of triangulation along with various triangulation figures.

7. What are station marks & signals? Give classification of signals.

8. In a triangulation survey, the altitudes of two proposed stations A & B 85 km apart, are

respectively 132 and 212m. The intervening obstruction is situated at C, 60km from and has an

elevation of 142m. Ascertain if A and B are intervisible, and if necessary find by how much B

should be raised so that the line of sight must nowhere be less than 3m above the surface of the

ground. The earth’s mean radius may be taken as 3000km and coefficient of refraction as 0.07.

9. Explain extension of base with neat sketch. Prepare a flow chart explaining the same.

10. Define reduction to centre. Explain the procedure.

Activity/Task 2: Triangulation system model making.

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Lect. Anuj Bhatt

Subject Partner






Assignment No. 3 – Theory Of Errors

1. The following are the three angles observed at a station closing the horizon, along with

their probable errors of measurements. Determine their corrected values.

A= 85° 13' 10" ±2" , B= 130° 49' 30" ±3" ,C= 143° 57' 10" ±4".

2. Define: (i) True Error (ii) Most Probable error (iii) Residual error.

3. The observed values of an angle are given below :

Angle Weight

85° 40' 20" 2

85° 40' 18" 2

85° 40' 19" 3

Find a. probable error of single observation values of unit weight

b. probable error of weighted arithmetic mean

c. Probable error of single observation of weight 3.

4. Define weight of an observed quantity. Discuss various laws of weights.

5. Define accidental error, true value, direct observation, conditioned quantity, most probable value,

true error, normal equation.

6. Following readings of levels were carried out 2.335, 2.345, 2.350, 2.300,2.315, 2.305, 2.325

and 2.315. Calculate ,(i) Probable error for single observation (ii) Probable error for mean

7. Find the most probable value of the angle A from the following observation Equations.

(1)A = 30° 28’ 40” weight 2

(2)3A = 91° 25’ 55” weight 3




8. Explain the theory of least squares.

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Lect. Anuj Bhatt Subject Partner




Assignment No. 4: Field Astronomy

1. Explain following terms with the neat sketch: Vertical circle, observer meridian, altitude of

star, declination of star, hour angle, azimuth, nautical mile, ecliptic.

2. Define: (i)Azimuth (ii)Nadir (iii)Zenith (iv)Latitude (v) Longitude

3. Explain the following astronomical terms:

(i) The celestial sphere (ii) The hour angle (iii) The horizon and (iv) Declination also write uses

of field astronomy.

4. What is Azimuth? Explain various methods for determination of Azimuth of a survey line.

5. What is latitude of a place? Prove that the altitude of the pole is always equal to the latitude of the

observer’s position.

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Lect. Anuj Bhatt

Subject Partner





Civil Engineering Department Branch: Civil Semester: IV


Assignment No. 5: Aerial Photogrammetry

1. Explain the displacement and errors in aerial Photogrammetry. The scale of an aerial photography

is 1 cm = 100m. The photograph size is 20 cm x 20 cm. Determine the number of photographs

required to cover an area 10 km x 10 km, if the longitudinal lap is 60% and the side lap is 30% .

2. Explain scale of vertical photograph.

3. What is function of aerial camera? Describe schematically its essential parts.

4. What is meant by scale of vertical photograph? Determine scale of photograph for terrain lying at

elevation of 50 m and 200m if vertical photograph was taken at altitude of 1200 meters. Take focal

length of camera as 15 cm.

5. What is relief displacement? Derive an expression for the relief displacement in a

vertical photograph.

6. Write short note on (i) Stereoscope (ii) Parallax Bar

7. Define: (i)Tilt (ii)Isocentre (iii)Overlap (iv)Side lap (v) Crab (vi)Drift (vii)Principal point

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Lect. Anuj Bhatt Subject Partner

Activity/Task 5: search for article on history and latest trends in

aerial photogrammetry from library.




Assignment No. 6: Modern Surveying Instruments

1) Explain electromagnetic spectrum.

2) Enumerate different types of EDM instruments and describe briefly the salient features of

Total station.

3) What are the properties of electromagnetic waves? Draw complete electromagnetic spectrum

showing all wavelengths.

4) Describe how a total station has brought revolution in surveying.

5) Describe briefly the salient features of total station.

6) Classify the Electromagnetic distance measurement instruments depending upon the type

of carrier wave employed. Write a short note on Geodimeter.

Activity/Task 6: Collection of brochure of latest surveying instruments

And attaching the same in the assignment file.

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



Lect. Anuj Bhatt

Subject Partner





SUBJECT: STRUCTURAL ANALYSIS-I (2140603)

SEMESTER IV

ASSIGNMENTS







Subject Name: STRUCTURAL ANALYSIS-I Subject Code: 2140603

1. Differentiate between statically determinate structures and statically indeterminate structure.

2. Describe Principle of Superposition and Maxwell’s Reciprocal Theorem.

3. Analyze the plane frame as shown in fig.no.-01. Draw shear force diagram, bending moment

diagram, and axial force diagram.

Fig. No-01

4. Draw the S.F and B.M diagram for the frame loaded as shown in the fig.no.-02

Assignment No. 1 – Fundamentals of Statically Determinate Structure


Note [UDL=40kN/m for Roll No. 01, UDL=40+02=42kN/m for Roll No.02 and value of UDL

changes as per your Roll No. i.e. UDL= (40+R.N.) kN/m]

5. Find static and kinematic indeterminacy for the structures shown in fig.no.-03. Also comment

about stability.

Fig no-03

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Hasumati B. Patel Ajit Dixit

Subject Co-ordinator Subject Partner






1. Find slope & deflection for the structure shown in fig.no.-04 below by Moment area method

Fig. No-04

2. Determine deflection at B, C and D for the cantilever beam loaded as shown in fig.no.-05 using

Macaulay’s method. Take E=2 x 105 N/mm2 & I = 2 x 108 mm4.

3. Find the slope and deflection at the free end B of a cantilever beam AB as shown in fig.no.-06 by moment area method. Take I= 2 x 108 mm4, E= 2 x 105 N/mm2

Note [AT FREE END CONCENTRATED/POINT LOAD (CL) =10kN for Roll No. 01,

CL=10+02=12kN for Roll No.02 and value of CL changes as per your Roll No. i.e. CL= (10+R.N.)

Assignment No. 2 (A) – Displacement of Determinate beams and plane truss


4. Find the slope and deflection at the center C of a simply supported beam AB as shown in fig.no.-07 by moment area method. Take I= 2 x 108 mm4, E= 2 x 105 N/mm2.

Note [CONCENTRATED/POINT LOAD (CL) =05kN for Roll No. 01, CL=05+02=07kN for

Roll No.02 and value of CL changes as per your Roll No. i.e. CL= (05+R.N.) kN]

5. A simply supported beam of 3m span carries two point loads of 120 kN and 80 kN at a distance of

0.6m and 2 m from the left support. If for the beam I = 16 x 108 mm4 and E = 2.1 x 105

N/mm2, calculate the deflection under loads using Macaulay’s method. Refer fig.no.-08

Note [CONCENTRATED/POINT LOAD (CL) =80kN for Roll No. 01, CL=80+02=82kN for

Roll No.02 and value of CL changes as per your Roll No. i.e. CL= (80+R.N.) kN]

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1. Find slope and deflection at point C for the beam shown in fig.no.-09 using Conjugate beam

method. Take EI = 20000 KN-m2.

2. For a beam as shown in fig.no.-10 calculate the slope at support C and deflection under point

load. Take E= 2 x 105 N/mm2, I= 5 x 108 mm4.

3. Calculate slope and deflection at point C for the beam as shown in fig.no.-11 using conjugate

beam method. Take EI = 32000 kN.m2.

Note [AT MID SPAN CONCENTRATED/POINT LOAD (CL) =30kN for Roll No. 01,

CL=30+02=32kN for Roll No.02 and value of CL changes as per your Roll No. i.e. CL=

(30+R.N.) kN]

Assignment No. 2 (B) – Displacement of Determinate beams and plane truss


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Assignment No. 3 – Direct and Bending Stress


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Assignment No. 4 – Columns and Struts


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Assignment No. 5 – Arches, Cables and Suspension Bridges


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Assignment No. 6 – Thin Cylinder


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Assignment No. 7 – Fixed Beams and Consistent Deformation Method


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Assignment No. 8 – Strain Energy


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




ACTIVITY BASED ASSIGNMENT

1. CRASH THE COLUMN

This activity involves making of a column using canvas and checking the strength by

applies axial load on it.

This will enhance the understanding of the students regarding the deflection and

slenderness ratio of any column.

The activity will be done in a group of 5 students in laboratory hours.

The practical application of this activity is that the students will come to know about

the long and short column, its failure envelope (crushing or buckling), use of

slenderness ratio and the use of end connections.

2. BEAM SAMARTHYA

This activity involves making of beams (cantilever, simply supported and fixed) using

candy sticks and comparing the slope and the deflection in the beams.

This will enhance the understanding of determinacy and indeterminacy of the beams

and also the idea of using indeterminate beam over determinate beam.

The activity will be done in a group of 5 students in laboratory hours.

The practical application of this activity involves understanding of various beams, its

slope and deflection and the practical applications of all such beams.


Criteria: Before Mid-I Complete 2 Module Test and Before Mid-II Complete 3 out of 5 Module Tests


Civil Engineering Department Branch: Civil Semester: IV

Subject Name: Structural Analysis-I Subject Code: 2140603

Week 1. A-1(Q.5), A-6(1,2,3)

Week 2. A-1(Q.3),A-6(4,5), A-7(Q.3)

Week 3. A- 1(Q.1,2,3 ), A-7( 5)

Week 4. A- 2(Q.2,5), A-4(1,2,3)

Week 5. A- 2(Q. 1,2,3), A-4( 4,5 )

Week 6. A- 3(Q. 3,4,5 ), A-8( 3,4 )

Week 7. A- 3(Q. 3,4,5 ), A-8( 3,4 )

Week 8. A- 5(Q. 1,2,3 )

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A/Prof. Hasumati B Patel A/Prof. Ajit Dixit Subject Co-ordinator Subject Partner

MODULE TEST QUESTION DISTRIBUTION

TUTORIALS

NUMERICAL AND STATISTICAL METHODS

(2140606)

Semester-IV

Branch-Civil

2018

Name: _______________________________ Enrolment No.:__________________________

COURSE CONTENT

Sr. No. Topics To Be Covered Weightage

1 Roots of Algebraic and Transcendental Equation 10

1.1 Bisection, false position

1.2 Secant methods

1.3 Newton –Rephson methods

1.4 Rate of Convergence

2 Numerical Integration 8

2.1 Newton-Cotes formula, Trapezoidal and Simpson’s formulae

2.2 Error formulae

2.3 Gaussian quadrature formulae

3 Finite Differences and interpolation- 15

3.1 Finite Differences

3.2 Forward, Backward differences

3.3 Central operators

3.4 Interpolation by polynomials

3.5 Newton’s forward, Backward interpolation

3.6 Gauss and Stirling’s central difference formulae

3.7 Newton’s divided formulae

3.8 Lagrange’s formulae for unequal intervals

4 Solution of a system of Linear Equations 7

4.1 Gauss elimination, Partial pivoting

4.2 Gauss-Jacobi

4.3 Gauss Seidel Method

5 Descriptive Statistics 8

5.1 Mean, median

5.2 Mode

5.3 Standard deviation, Skewness

6 Correlation and Regression 10

6.1 Bivariate distribution

6.2 Correlation coefficients, Regression lines

6.3 Formulas for Regression coefficients,

6.4 Rank correlation

7 Numerical solution of Ordinary Differential Equations 15

7.1 Basic concept

7.2 Taylor series method,

7.3 Continue Taylor series

7.4 Euler method

7.5 Runge – Kutta method

7.6 Milne’s predictor-corrector method

8 Probability 7

8.1 Definition of probability, Exhaustive events, Pair wise independent

events

8.2 Multiplicative law of probability, Conditional probability

8.3 Baye’s theorem

9 Probability Distributions 12

9.1 Random variable. Mathematical Expectation

9.2 Standard deviation

9.3 Binomial

9.4 Poisson and normal distributions

9.5 Mean median, mode

10 Curve Fitting 8

10.1 Fitting of linear Quadratic, Exponential and logarithmic

10.2 Least squares method

Text Book:

Dr. R.C. Shah, Numerical and statistical methods for civil engineering, BOOKS INDIA

PUBLICATIONS

Reference Books:

1. S.C. Gupta and V.K. kapoor,Fundamental of mathematical Statistics (11th Edition) sultan

Chand and Sons.

2. Jphnson Richard A Miller and-ProbabilityFreund’sandStatistics (8th Edition) PHI.

3. Geraldo C.F. and Wheatley P.O.Applied Numerical Analysis (2nd Edition ), Addison-

wesley.1981

4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999).

5. S. D. Conte and Carl de Boor, Elementary Numerical Analysis- An Algorithmic Approach (3rd

Edition), McGraw-Hill, 1980

6. C. E. Froberg, Introduction to Numerical Analysis (2nd Edition), Addison-Wesley, 1981

Mid-Semester Exam- 1 Starts from 27 / 01 / 2018

Mid Semester Exam-1 Syllabus Unit: 1 to 4

Mid-Semester Exam-2 Starts from 7/ 04 / 2017

Mid-Semester Exam-2 Syllabus Unit 5 to 9

TUTORIAL 1- ROOTS OF ALGEBRAIC AND TRANSCENDENTAL

EQUATIONS

Sr.

No. Questions Answer Year

1. Find a real root of the following equation using mentioned method.

1. BISECTION METHOD

a. 𝑥 − 𝑐𝑜𝑠𝑥 = 0 correct up to 3 decimal places . 0.738 2014

b. 𝑥3 − 5𝑥 + 3 = 0 correct up to 4 decimal places. 0.6566 2015

c. 𝑥3 − 7𝑥 + 3 = 0 correct up to 4 decimal places. -2.838

2. FALSE POSITION METHOD

a. Explain False position method for finding the root of the equation 𝑓(𝑥) = 0.Use this method to find the root of an equation 𝑥 = 𝑒−𝑥 correct up to three decimal places.

0.567 2015

b. Find a positive root of 𝑥3 − 4𝑥 + 1 = 0correct up to 3

decimal places. 0.254 2015

3. NEWTON RAPHSON’S METHOD

a. 𝑥4 − 𝑥 − 9 = 0 correct to three decimal places. 1.813 2016

b. Find Iterative formula for

i. 𝑞𝑡ℎroot

ii. Reciprocal of a positive number N using N-R method and

iii. Compute:

1. √113

2.2240 2015

2. √28 5.291 2015

3. √583

3.8709 2015

4. √123

2.2894 2016

4. SECANT METHOD

a. 𝑓(𝑥) = 𝑥 − 2𝑠𝑖𝑛𝑥 = 0 using 𝑥0 = 2, 𝑥1 = 1.9 1.8955 2014

b. 𝑥𝑒𝑥 − 1 = 0 between 0and 1 0.5671 2016

c. 2𝑥3 − 3𝑥2 + 5𝑥 − 6 = 0(0.5 ≤ 𝑥 ≤ 1.5)(correct up to e

points)

ASSIGENMENT 1- ROOTS OF ALGEBRAIC AND TRANSCENDENTAL

EQUATIONS

Sr.


1. Explain Bisection method for solving 𝑓(𝑥) = 0. Find the real root of equation

𝑥2 − 4𝑥 − 10 = 0 using this method correct to three decimal places.

2 Find the real root of the equation 𝑥𝑙𝑜𝑔10𝑥 = 1.2by Regula-Falsi method

correct to four decimal places.

2.740 2015

3 Find an approximate value of the root of the equation𝑥3 + 𝑥 − 1 = 0 using

this method of False position.

0.682 2013

4 Use secant method to find root of the equation 𝑐𝑜𝑠𝑥 − 𝑥𝑒𝑥 = 0 up to four

decimal places.

Or

Use secant method to find root of the equation 𝑐𝑜𝑠𝑥 = 𝑥𝑒𝑥 up to four

decimal places.

0.517 2016

5 Discuss the rate of convergence of Newton Raphson’s method.

6 Find the √10 correct to three decimal places by using Newton-Raphson

iterative method.

3.1623 2015

7 Find the √7 correct to three decimal places by using Newton-Raphson

iterative method.

2.6457 Dec

2013

8 Find an Iterative formula to find √𝑁and hence find

1. √5

2. √27

3. √65

4. √3

2013

2013

2014

2014

2.2361

5.1962

8.0623

1.7321

SHORT QUESTIONS

Sr.

No.

Questions Answer Year

1. Can you apply False position method to obtain the root of

the equation𝑓(𝑥) = 𝑥𝑒𝑥 − 2 = 0 in the interval(0,0.5)?

Justify your answer.

No, intermediate value

theorem is not satisfied.

2016

2. Write at least two differences between Secant method and

False position method.

2015

3. Which method is also known as method of tangent? Write

down the iterative formula for it.

NR method

𝑥𝑛+1 = 𝑥𝑛 −𝑓(𝑥𝑛)

𝑓′(𝑥𝑛);

𝑛 = 0,1, …

2015

4. Find the approximate root of the equation 𝑓(𝑥) = 𝑥3 +𝑥 = 0 after the first iteration of NR method with initial

guess 𝑥0 = 1.

0.5 2016

5. What is convergent rate of Bisection method and NR

method?

Bisection method has linear

convergent and NR has

Quadratic convergent

2016

6. Define accuracy and precision. 2016

7. If 𝑎 = 0.8461538461 is approximately by 0.84615, then

find percentage relative error.

0.00045453% 2016

8. The error cause by truncating an infinite series to a finite

number of terms is called __________ and the error

associated with chopping and rounding is

called_________.

Truncation error

&

Rounding off error

2016

TUTORIAL 2- NUMERICAL INTEGRATION

Sr.


1. Estimate the following definite integrals using the trapezoidal rule with

eight, ten, six respectively

a. ∫ 𝑐𝑜𝑠𝑡𝑑𝑡4

0

b. ∫ 𝑒−𝑥2𝑑𝑥

1

0

c. ∫ (𝑡2 + 1)3

2𝑑𝑡6

−2

a. -

0.7408

5 b. 0.7462

11

c. 378.17

3

2012

2010

2011

2. Evaluate using Simpson’s 1

3 rule.

a. ∫ (𝑥2 + 1)3

2𝑑𝑥1

0 using four strips

b. ∫𝑠𝑖𝑛2𝑡

𝑡𝑑𝑡

1.6

1 using six strips

c. ∫ 𝑥𝑒−𝑥2𝑑𝑥

0.4

−2𝑛 = 2𝑚 = 4

a. 1.5673 b. 0.2459

6 c. -

0.4189

2

2012

3. Evaluate ∫𝑑𝑥

1+𝑥

3

0 with 𝑛 = 6 by using Simpson’s

3

8 rule and hence

calculate 𝑙𝑜𝑔2. Estimate the bound of error involved in the process.

𝑙𝑜𝑔2 = 0.6944

UB: 1.4451

LB: 1.3325

2011

2014

4. Given the data below, find the isothermal work done on the gas as it is

compressed from 𝑉1 = 22to 𝑉2 = 2𝐿. Use 𝑤 = − ∫ 𝑃𝑑𝑉.𝑉2

𝑉1 Use

Trapezoidal rule.

X 2 7 12 17 22

Y 12.20 3.49 2.04 1.44 1.11

68.17 2012

5. a. Evaluate∫ 𝑙𝑜𝑔𝑒𝑥𝑑𝑥5.2

4 by trapezoidal rule using h=0.2

b.State Simpson’s 3

8 rule and evaluate∫

𝑑𝑥

1+𝑥2 𝑑𝑥1

0using ℎ =

1

6.

a 1.82780 b 0.78536

2011

6. Evaluate the integral ∫ (1 + 𝑥2)

3

26

−2𝑑𝑥 by the Gaussian formula for 𝑛 =

3. 358.693 2012

7. Consider following tabular values. Determine the area bounded by the

given curve and 𝑋 −axix between 𝑥 = 25 to 𝑥 = 25.6 by Trapezoidal

rule and Weddle’s rule.

X 25.0 25.1 25.2 25.3 25.4 25.5 25.6

Y 3.205 3.217 3.232 3.245 3.256 3.268 3.280

1.946

2012

8. A river is 80 meters wide. The depth ′𝑑′ in meter at a distance 𝑥 meter

from one bank is given by the following table calculate th area of cross

section of the river using Simpson’s 1

3 rule

X 0 10 20 30 40 50 60 70 80

d 0 4 7 9 12 15 14 8 3

710 sq.mt 2010

9. Evaluate ∫ 𝑒−𝑥2𝑑𝑥

1

0 by the Gauss integration formula with 𝑛 = 3.

0.746815 2010

10. The speed,𝑣 meter per second, of a car, 𝑡 second after it starts, is shown

in the following table.

1.22256 2010

Using

Simpson’s 1

3

rule, find the

distance travelled by the care in 2 minutes.

𝑇 0 12 24 36 48 60 72 84 96 108 120

𝑣 0 3.6 10.08 18.90 21.60 18.54 10.26 4.50 4.50 5.40 9.0

ASSIGENMENT 2- NUMERICAL INTEGRATION

Sr.


1. Consider the following values. Find ∫ 10𝑦 𝑑𝑥 by Simpson’s 1

3 rule

and Weddle’s rule

X 10 11 12 13 14 15 16

Y 1.02 .094 0.89 0.79 0.71 0.62 0.55

4.713 2012

2. Write the trapezoidal rule for numerical integration. Using Simpson’s 1

3 rule evaluate ∫ 𝑓(𝑥)

2.5

1𝑑𝑥 from the following data. Take ℎ = 0.3

X 1 1.3 1.6 1.9 2.2 2.5

Y 1 1.69 2.56 3.61 4.84 6.25

4.7466 2012

3. Evaluate ∫𝑑𝑡

1+𝑡

1

0by the Gaussian formula with one point, two point

and three points.

i. 0.6667

j. 0.6923

k. 0.6931

2011

4. Evaluate ∫ (𝑠𝑖𝑛𝑥 − 𝑙𝑜𝑔𝑥 + 𝑒𝑥)𝑑𝑥1.4

0.2with ℎ = 0.2 by Simpson’s

1

3

and 3

8rule.

2016

5. Write the Simpson 1

3 rule for numerical integration. Using Simpson’s

1

3 rule evaluate ∫ 𝑓(𝑥)

6

0𝑑𝑥 from the following data. Take ℎ = 1

X 0 1 2 3 4 5 6

Y 1 0.5 0.3333 0.25 0.2 0.1666 0.1428

1.95853

Dec

2013

6. Evaluate ∫𝑑𝑥

1+𝑥

6

0 by using

a. Trapezoidal rule

b. Simpson’s 1

3 rule taking ℎ = 1.

1.9588

June

2014

2011

7. Derive Trapezoidal rule and evaluate ∫ 𝑒𝑥21.3

0.5𝑑𝑥 by using

Simpson’s 1

3rule.

2015

8. Evaluate ∫𝑒𝑥

1+𝑥

6

0𝑑𝑥 by using Simpson’s

3

8rule with ℎ = 1.

2016

9. Calculate

a. ∫ 2𝑒𝑥𝑑𝑥1

0 with 𝑛 = 10 using the trapezoidal rule.

b. ∫ 𝑒𝑥𝑑𝑥1

0 with 𝑛 = 10 using the trapezoidal rule

3.4394

1.7197

2014

2011

10. Evaluate ∫ 𝑒−𝑥2𝑑𝑥

0.6

0 by using Simpson’s

1

3rule,with 𝑛 = 6. 0.5351 2015

SHORT QUESTIONS

Sr.

No.


1. Write appropriate Simpson’s integration formula to solve the integration

∫ 𝑓(𝑥)1.8

0𝑑𝑥 dividing into 9 equal parts.

Simpson’s 3

8

2016

2. What is approximate value of the ∫ 𝑓(𝑥)2

0𝑑𝑥 using trapezoidal rule with

ℎ = 1 where 𝑓(1) = 2, 𝑓(2) = 4. 3 2016

TUTORIAL 3- FINITE DIFFERENCES AND INTERPOLATION

Sr.


1. Using Newton’s forward formula, find the value of 𝑓(1.6) if

𝑥 1 1.4 1.8 2.2

𝑓(𝑥) 3.49 4.82 5.96 6.5

5.4393 June

2011

2. Determine the polynomial by Newton’s forward difference formula

from the following table.

𝑥 0 1 2 3 4 5

𝑦 -10 -8 -8 -4 10 40

𝑥3 − 4𝑥2 + 5𝑥− 10

June

2012

3. Use Newton’s difference method to find the approximate value of

𝑓(1.3) from the following data

𝑥 1 2 3 4

𝑓(𝑥) 1.1 4.2 9.3 16.4

1.82 June

2013

4. Use Newton’s forward difference method to find the approximate

value of 𝑓(2.3) from the following data

𝑥 2 4 6 8

𝑓(𝑥) 4.2 8.2 12.2 16.2

4.8 Dec

2013

5. Using Newton’s forward interpolation formula, find the value of

𝑓(218), if

𝑥 100 150 200 250 300 350 400

𝑓(𝑥) 10.63 13.03 15.04 16.81 18.42 19.90 21.27

15.6993 June

2014

6. Write 𝑓(𝑥) = 𝑥4 − 2𝑥3 + 𝑥2 − 2𝑥 + 1 is factorial notation and find

∆4𝑓(𝑥) 24

June

2012

7. Determine the interpolating polynomial of degree 3 by using

Lagrange’s interpolation for the following data. Also find 𝑓(2)

𝑥 -1 0 1 3

𝑓(𝑥) 2 1 0 -1

-0.75 2013

2015

8. Using Lagrange’s formula find the form of the function 𝑓(𝑥) given

that

𝑥 0 2 3 6

𝑓(𝑥) 659 705 729 804

2016

9. Employ Stirling’s formula to calculate 𝑦(35)from the following table.

𝑥 20 30 40 50

𝑓(𝑥) 512 439 346 243

394.6875 June

2011

10. Compute 𝑐𝑜𝑠ℎ(0.56) from the following table and estimate the error.

𝑥 0.5 0.6 0.7 0.8

𝑐𝑜𝑠ℎ𝑥 1.127626 1.185465 1.255169 1.337435

𝑥 =0.56y=1.1609442

June

2010

ASSIGENMENT 3- FINITE DIFFERENCES AND INTERPOLATION

Sr.


1. Determine the interpolating polynomial of degree three using

Lagrange’s interpolation for the table below

𝑥 -1 0 1 3

𝑓(𝑥) 2 1 0 -1

1

24(𝑥3 − 25𝑥

+ 24)

June

2010

2. Compute 𝑓(9.2) from the following values using Newton’s divided

difference formula.

𝑥 8 9 9.5 11.0

𝑓(𝑥) 2.079442 2.197225 2.251292 2.397895

2.219208

June

2010

3. Evaluate 𝑓(9), using Lagrange’s interpolation and Newton’s divided

difference from the following data

𝑥 5 7 11 13 17

𝑓(𝑥) 150 392 1492 2366 5202

810

June

2014

4. Using Lagrange’s formula to fit a polynomial to the data and hence

find 𝑦(𝑥 = 0.2)

𝑥 -1 0 2 3

𝑦(𝑥) 8 3 1 12

𝑥 = 2𝑦 = 1

Dec

2011

5. Explain Quadratic Lagrange interpolation. Compute 𝑓(9.2) by using

Lagrange interpolation method from the following data

𝑥 9 9.5 11

𝑓(𝑥) 2.1972 2.2513 2.3979

2.2192

June

2013

6. Write the usual notation, show that

(1)∆= 1 − 𝑒ℎ𝐷 (2)(1 + ∆)(1 − 𝛻) = 1

Hint:

𝐸 = 1 + ∆

𝛻 = 1 − 𝐸

7. Let 𝑓(40) = 836, 𝑓(50) = 682, 𝑓(60) = 436, 𝑓(70) = 272. Use

Stirling’s formula to find 𝑓(55). 565.0625

Hint: 50, ℎ = 10, 𝑝 = 0.5

June

2012

8. By using Lagrange’s formula, find 𝑦 when 𝑥 = 10

𝑥 5 6 9 11

𝑦 12 13 14 16

14.6667 2015

9. Compute values of 𝑓(0.12) and𝑓(0.40) using suitable interpolation

formula for the following data :

𝑥 0.10 0.15 0.20 0.25 0.30

𝑓(𝑥) 0.1003 0.1511 0.2027 0.2553 0.3093

2015

SHORT QUESTIONS Sr.

No.


1. State at least two

differences between

Newton’s divided

difference and

Newton’s forward

interpolation

formula.

Newton’s Divided

Difference

Newton’s Forward Interpolation

It is used for both equal and

unequal spaced arguments.

It is used only for equally

spaced arguments.

It is applicable for the middle

of the tabulated values of 𝑥𝑖.

It is applicable for the beginning

of the tabulated values of 𝑥𝑖

when 𝑥𝑖’s are increasing order.

2016

TUTORIAL 4- SOLUTION OF A SYSTEM OF LINEAR EQUATIONS

Sr.


1. Solve the following system of equations using partial pivoting by Gauss

elimination Method. 8𝑥2 + 2𝑥3 = −7,3𝑥1 + 5𝑥2 + 2𝑥3 = 8,6𝑥1 + 2𝑥2 +8𝑥3 = 26

4, −1,1

2

June

2011

2014

2010

2. Solve the following linear system of equations by Gauss-Seidel

1. 1. 10𝑥1 + 𝑥2 + 𝑥3 = 12,2𝑥1 + 10𝑥2 + 𝑥3 = 13, 2. 2𝑥1 + 2𝑥2 + 10𝑥3 = 14 3.

4. 2. 2𝑥 − 𝑦 = 3, 𝑥 + 2𝑦 + 𝑧 = 3, −𝑥 + 𝑧 = 3

𝑥1 = 𝑥2 = 𝑥3

= 1

𝑥 = 1, 𝑦 = −1,

𝑧 = 4

Nov,

Dec

2010

June

2013

3. Solve:𝑥 + 𝑦 + 𝑧 = 9,2𝑥 − 3𝑦 + 4𝑧 = 13,3𝑥 + 4𝑦 + 5𝑧 = 40 by Gauss

elimination method.

𝑥 = 1, 𝑦 = 3, 𝑧= 5

June 2011

4. Solve the following system of equation using Gauss Elimination method

with partial Pivoting.

𝑥1 + 2𝑥2 + 3𝑥3 = 10,6𝑥1 + 5𝑥2 + 2𝑥3 = 30, 𝑥1 + 3𝑥2 + 𝑥3 = 10.

May 2016

5. Solve:3𝑥 + 𝑦 − 𝑧 = 3,2𝑥 − 8𝑦 + 𝑧 = −5, 𝑥 − 2𝑦 + 9𝑧 = 8 by Gauss

elimination method. Dec

2016

6. Solve following system of equation using Gauss-Seidel method correct up

to two decimal places

a) 20𝑥 + 2𝑦 + 𝑧 = 30, 𝑥 − 40𝑦 + 3𝑧 = −75, 2𝑥 − 𝑦 + 10𝑧 = 30

b) 8𝑥 + 𝑦 + 𝑧 = 5, 𝑥 + 8𝑦 + 𝑧 = 5, 𝑥 + 𝑦 + 8𝑧 = 5

𝑥 = 1.13, 𝑦 = 2.12, 𝑧 = 2.98 𝑥 = 0.5, 𝑦 = 0.5, 𝑧 = 0.5

June 2011 Dec

2013

7. Solve the following linear system of equations by Gauss-Seidel method :

10𝑥 − 𝑦 − 𝑧 = 13, 𝑥 + 10𝑦 + 𝑧 = 36, 𝑥 + 𝑦 − 10𝑧 = −35

May 2016

ASSIGENMENT 4- SOLUTION OF A SYSTEM OF LINEAR EQUATIONS

Sr.


1. Solve , by Gauss-Seidel iteration method ,the equations

20𝑥 + 𝑦– 2𝑧 = 17 3𝑥 + 20𝑦– 𝑧 = −18 2𝑥– 3𝑦 + 20𝑧 = 25

2. Solve the following system of equations by Gauss-Seidel

Method correct up to three decimal places

2𝑥 + 𝑦 + 54𝑧 = 110,27𝑥 + 6𝑦 − 𝑧 = 85,6𝑥 + 15𝑦 + 2𝑧= 72

𝑥 = 2.4255, 𝑦= 3.5730, 𝑧 = 1.9260

Nov, Dec

2011

3. Solve the following system of equation using Gauss

Elimination method with partial Pivoting.

𝑥 + 𝑦 + 𝑧 = 7,3𝑥 + 3𝑦 + 4𝑧 = 24,2𝑥 + 𝑦 + 3𝑧 = 16

𝑥 = 3, 𝑦 = 1, 𝑧 = 3 Dec 2011



6𝑥 + 𝑦 + 𝑧 = 105,4𝑥 + 8𝑦 + 3𝑧 = 155,5𝑥 + 4𝑦 − 10𝑧 =16

𝑥 = 15, 𝑦 = 10, 𝑧 = 5 June 2015



2𝑥 + 𝑦 + 6𝑧 = 9,8𝑥 + 3𝑦 + 2𝑧 = 13, 𝑥 + 5𝑦 + 𝑧 = 7

𝑥 = 1, 𝑦 = 1, 𝑧 = 1 Dec. 2015

6. Solve the following system of equation using Gauss

Elimination method with partial Pivoting.

2𝑥1 + 2𝑥2 + 𝑥3 = 6,4𝑥1 + 2𝑥2 + 3𝑥3 = 4, 𝑥1 + 𝑥2 + 𝑥3 =0.

X1=5,x2=1,x3=-6 Dec. 2015

SHORT QUESTIONS

Sr.

No.


1. In the Gauss Elimination method for solving the system of linear

equations name the matrix which is obtained after triangularization.

Upper Triangular

matrix

2016

2. Check whether the following system is diagonally dominant or not

justify your answer.

10𝑥 − 4𝑦 + 𝑧 = 7, 𝑥 + 5𝑦 − 2𝑧 = 5,8𝑥 − 4𝑦 − 3𝑧 = 6

Not diagonally

dominate

2016

3. Employ partial pivoting to the following system of the equations

4𝑥 + 2𝑦 − 𝑧 = −2,5𝑥 + 𝑦 + 2𝑧 = 4,6𝑥 + 𝑦 + 𝑧 = 6

6𝑥 + 𝑦 + 𝑧= 64𝑥 + 2𝑦 − 𝑧= −2

5𝑥 + 𝑦 + 2𝑧 = 4

2016

TUTORIAL 5- DISCRIPTIVE STATISTICS

Sr.


1. Find the mean of -1.5, 0, 1, 0.8. 0.075

2. Calculate the arithmetic mean by short-cut method for the following

data

𝑥 0 1 2 3 4 5 6 7 8 9 10

𝑓 2 8 43 133 207 260 213 120 54 9 1

5.0114

3. Calculate the average marks of the students by standard deviation

method from the following data

Marks 0-10 10-20 20-30 30-40 40-50 50-60

No. of Students 40 41 55 30 21 16

24.95

4. For the following data, find mean

Class 10-19 20-29 30-39 40-49 50-59

Frequency 1 1 15 10 20

44.5

5. Find standard deviation for the following data

𝑋 5 10 15 20 25

𝐹 7 4 6 3 5

10.1

6. Find the standard deviation for 48, 65, 57, 31, 60, 37, 48, 59, 78. 13.26

7. Calculate the Mean, Median and mode for the following data:

Class

interval

50-53 53-56 56-59 59-62 62-65

Frequency 3 8 14 30 36

Class

interval

65-68 68-71 71-74 74-77

Frequency 28 16 10 5

63.82,63.29, 65.75

Dec.

2015

ASSIGENMENT 5- DISCRIPTIVE STATISTICS

Sr.


1. Find the arithmetic mean from following frequency distribution

𝑥 5 6 7 8 9 10 11 12 13 14

𝑓 25 45 90 165 112 96 81 26 18 12

8.83

2. Daily earning (in Rs) of employees working on a daily basis in a firm are

Earning in

Rs

100 120 140 160 180 200 220

No. of

Employees

3 6 10 15 24 42 75

Calculate the mean of daily earnings.

194.51

3. The mean marks scored by 100 students were found to be 40. Later on it

was discovered that a score of 53 was misread as 83. Find the correct mean. 39.7

SHORT QUESTIONS

Sr.

No.


1. Define mode and also give the relation between mean, median and

mode.

Mode=3median-

2mean 2016

2. Find the arithmetic mean of the following frequency distribution

𝑥 1 2 3 4

𝑓 4 5 2 1

2

2016

3. What is the mode of the following frequency distribution

𝑥 1 2 3 4

𝑓 4 7 10 8

3

2016

4. Find the median of the following distribution

Mid-

values

1500 2500 3500 4500 5500 6500 7500

Frequency 27 32 65 78 58 32 8

4333.33

5. Find the mode of the following frequency distribution

𝑥 10 11 12 13 14 15 16 17 18 19

𝑓 8 15 20 100 98 95 90 75 50 30

14.82

6. Find the standard deviation for the following data

Class

interval

0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 6 14 10 8 1 3 8

19.62

7. Two automatic filling machines A and B are used to fill a mixture of

cement concrete in a beam. A random sample of beams of each machine

showed the following information

Machine_A 32 28 47 63 71 39 10 60 96 14

Machine_B 19 31 48 53 67 90 10 62 40 80

Find standard deviation of each machine and also comment on the

performance of the two machines.

𝜎𝐴

= 25.495𝜎𝐵

= 24.429

2015

8. Calculate Karl Person’s coefficient of skewness from the following data

Wages(Rs) 10-

15

15-

20

20-

25

25-

30

30-

35

35-

40

40-

45

45-

50

No. of

Workers

8 16 30 45 62 32 15 6

-0.223

TUTORIAL 6- CORRELATION AND REGRESSION

Sr.


1.

Find the correlation coefficient from the following data

𝑋 1 2 3 4 5 6 7

𝑌 6 8 11 9 12 10 14

0.845

2. Calculate the coefficient of correlation and obtain the lines of

regression for the following :

𝑋 1 2 3 4 5 6 7 8 9

𝑌 9 8 10 12 11 13 14 16 15

2015

3. Obtain the line of regression of monthly sales (Y) on advertisement

Expenditure (x) and estimate the monthly sales when the company

will spendRs.50,000 on advertisement, if the data on Y and X are as

follows :

𝑌(𝑙𝑎𝑐) 74 76 60 68 79 70 71 94

𝑋(𝑡ℎ𝑜𝑢𝑠𝑎𝑛𝑑) 43 44 36 38 47 40 41 54

2016

4. The following data give the experience of machine operators and

their performance rating as given by the number of good parts

turned out per 100 pieces.

Operator 1 2 3 4 5 6

Performance

rating (x)

23 43 53 63 73 83

Experience(y) 5 6 7 8 9 10

Calculate the regression line of performance rating on experience

and also estimate the probable performance if an operator has 11

years of experience.

96.3315 2015

ASSIGENMENT 6- CORRELATION AND REGRESSION

Sr.


1. Calculate the coefficient of correlation from the following date:

𝑋 12 9 8 10 11 13 7

𝑌 14 8 6 9 11 12 3

0.949

2. Calculate the coefficient between the following data:

𝑥 5 9 13 17 21

𝑦 12 20 25 33 35

0.986

3. Define Regression.

4. Define Line Regression.

5. Define Rank Correlation.

SHORT QUESTIONS

Sr.

No.


1. If the value of the coefficient of correlation is negative then

what does it signify about the relation of two variables?

Two variables are

inversely proportional to

each other. 2016

2. Which is the point of intersection of the regression line of 𝑦 on

𝑥 and regression line of 𝑥 on 𝑦. At (�́�, �́�) 2016

TUTORIAL 7- NUMERICAL SOLUTION OF ORDINARY

DIFFERENTIAL EQUATIONS

Sr.


1. Solve 𝑑𝑦

𝑑𝑥= 3 + 2𝑥𝑦 where 𝑦(0) = 1 for 𝑥 = 0.1 by Picard’s

method. 1.31665

2.

Use Taylor’s series method to solve

𝑑𝑦

𝑑𝑥= 𝑥2𝑦 − 1, 𝑦(0) = 1. Also

find 𝑦(0.03). 0.970009

3. Using Taylor series method, find correct to four decimal places, the

value of 𝑦(0.1), given 𝑑𝑦

𝑑𝑥= 𝑥2 + 𝑦2and 𝑦(0) = 1.

1.1114

4. Use the Euler method to find 𝑦(1.4) given that

𝑑𝑦

𝑑𝑥= 𝑥𝑦

1

2, 𝑦(0) =

1.(Take ℎ = 0.1) 𝑦4 = 1.4986

5. Describe Euler’s method for first order ordinary differential equation.

6. Using improved Euler’s method, solve 𝑑𝑦

𝑑𝑥= 2𝑥𝑦 = 0 with the initial

condition 𝑦(0) = 1 and compute 𝑦(0.2) taking ℎ = 0.2. Compare

the answer with exact solution.

0.5034

7. Explain the Euler’s method to find Numerical solution 𝑑𝑦

𝑑𝑥=

𝑓(𝑥, 𝑦), 𝑦(𝑥0) = 𝑦0.

8. Using improved Euler’s method, solve 𝑑𝑦

𝑑𝑥= 1 − 𝑦 with the initial

condition 𝑦(0) = 0 and tabulate the solutions at 𝑥 = 0.1,0.2. Compare the answer with exact solution.

𝑦(0.1)= 0.09516𝑦(0.2)= 0.18126

ASSIGENMENT 7- NUMERICAL SOLUTION OF ORDINARY

DIFFERENTIAL EQUATIONS

Sr.


1. Use Runge-Kutta second order method to find the approximate

value of 𝑦(0.2) given that 𝑑𝑦

𝑑𝑥= 𝑥 − 𝑦2, 𝑦(0) = 1 and ℎ = 0.1. 0.8523

Nov,

Dec

2010

2. Apply Runge-Kutta fourth order method, to find an approximate

value of 𝑦 when 𝑥 = 0.2 in steps of 0.1if 𝑑𝑦

𝑑𝑥= 𝑥 + 𝑦2, given that

𝑦 = 1, 𝑥 = 0.2.

June

2014

3. Given that 𝑦 = 1.3 when 𝑥 = 1and 𝑑𝑦

𝑑𝑥= 3𝑥 + 𝑦. Use second order

Runge-Kutta method (i.e. Heun method) to approximate when 𝑥 =1.2 Use step size 0.1.

2.3134 Dec

2012

4. Apply Runge-Kutta method of fourth order to calculate 𝑦(0.2)

given 𝑑𝑦

𝑑𝑥= 𝑥 + 𝑦, 𝑦(0) = 1taking ℎ = 0.1. 1.242

June

2010

June

2011

5. Solve the differential equation 𝑑𝑦

𝑑𝑥= 𝑥 + 𝑦, with fourth order

Runge-Kutta method, where

i. 𝑦(0) = 1, 𝑥 = 0to𝑥 = 0.2with ℎ = 0.1.

ii. Y(0)=0 and ℎ = 2.

0.489

June

2010

June

2011

June

2013

6. Use the Euler method to find 𝑦(0.2) given that 𝑑𝑦

𝑑𝑥= 𝑦 −

2𝑥

𝑦, 𝑦(0) = 1.(Take ℎ = 0.1)

1.1918 June

2011

SHORT QUESTIONS

Sr.

No.


1. Determine 𝑓(𝑥, 𝑦) for solving the following differential

equation by Euler’s method3𝑑𝑦

𝑑𝑥+ 5𝑦2 = 𝑠𝑖𝑛𝑥; 𝑦(0) = 5.

𝑓(𝑥, 𝑦) =1

3(𝑠𝑖𝑛𝑥

− 5𝑦2)

2016

TUTORIAL 8- PROBABILITY

Sr.


1. Eight boys and three girls are to sit in a row for a photograph. Find

the probability that no two girls are together.

28

55

2. A person is known to hit a target in 2 out of 4 shots, whereas

another person B is known to heat the same target in 1 out of 3

shots. Find the probability of the target being hit at all when they

both try.

2

3

May-

2015

3. An urn contains 10 red, 5 white and 5 blue balls. Two balls are

drawn at random. Find the probability that they are not of same

color.

25

38

4. In a certain assembly Plant, three machines 𝐵1, 𝐵2 ∧ 𝐵3 produce

30%, 45% ∧ 25% of the products, respectively. It is known from

the past experience that 2%, 3% ∧ 2% of the product made by each

machine, respectively, are defective. Supposed that a finished

product is randomly selected. What is the probability that it is

defective?

0.0245 May-

2016

5. A bag A contains 2 white and 3 red balls, and a bag B contains 4

white and 5 red balls. One ball is drawn at random from one of the

bags and it is found to be red. Find the probability that the red ball

is drawn from the bag B.

25

52

ASSIGENMENT 8- PROBABILITY

Sr.


1. An unbiased coin tossed 3 times, what is the probability of obtaining

two heads ?

3

8

May-

2016

2. A card drawn at random from a pack of 52 cards. Find the probability

of getting a king or a heart or a red card.

7

3

3. Two students X and Y work independently on a problem. The

probability that X will solve it is 3/4 and the probability that the Y will

solve it is 2/3. What is the probability the problem will be solved?

11

12

Winter-

2015

4. A company has two plants to manufacture hydraulic machines. Plant I

manufactures 70% of the hydraulic machines, and plant II

manufactures 30%. At plant I, 80% of hydraulic machines are rated

standard quality, And plant II, 90% of hydraulic machines are rated

standard quality. A machine is picked up at random and is found to be

standard quality. What is the chance that it has come from Plant I ?

0.6747 May-

2015

5. State Baye’s theorem. In a bolt factory, machines A,B,C manufactures

25%,35% and 40% of the total output and of the total manufacturing ,

5%,4% and 2% are defective bolts. A bolt is drawn at random from the

product and is found to be defective. What are the probabilities that it

was manufactured by machines A,B and C ?

By A, 0.3623

By B,

0.4058

By C,

0.2319

Winter-

2015

TUTORIAL 9- PROBABILITY DISTRIBUTIONS

Sr.


1. A machine produces an average of 500 items during the first week

of the month and average of 400 items during the last week of the

month, the probability for these being 0.68 and 0.32 respectively.

Determine the expected value of the production.

468 May-

2015

2. In a large number of parts manufactured by a machine, the mean

number of defective in a sample of 20 is 2. Out of 1000 such

samples, how many would be expected to contain exactly two

defective parts?

≈ 285 May-

2015

3. The compressive strength of samples of cement can be modelled by

a binomial distribution with a mean 6000 𝑘𝑔 𝑐𝑚2⁄ and a standard

deviation of 100 𝑘𝑔 𝑐𝑚2⁄ .

(a) What is the probability that the sample’s strength is less

than 6250 𝑘𝑔 𝑐𝑚2⁄ ?

(b) What is the probability, if sample strength is between

5800and 5900 𝑘𝑔 𝑐𝑚2⁄ ?

(c) What strength is exceeded by 95% of the samples ?

0.99379

0.13591

6165

May-

2016

4. What are the properties of Binomial Distribution? The average

percentage of failure in a certain examination is 40. What is the

probability that out of 6 candidate, at least 4 passed in examination?

0.1792 Winter-

2015

5. A book contains 100 misprints distributed randomly throughout its

100 pages. What is the probability that a page observed at random

contains at least two misprints? Assume Poisson distribution.

Winter-

2015

6. A multiple choice test consists of 8 questions with 3 answers to each

question (of which only one answer is correct). A student answers

each questions by rolling a balanced dice and checking the first

answer if he gets 1 or 2, the second answer if he gets 3 or 4 and the

third answer if he gets 5 or 6. To get distinction, the student must

secure at least 75% correct answers. If there is no negative marking,

what is the probability that the student secure a distinction?

0.0197 May-

2015

ASSIGENMENT 9- PROBABILITY DISTRIBUTIONS

Sr.


1. The probability distribution of a random variable X is given

below

X -2 -1 0 1 2

P(x) 1/12 1/3 k 1/4 1/6

Find (1)𝐸(𝑥) (2) 𝐸(2𝑥 + 3) (3) 𝐸(𝑥2 + 2)

(1) 1

12

(2) 19

6

(3) 43

12

2. Six coins are tossed 6400 times. Using the Poisson distribution,

what is the approximate probability of getting six heads 10

times? 1.025 × 10−30

3. Find the value of k such that f(x) is a probability density

function. Find also, 𝑃(𝑋 ≤ 1.5).

1

2,1

2

4. The mean and variance of a binomial distribution are 4 and 4/3

respectively. Find 𝑃(𝑋 ≥ 1). 0.9986

5. A manufacturer knows from his experience that the resistances

of resistors he produces is normal with 𝜇 = 100𝑜ℎ𝑚𝑠and 𝑆𝐷 =𝜎 = 2𝑜ℎ𝑚𝑠. What percentage of resistors will have resistances

between 98𝑜ℎ𝑚𝑠and 102𝑜ℎ𝑚𝑠.

0.6826

TUTORIAL 10- CURVE FITTING

Sr.


1. Define a curve fitting -

May-

2016

2. Fit a second degree polynomial using least square method to the

following data:

𝑥 0 1 2 3 4

𝑦 1 1.8 1.3 2.5 6.3

𝑦= 1.42− 1.07𝑥+ 0.55𝑥2

May-

2015

3. Fit the exponential curve 𝑦 = 𝑒𝑏𝑥 to the following data:

𝑥 0 2 4 6 8

𝑦 150 63 28 12 5.6

𝑦 = 146.28

𝑒−0.4117𝑥

May-

2015

4. Fit a second degree parabola 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 in the least square

sense for the following data:

𝑥 1 2 3 4 5

𝑦 10 12 13 16 19

Winter-

2015

5. A simply supported beam carries a concentrated load P(lb) at its

mid-point. Corresponding to different values of P, the maximum

deflection Y(in) is measured. The data is given below:

P 100 120 140 160 180 200

Y 0.45 0.55 0.60 0.70 0.80 0.85

Find a law of the form Y=a+bP using the least square method.

𝑌= 0.0476+ 0.0041𝑃

May-

2015

ASSIGENMENT 10- CURVE FITTING

Sr.


1. Fit a straight line to the following data. Also estimate the value of y

at x=2.5

𝑥 0 1 2 3 4

𝑦 1 1.8 3.3 4.5 6.3

4.045

2. Fit a curve of the form 𝑦 = 𝑎𝑏𝑥 to the following data by the

method of least square.

𝑥 1 2 3 4 5 6 7

𝑦 87 97 113 129 202 195 193

𝑦 = 73.744 (1.1688)𝑥

3. Fit a straight line to the following data:

𝑥 1 2 3 4 5

𝑦 1 2 3 4 5

𝑦 = 1.6 + 1.2𝑥

4. Fit a curve of the form 𝑦 = 𝑎𝑥𝑏 to the following data:

𝑥 1 2 3 4

𝑦 2.5 8 19 50

𝑦 = 2.227𝑥2.09

SHORT QUESTIONS

Sr. No. Questions Answer Year

1. Define curve fitting. 2016

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


SUBJECT: BUILDING & TOWN PLANNING (2140607)

SEMESTER IV

ASSIGNMENTS



Silver Oak College of Engineering & Technology Page1



Branch: Civil Semester: 4

Subject Name: Building and Town Planning Subject Code: 2140607

1. Explain the principle of planning in detail with figures.

2. Explain the principle of architecture in detail with figures.

3.. Explain the objective and scope of building bye laws.

4. Classify the type of buildings in detail based on use of building.

5. Explain the various components of building with help of neat sketch.

6. Explain the various type of buildings in general.

7. Short notes on :

1. Set – back.

2. Light Plane.

3. FSI (Floor Space Index).

4. Site Plan.

5. Layout Plan.

6. National Building Code (NBC)

8. Define the following terms.

1. Plinth Area.

2. Carpet Area

3. Floor Area

4. Built Up Area

5. Building Line

6. Basement / Cellar.

A/Prof. Viranchi Shah A/Prof. Ninaad Athalye

A/Prof. Mrunalini Rana


Assignment No. 1: Introduction to buildings and building bye laws.






1. Explain behavior of structures during earthquake and possible mode and pattern of

failure.

2. Explain briefly the guideline for design of non-engineered earthquake resistant brick

masonry structures.

3.. Explain the below terms in planning of earthquake resistant buildings.

1. Dimensions of building.

2. Symmetry

3. Simplicity.

4. Connectivity.

5. Separations

6. Regularity.

4. Define the following terms.

1. Picture Plane.

2. Eye level.

3. Centre of vision.

4. Ground Line.

5. Cone of vision.

6. Station point.

7. Vanishing point and line.

8. Ground Plane.

5. Differentiate one point, two point and three point perspectives with neat sketch.




Assignment No. 2: Planning of Earthquake resistant building.

Elements of perspective views.






1. Explain town planning.

2. Explain the different names used for town planning at different periods in India in detail.

3. Write Short Notes on :

1. Origin of towns and growth of towns.

2. Ribbon Development.

3. Satellite town.

4. What do you mean by “civic surveys”? What is necessity of civic surveys for town

planning purpose?

5. Describe various types of surveys to be conducted for town planning scheme.

6. Differentiate between functional land territorial surveys.

7. Explain aims and objectives of town planning.

8. Explain fundamental principles of town planning.

9. Define “land use”. Explain its types and principles.




Assignment No. 3: Town Planning History and Civic Surveys.

Land use planning.






1. Explain the main elements of town planning.

2. Explain the principle of architecture in detail with figures.

3.. Discuss urban road system in city planning.

4. Define slums and give causes and effects of slums.

5. Give remedial measures for avoiding slum formation.

6. Write a short note on slum clearance.

7. Short notes on ( definition, importance, objects, principles and aspects) :

1. Zoning.

2. Neighborhood planning.

3. Master plan / development plan.

4. Characteristics of CBD.

8 Discuss four basic pillars of smart city with chart.

9 Explain the concept of smart city.




Assignment No. 4: Zones, Neighbourhood planning, slums, smart city.


Activity/Task 1:

a) Prerequisite – Collect brochure of any residential building.

b) Drawing Sheet 1: Residential Building Planning.

c) Two Storeyed Load Bearing Building. – Plans, Elevations, Sections ,

layout plans , key plan , site plan , area table, schedule of opening and

scale ( 1:100)

d) Drawing Sheet – A1 size.

Activity/Task 2:

Visit to Earthquake Laboratory in our Campus-‘A’ Building Ground Floor

Sheet 2: Public Building. : Ground floor plan, elevation, section plan, key plan,

layout, site plan, area table, schedule of opening.

d) A1, B1, C1 – post office/bank.

e) A2, B2, C2 – hospital / shopping centre.

f) A3, B3, C3 – School / guest house.

Activity/Task 3:

Visit to Earthquake Laboratory.

Sheet 3: Furniture Plan, sanitation layout, electrical layout.

a) A1, B1, C1 – case study of historical town planning in India.

b) A2, B2, C2 – case study of any slum area in Gujarat or India.

c) A3, B3, C3 – case study of any smart city in world.

Activity/Task 4:

Drawing Sheet 4: Perspective Drawing.

Two point perspective of a building

Neighbourhood centre planning design.








ACTIVITIES/ DRAWING SHEETS






1. Small sketch book, one graph book, tracing paper, compass box.

Reference Books.

1. Planning and Building Design by Y.S. Sane.

2. Town Planning by G.K. Hiraskar.

3. National Building Code (2005) , New Delhi.

4. General Development Control Regulations published by AUDA.

5. Town Planning by S.C. Rangwala.

6. Architecture,Form , Space and order by Francis D.K. Ching.




Common Instructions and Reference Books.


SUBJECT: CONCRETE TECHNOLOGY (2140608)

SEMESTER IV

ASSIGNMENTS




Activity/Task 1: Visit to J. K. Laxmi Plant and prepare the

small plan in sketchbook.




Subject Name: Concrete Technology Subject Code:2140608

1) Draw a Diagram or flowchart or in a tabular form of historical Background of cement and

concrete using any source. Write down the reference books, links if used. (Dec’11, June’12)

2) Compared to other materials, what are the advantages of using concrete for structures?

3) Explain dry process and wet process for manufacturing of cement. Recently Which process we

are using? Justify. (Mar’10, Dec’10, May’12, Jan,13, Dec’14, Nov’17)

4) Distinguish between Entrapped air and Entrained air. (Dec’14)

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

Lect. Reecha Panchal Lect. Harsh Rathod


Assignment No. 1 –Introduction of Concrete


Activity/Task 2: Make a chart of classification of aggregate

with photographs in sketch-book.





1) Give the Bogue’s compound for cement and explain their role in hydration process. (Dec’09,

Dec’11, May’11, May’12, Jan’13, Nov’16, June’16) OR Describe briefly the chemical

composition, major compounds formed and hydration of cement. (June’17) OR State the major

Compounds of OPC and importance of them. (Nov’17)

2) Define: Heat of Hydration and give the difference between setting and hardening of cement.

(Dec’11,May’14,Nov’17, Nov’16)

3) State any four different types of cement and explain any two in brief. (Nov’17) or Enlist different

types of cement. Explain in brief any two in detail. (Dec’09, May’11,June’17)

4) Define Initial and Final setting time of cement. Describe the test for determining initial and final

setting time of cement. Give IS requirements for setting time for OPC.(Mar’10, Dec’11,

May’14,Nov’17, Nov’16)

5) Which apparatus can be used for soundness test? Explain it in brief. (Dec’10, Dec’11, Jan’13)

6) Explain importance of grading of aggregates. (Nov’17. Nov’16) AND Write short note on

Bulking of sand. (Nov’17, Nov’16) OR Explain bulking of aggregate. (March’10, May’12,

June’16)

7) Enlist the tests for the determination of strength of aggregate. Explain any one in detail. (Dec’11,

May’12, Dec’14)

8) Define: (i) Fineness Modulus and write down its range for different size aggregates. (ii) Flakiness

Index and (iii) Elongation Index (iv) Gap grading. (Mar’10, Dec’11,Dec’14)

9) Explain the qualities of water required for production of concrete. (Dec’11, Jan’13, June’17) OR

Describe the importance of the quality of water used for concrete. (June’16)

10) Define admixture and state purpose of adding admixtures in concrete. (Nov’17) Write a short note

any one admixture in detail. (Dec’11, Jan’13, May’14, Dec’14)

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



Assignment No. 2 – Concrete Making Materials.


Activity/Task 3: Visit any construction site. Take selfie or your photograph with slump while the workability (Slump test) is carried

out on site.





1) What is workability? List the factors affecting the workability of concrete and explain any three

out of them. ( March’10, Dec’10, May’11, Dec’10, Nov’16, June’17, Nov’17)

2) Explain Segregation and bleeding of concrete in detail. (June’17, Nov’17, June’16) OR Explain

the segregation and bleeding effect on concrete. (June’17, June’16) OR Define segregation and

bleeding of concrete. Explain the factors affecting it. (Dec’09, Dec’10, May’11, Jan’13,

May’14, Dec’14, Nov’16)

3) Recently which type of batching is used in RMC plant? Explain in brief. (May’12, June’15)

4) List out the methods of compaction and explain any one method in detail.

5) Write the requirements of curing. State the different methods of curing with one in detail.

(Dec’11, May’12)

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



Assignment No. 3 – Fresh Concrete


Activity/Task 4: Read test of Compression test from IS: 456

and take important points for cylinder and cube moulds.





1) Give the difference between hardened concrete and fresh concrete. (June’17)

2) State factors affecting Compressive strength of concrete and explain any four in detail. (Nov’17,

June’17, Nov’16) or Explain Water–Cement ratio. (June’17) or Explain the effect of water

cement ratio on the strength of concrete? Explain Mechanism. (Dec’09, May’11, June’16)

3) Define Shrinkage. Explain Plastic shrinkage. (Nov’17) or what is shrinkage? Give the

classification of shrinkage. (June’16)

4) Define Creep. Explain factors affecting creep of concrete. (May’12, Jan’13,Nov’17)

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



Assignment No. 4: Hardened Concrete


Activity/Task 5: collect exposure conditions in different

weather conditions of different cities of India.





1) Define Durability. Explain its significance. (Nov’17, Nov’16) OR What is durability of concrete?

Enlist factors affecting durability of concrete. Explain any one in detail. (June’16) Explain

breakeven analysis, giving example. Discuss various aspect of durability of concrete. What

measures are taken by IS code to ensure durable structure? (Dec’09, Dec’10, May’11,

Dec’11,June’17)

2) What are the factors that affect permeability of concrete? (Nov’16 , June’17) OR Explain the

factors affecting Permeability. (Nov’16) OR What is permeability of concrete? Enlist factors

affecting permeability of concrete. Explain any one in detail. (Dec’09, May’14, Dec’14, June’16)

3) Explain Sulphate Attack and chloride attack on concrete. (March’10, March’11, Nov’16,

Nov’17) or Explain mechanism of Sulphate Attack on concrete. (May’11, Dec’14, June’16)

4) Explain alkali-aggregate reaction. What are the factors promoting it and how it can be controlled?

(May’11, Dec’10, Dec’11, Dec’14, May’15)

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



Assignment No. 5: Durability and Permeability of Concrete


Activity/Task 6: (a) Visit any RMC Plant in January Month and collect

the data which are required for mix design (b) Design concrete mix with

cement and fly ash as a cementatious material





1) Explain principle of mix design. Explain parameters and factors influencing mix design.

(Nov’17, June’16) OR Which factors are affecting the choice of mix design. (June’17) OR List

factors affecting the choice of mix design. (March’10, Dec’11, May’11, May’12,Nov’16)

2) Define nominal mix concrete and design mix concrete. Describe step by step procedure of IS

method of mix design. (Dec’11, Nov’17, Nov’16) OR Write the steps of mix design using IS

10262. (June’17) OR Explain Indian Standard Mix design method as per IS: 10262:2009 with its

salient features. (Jan’13, June’16)

3) Give advantages of Quality control. (Nov’17) or Explain quality control of concrete and factors

affecting it. (June’17, Nov’16)

4) Define: (i) Mean (ii) Variance (iii) Range (Nov’17, June’17, and Nov’16). Mention acceptance

criteria for mix design and variation of test results. (May’11)

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



Assignment No. 6: Concrete Mix Design


Activity/Task 7: Prepare a presentation of special concrete and

special concreting methods for a topic which are given to the

students





1) Which are the basic requirements or property of the Self Compacting concrete? Enlist various

tests for measurement of each property. (June’16)

2) Write short note on cold weather concreting. (Nov’16) OR Explain the effect of cold weather on

concrete. (May’11, June’16)

3) Explain the effect of hot weather on concrete. (March’10, May’11, Dec’14, May’14)

4) Enlist various methods of concreting under water and explain ‘Tremie method’. (Dec’09, Jan’13,

Dec’14, June’17, Nov’16)

5) Write short note on ready mix concrete and Polymer concrete. (Mar’10, Dec’11, Jan’13,

June’17)

6) How fly ash concrete gain strength in later age? Explain Mechanism. (June’16) AND also Enlist

factors affecting properties of fibre reinforced concrete. (Dec’11, May’12,Nov’16, Nov’17,

June’16)

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



Assignment No. 7: Special Concrete and Concreting Method


Activity/Task 8: Take a photograph of a crack in any structure.

Find out the crack type, causes, effects and solution.




Subject Name: Concrete Technology Subject Code: 2140608.

1) Explain ultrasonic pulse velocity test for hardened concrete. (June’17) OR Explain ultrasonic

pulse velocity test. (Nov’16) OR Give the factors affecting the measurement of Ultrasonic pulse

velocity test. (May’10, Dec’14,June’16)

2) Differentiate between destructive and non- destructive tests. Give the Limitation of Rebound

hammer test. (Dec’10, Dec’11, May’12, May’14)

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Assignment No. 8: Miscellaneous Topics

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