Name of the University : Mahatma Gandhi University
Degree : M.Tech
Name Of The Subject : Civil Engineering
Document type : Model Question Paper
Website : mgu.ac.in
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MGU Civil Engineering Model Question Paper
Applied Statistics & Probability
(i) State and prove the following (i) Baye’s theorem (ii) Addition theorem .
(ii) Find the first four central moments for the following data.
X: 1 2 3 4 5 6 7 8 9
f: 1 6 13 25 30 22 9 5 2
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OR
2. (i) Fit a Normal Distribution and hence find the theoretical frequencies
Class: 120-130 130-140 140-150 150-160 160 -170 170 -180
Freq: 2 2 14 22 25 20
3. (i) From the following data obtain the regression equations
Sales – 91 97 108 121 67 124 51 73 111 57
Purchase – 71 75 69 97 70 91 39 61 80 47
(iii) The following are the data on the drying time of a certain varnish and the amount of additive that is intened to reduce the drying time .
Amount of varnish additive ( gms ) : 0 1 2 3 4 5 6 7 8
Drying time : 12.0 10.5 10.0 8.0 7.0 8.0 7.5 8.5 9.0
(i) Draw a scatter diagram to verify that it is reasonable to assume that the relationship is parabolic
(ii) Fit a second degree polynomial with the method of least squares
(iii) Use the result of part (ii) to predict the drying time of the varnish when 6.5 gms of the additive is being used . ( 15 marks )
OR
4. (i) Expalin systematic sampling and stratified sampling with its major applications in environmental engineering
5. (i) Discuss different types of tests of significance concerning small samples .
(ii) Define (a) Type I error (b) Type II error (c) Level of significance of a test. Find how many heads in 54 tosses of a coin will ensure its fairness at 5% level of significance.
OR
6. (i) Records taken of the number of male and female births in 800 families having four children are as follows
No. of male births – 0 1 2 3 4
No. of female births – 4 3 2 1 0
No. of families – 32 178 290 236 94
Test whether the data are consistent with the hypothesis that the binomial law holds
and the chance of male birth is equal to that of the female birth, namely, p = q = 1/2 .
(ii) The following are the number of minutes it took 10 mechanics to assemble a piece of machinery in the morning, X and in the afternoon Y
X : 11.1 10.3 12.0 15.1 13.7 18.5 17.3 14.2 14.8 15.3
Y : 10.9 14.2 13.8 21.5 13.2 21.1 16.4 19.3 17.4 19.0
Calculate r .Test the null hypothesis ? =0 against the alternative hypothesis ? ?0 at 0,05 level of significance .
(ii) The following are the number of minutes it took 10 mechanics to assemble a piece of machinery in the morning, X and in the afternoon Y
X : 11.1 10.3 12.0 15.1 13.7 18.5 17.3 14.2 14.8 15.3
Y : 10.9 14.2 13.8 21.5 13.2 21.1 16.4 19.3 17.4 19.0
Calculate r .Test the null hypothesis ? =0 against the alternative hypothesis ? ?0 at 0,05 level of significance .
Environmental Chemistry
1. a) State and Explain Raoult’s law.
b) What are buffer solutions? Explain. Derive Henderson Hasselbalch’s equation for pH of a buffer solution. (10)
c) Calculate the pH of a buffer solution prepared with 20 mg/L carbonic acid and 50 mg/L of bicarbonate ion, under the following conditions. Assume a closed system.
i) Initially
ii) After 3ml of 0.02 N H2SO4 is added
iii) After 3ml of 0.02 N NaOH is added
OR
2.a) State and explain Le Chatlier’s principle.
b) What is the molar concentration of a solution containing 10 g/L of i) NaOH ii) Na2SO4.
c) Explain the different types of adsorptions.
d) Briefly explain
i) Zeta Potential
ii) Osmosis
iii) Principle of Solvent extraction
3. a) What is the relationship between i) pH and hydrogen ion activityii) pH and hydroxyl ion activity
b) Explain the three major kinds of alkalinity found in natural waters.
c) Discuss the principles involved in the EDTA titrimetric method of measuring hardness.
d) Explain the importance of following parameters in water analysis.
i) BOD ii) COD iii) DO
OR
4. a) Give the applications of COD analysis in environmental engineering.
b) Explain the environmental significance of iron and manganese in water supplies.
c) Briefly explain anyone method for determination of chloride concentration in water.
d) Discuss the i) acid – base reaction and ii) Ion exchange reaction in soil.
a) Define Microbiology. What are the major characteristics of a microorganism?