Loyola College Question Paper 2003

Loyola College B.Sc. Statistics Nov 2003 Statistical Mathematics – II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2003

ST-3500/STA502 – STATISTICAL MATHEMATICS – II

04.11.2003                                                                                                           Max:100 marks

9.00 – 12.00

SECTION-A

Answer ALL the questions.                                                                              (10×2=20 marks)

 

  1. If P* is a partition of [a , b] finer than the partition P, state the inequality governing the upper sums lower sums of a function f corresponding to P and P*.
  2. Find .
  3. State the first Fundamental Theorem of Integral calculus.
  4. Solve: .
  5. “The function f(x,y) =   xy/(x2+y2) ,    (x,y)  ¹(0,0)

 

0                ,   (x, y) = (0, 0)

does not have double limit as (x, y)   – verify.

  1. State the rule for the partial derivative of a composite function of two variables.
  2. Define Gamma distribution.
  3. Write down the Beta integral with integrand involving Sine and Cosine functions.
  4. Define a symmetric matrix.
  5. Find the rank of the matrix .

 

SECTION-B

Answer any FIVE  questions.                                                                          (5×8=40 marks)

 

  1. Evaluate (a) . (4+4)

(b)

  1. If f(x) = kx2 , 0 < x¸< 2 , is the probability density function (p.d.f) of X, find (i) k

(ii) P[X<1/4],  (iii) P,  (iv) P[X >1].

  1. Solve the non-homogeneous differential equation:

(y – x – 3) dy = (2x + y +6) dx

  1. For the function          xy(x2 – y2) / (x2 + y2)  ,    (x,y)  ¹(0,0)

f(x,y) =

0                                ,      (x, y) = (0, 0)

Show that fx (x, 0) = fy (0,y) = 0 , fx (0, y) = -y , fy (x, 0) = x.

  1. Find the mean and variance of Beta distribution of II kind stating the conditions for their existence.
  2. If f(x,y) = e-x-y , x > 0, y > 0, is the joint p.d.f of (x, y),  find the joint c.d.f. of (x, y).  Verify that the second order mixed derivative of the joint c.d.f.is indeed the joint p.d.f.
  3. Establish the reversal law for Transpose of product of matrices. Show that the operations of Inversion and Transpositions are commutative.
  4. Find the inverse of using Cayley – Hamilton Theorem.

 

SECTION-C

Answer any TWO  questions.                                                                          (2×20=40 marks)

 

  1. a) Show that, if fÎ R [a, b] then f2 Î R [ a, b].
  2. b) If f(x) = c.e-x, x > 0, is the p.d.f. of X, find (i) c (ii) E(X), (iii) Var (X).
  3. c) Discuss the convergence of (8+6+6)
  4. a) Investigate for extreme values of the function

f (x, y) = x3 + y3 – 12x – 3y + 5, x, y Î R.

  1. b) Define joint distribution function for bivariate case and state its properties. Establish

the property which gives the probability P[x1 < X £ x2,  y1 < Y £ y2] in terms of the

joint distribution function of (X, Y).                                                               (10+10)

  1. If x + y ,   0 < x, y < 1

f (x, y) =

0        ,   otherwise

is the joint p.d.f of (x, y),  find the means and variances  of X and Y and covariance

between X and Y.  Also find  P [ Y < X] and the marginal p.d.f’s of X and Y.

  1. a) By partitioning into 2 x 2 submatrices find the inverse of
  2. b) Find the characteristic roots and any characteristic vectors for the matrix

 

(10 + 10)

 

 

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Loyola College B.Sc. Statistics Nov 2003 Statistical Methods Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600  034

B.Sc. DEGREE EXAMINATION  –  STATISTICS

First SEMESTER  – NOVEMBER 2003

           ST 1500/ STA  500  STATISTICAL  METHODS

07.11.2003                                                                                        Max: 100 Marks

9.00 – 12.00

 

section – A                    

Answer ALL questions                                                            (10 ´ 2 = 20 Marks)

  1. Give the definition of statistics according to Croxton and Cowden.
  2. Comment on the following: “ Sample surreys are more advantageous than census”.
  3. Give an example for

(i) Quantitative continuous data     (ii)  Discrete time series data

 

  1. Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
  2. Mention any two limitations of geometric mean.
  3. From the following results obtained from a group of observations, find the standard deviation. S(X-5) = 8 ;  S(X-5)2 = 40;  N = 20.

 

  1. For a moderately skewed unimodal distribution, the A.M. is 200, the C.V.

is 8 and the  Karl Pearson’s coefficient of skewness is 0.3.  Find the mode

of the distribution.

 

  1. Given below are the lines of regression of two series X an Y.

5X-6Y + 90 = 0

         15X -8Y-130 = 0

Find the values of .

  1. Write the normal equations for fitting a second degree parabola.
  2. Find the remaining class frequencies, given (AB) = 400;

(A) = 800; N=2500; (B) = 1600.

                                                 SECTION – B

Answer any FIVE questions.                                                   (5 ´8 = 40 Marks)

  1. Explain any four methods of collecting primary data.
  2. Draw a histogram and frequency polygon for the following data.
Variable Frequency Variable Frequency
100-110 11 140-150 33
110-120 28 150-160 20
120-130 36 160-170 8
130-140 49

 

Also determine the value of mode from the histogram.

 

 

 

 

 

 

  1. Calculate arithmetic mean, median and mode from the following

frequency distribution.

 

Variable Frequency variable Frequency
10-13 8 25-28 54
13-16 15 28-31 36
16-19 27 31-34 18
19-22 51 34-37 9
22-25 75 37-40 7

 

  1. The number of workers employed, the mean wages (in Rs.) per month and standard deviation (in Rs.) in each section of a factory are given below. Calculate the mean wages and standard deviation of all the workers taken together.

 

Section No. of workers

employed

 Mean Wages

(in Rs.)

 Standard  deviation

(in Rs.)
A 50 1113 60
B 60 1120 70
C 90 1115 80

 

  1. Calculate Bowley’s coefficient of skewness from the following data.

 

Variable frequency
0-10 12
10-20 16
20 -30 26
30- 40 38
40 -50 22
50-60 15
60- 70 7
70 -80 4

 

  1. Calculate Karl Person’s coefficient of correlation from the following data.
X 44 46 46 48 52 54 54 56 60 60
Y 36 40 42 40 42 44 46 48 50 52

 

  1. Explain the concept of regression with an example.
  2. The sales of a company for the years 1990 to 1996 are given below:

 

Year 1990 1991 1992 1993 1994 1995 1996
Sales (in lakhs of  rupees) 32 47 65 88 132 190 275

 

Fit an equation of the from Y = abX  for the above data and estimate the

sales for the year 1997.

 

 

 

 

 

SECTION – C

Answer any TWO questions.                                                   (2 ´ 20 = 40 Marks)

 

  1. a) Explain (i) Judgement sampling (ii) Quota sampling and

(iii) Systematic sampling methods with examples.

 

  1. (i) Draw a blank table to show the distribution of personnel  in a

manufacturing concern according to :

  • Sex: Males and Females.
  • Salary grade: Below Rs.5,000; Rs.5,000 -10,000;

Rs.10,000 and above.

  • Years: 1999 and 2000
  • Age groups: Below 25, 25 and under 40, 40 and above

 

(ii) Draw a multiple bar diagram for the following data:

 

Year Sales (in’000Rs.) Gross Profit Net profit
1992 120 40 20
1993 135 45 30
1994 140 55 35
1995 150 60 40

(10+5+5)

 

  1. a) (i)  An incomplete distribution is given below

 

Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 10 20 f1 40 f2 25 15

 

       Given the median value is 35 and the total frequency is 170, find

the missing frequencies f1 and f2.

  • Calculate the value of mode for the following data:
Marks 10 15 20 25 30 35 40
Frequency 8 12 36 35 28 18 9

 

  1. b) Explain any two measures of dispersion.                                       (7+7+6)
  2. a) The scores of two batsman A and B is 10 innings during a certain season are:

 

 A 32 28 47 63 71 39 10 60 96 14
 B 19 31 48 53 67 90 10 62 40 80

 

Find which of the two batsmen is consistent in scoring.

 

 

 

 

 

 

 

 

 

 

 

  1. Calculate the first four central moments and coefficient of skewness from the

following distribution.

 

Variable frequency Variable Frequency
25-30 2 45-50 25
30-35 8 50-55 16
35-40 18 55-60 7
40-45 27 60-65 2

(10+10)

  1. a) From the following data obtain the two regression equations and calculate

the correlation coefficient.

 

X 60 62 65 70 72 48 53 73 65 82
Y 68 60 62 80 85 40 52 62 60 81

 

  1. b) (i)   Explain the concept of Kurtosis.

(ii)   In a co-educational institution, out of 200 students 150 were boys.

They took an examination and it was found that 120 passed, 10 girls

had failed. Is there any association between gender and success in the

examination?                                                                 (10+5+5)

 

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Loyola College B.Sc. Statistics Nov 2003 Estimation Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2003

ST-5500/STA 505/S 515 – ESTIMATION THEORY

03.11.2003                                                                                                           Max:100 marks

1.00 – 4.00

SECTION-A

Answer ALL questions.                                                                                   (10×2=20 marks)

 

  1. State the problem of point estimation.
  2. Define ‘bias’ of an estimator in estimating a parametric function.
  3. Define a ‘Uniformly Minimum Variance Unbiased Estimator’ (UMVUE).
  4. Explain Cramer-Rao lower bound.
  5. Define completeness and bounded completeness.
  6. Examine if is complete.
  7. Let X1, X2 denote a random sample of size 2 from B(1, q), 0<q<1. Show that X1+3X2 is sufficient of q.
  8. Give an example where MLE is not unique.
  9. Define BLUE
  10. State Gauss – Markoff theorem.

 

SECTION-B

Answer any FIVE questions.                                                                           (5×8=40 marks)

 

  1. Show that the sample variance is a biased estimator of the population variance. Suggest an UBE of .
  2. If Tn is asymptotically unbiased with variance approaching zero as n , show that Tn is consistent.
  3. Show that UMVUE is essentially unique.
  4. Show that the family of Binomial distributions is complete.
  5. State and establish Lehmann – Scheffe theorem.
  6. State and prove Chapman – Robbin’s inequality.
  7. Give an example where MLE is not consistent.
  8. Describe the linear model in the Gauss – Marboff set-up.

 

SECTION-C

Answer any TWO questions.                                                                           (2×20=40 marks)

 

  1. a) Let X1, X2,….., Xn (n > 1) be a random sample of size n from P (q), q > 0. Show that the class of unbiased estimator of q is uncountable.
  2. b) Let X1, X2,….., Xn denote a random sample of size n from a distribution with pdf

 

 

 

f(x) ;q) =

0              ,   other wise.

Show that X(1) is a consistent estimator of q.                                                          (10+10)

 

  1. a) Obtain CRLB for estimating q, in the case of

f  based on random sample of size n.

  1. b) State and establish factorization theorem in the discrete case. (8+12)
  2. a) Explain the method of maximum likelihood.
  3. b) Let X1, X2, …., Xn denote a random sample of size n from N (. Obtain MLE of q = (.                                                                                           (5+15)
  4. a) Let Y = Ab + e be the linear model where E (e) = 0. Show that a necessary and sufficient condition for the linear function  of the parameters to be linearly estimable is that rank (A) = rank .
  5. b) Explain Bayesian estimation procedure with an example. (10+10)

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Loyola College B.Sc. Statistics Nov 2003 Distribution Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – NOVEMBER 2003

ST-4501/STA503 – DISTRIBUTION THEORY

31.10.03                                                                                                          Max:100 marks

9.00-12.00

SECTION-A

Answer ALL the questions.                                                                              (10×2=20 marks)

 

  1. Let f(x,y) = e

0          else where.

Find the marginal p.d.f of X.

  1. Let the joint p.d.f of X1 and X2 be f(x1,y1) = and x2 = 1, 2.

Find P(X2 = 2).

  1. If X ~ B (n, p), show that E
  2. If X1 andX2 are stochastically independent, show that M (t1, t2) = M (t1, 0) M (0, t2), ” t1, t2.
  3. Find the mode of the distribution if X ~ B .
  4. If the random variable X has a Poisson distribution such that P (X = 1) = P (X = 2),

Find p (X = 4).

  1. Let X ~ N (1, 4) and Y ~ N (2, 3). If X and Y are independent, find the distribution of

Z = X -2Y.

  1. Find the mean of the distribution, if X is uniformly distributed over (-a, a).
  2. Find the d.f of exponential distribution.
  3. Define order statistics based on a random sample.

 

SECTION-B

Answer any FIVE questions.                                                                           (5×8=40 marks)

 

  1. Let f(x­1, x2) = 12

0        ;   elsewhere

 

Find P .

  1. The m.g.f of a random variable X is

Show that P (= .

  1. Find the mean and variance of Negative – Binomial distribution.
  2. Show that the conditional mean of Y given X is E (Y÷X=x)for trinomial
  3. Find the m.g.f of Normal distribution.

 

  1. If X has a standard Cauchy distribution, find the distribution of X2. Also identify its

distribution.

  1. Let (X, Y) have a bivariate normal distribution. Show that each of the marginal

distributions is normal.

  1. Let Y1, Y2 , Y3 andY4 denote the order statistics of a random sample of size 4 from a

distribution having a p.d.f.

f(x) =    2x  ;  0 < x < 1

0   ;    elsewhere   .   Find p .

 

 

SECTION-C

Answer any TWO questions.                                                                           (2×20=40 marks)

 

  1. Let x (X1, X2) be a random vector having the joint p.d.f.

 

 

f (x1, x2) =         2  ;   0 < x1 < x2 <1

 

0  ;   elsewhere

(i) Find the correlation between x1 and x2                                                                        (10)

(ii) Find the conditional variance of x1 / x2                                                                      (10)

 

  1. a) Find the mean and variance of hyper – geometric distribution. (10)
  2. b) Let X and Y have a bivarite normal distribution with

 

Determine the following probabilities

  1. i) P (3 < Y <8) ii) P (3 < Y< 8 ½X =7)                                                       (10)
  2. i) Derive the p.d.f of ‘t’ – distribution with ‘n’ d.f (10)
  3. ii) If X1 and X2 are two independent chi-square variate with n1 and n2f. respectively,

show that                                                                          (10)

  1. i) Let Y1, Y2 and Y3 be the order statistics of a random sample of size 3 from a

distribution having p.d.f.

1      ;      0 < x < 1

f (x) =

0     ;       elsewhere.

 

Find the distribution of sample range.                                                             (10)

ii)Derive the p.d.f of  F variate with (n1, n2) d.f.                                                   (10)

 

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Loyola College B.Sc. Statistics Nov 2003 Computational Statistics – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2003

ST-5503/STA508 – COMPUTATIONAL STATISTICS – I

10.11.2003                                                                                                           Max:100 marks

1.00 – 4.00

SECTION-A

Answer ALL questions.                                                                                       

  1. a) In a survey conducted to estimate the cattle population in a district containing 120

villages, a simple random sampling of 20 villages was chosen without replacement.

The cattle population in the sampled villages is given as follows: 150, 96, 87,101, 56,

29, 120, 135, 141, 140,  125, 131, 49, 59, 105, 121, 85, 79, 141, 151.  Obtain an

unbiased estimator of the total cattle population in the district and also estimate its

standard error.                                                                                                                (14)

  1. b) The data given in the table represents the summary of farm wheat census of all the

2010 farms in a region.  The farms were stratified according to farm size in acres into

seven strata.  (i) Calculate the sampling variance of the estimated area under wheat for

the region from a sample of 150 farms case (a) If the farms are selected by the method

of SRS without stratification.  Case (b): The farms are selected by the method of SRS

within each stratum and allocated in proportion to 1) number of farms in each stratum

(Ni).  And 2) product of Ni Si . Also calculate gain in efficiency resulting from case (b)

1 and 2 procedures as compared with unstratified SRS.

Stratum number Farm Size (in acres No.of farms (Ni) Average Area under wheat Standard deviations (sI)
1

2

3

4

5

6

7

 0-40

41-80

81-120

121-160

161-200

201-240

More than 240

 394

461

391

334

169

113

148

 5.4

16.3

24.3

34.5

42.1

50.10

63.8

 8.3

13.3

15.1

19.8

24.5

26.0

35.2

(20)

  1. c) Consider a population of 6-units with values 1,5,8,12,15 and 19. Writ down all possible

samples of size 3 without replacements from the population and verify that the sample

mean is an unbiased estimator of the population mean.  Also i) calculate the sampling

variance and verify that it agrees with the formula of variance of the sample mean.  (ii)

Verify that the sampling variance is less than the variance of the sample mean from

SRSWOR.                                                                                                                                    (14)

  1. d) Five samples were collected using systematic sampling from 4-different pools located in a

region to study the mosquito population, where the mosquito population exhibits a

fairly steady raising trend.  i] Find the average mosquito population in all 4-poolss

ii] Find sample means iii] Compare the precision of systematic sampling, SRSWOR and

stratified sampling.

Pool no Systematic Sample Number

1        2       3        4       5
I

II

III

IV

 2        5       6        8        10

4        8      10      11       13

8       10     11      13       14

16      18     19     20       22

(20)

 

 

 

 

 

  1. a) The following is a sequence of independent observations on the random variable X with the

density function

f(x ; q1, q2)  = .

The observations are 1.57  0.37  0.62  1.04   0.21  1.8   1.03    0.49   0.81  0.56.  Obtain the maximum likelihood estimates of q1 and q2 .                                                                   (15)

  1. b) Obtain a 95% confidence interval for the parameter l of the Poisson distribution based

on the following data:

No. of blood corpuscles :                     0         1         2         3         4          5

No. of cells                  :          142       156      96        27        5          1                     (12)

  1. c) Find a 99% confidence interval for m if the absolute values of the random sample of 8

SAT scores (scholastic Aptitude Test) in mathematics assumed to be N(m, s2) are 624,

532,565,492, 407,  591, 611 and 558.                                                                           (7)

(OR)

  1. d) The following data gives the frequency of accidents in Chennai City during 100 weeks.

No of accidents:          0          1          2          3          4          5

No. of weeks:              25        45        19        5          4          2

If P(X = x) =

x = 0 ,1, 2,….

estimate the parameters by the method of moments.                                                 (12)

  1. e) The following is a sample from a geometric distribution with the parameter p. Derive a

95% confidence interval for p.

x:         0          1          2          3          4          5

f:          143      103      90        42        8          14                                            (5)

  1. f) An absolute sample of 11 mathematical scores are assumed to be N (m, s2). The

observations are 26, 31, 27,28, 29, 28, 20, 29, 24, 31, 23.

Find a 99% confidence interval fo s.                                                                          (7)

  1. a) A vendor of milk products produces and sells low fat dry milk to a company that uses it to

produce baby formula.  In order to determine the fat content of the milk, both the company and

the vendor take a sample from each lot and test it for fat content in percent.  Ten sets of paired

test results are

Lot number Company Test Results (X) Vendor Test Results (Y)
1

2

3

4

5

6

7

8

9

10

 0.50

0.58

0.90

1.17

1.14

1.25

0.75

1.22

0.74

0.80

 0.79

0.71

0.82

0.82

0.73

0.77

0.72

0.79

0.72

0.91

Let D = X – Y and let mD denote the median of the differences.

Test  H0 : mD = 0  against  H1 : mD > 0  using the sign test.    Let a = 0.05 approximately.                                                                                                                              (14)

 

 

 

 

 

 

  1. b) Freshmen in a health dynamics course have their percentage of body fat measured at the

beginning (x) and at the end (y) of the semester.  These measurement are given for 26

students in Table below.  Let m equal the median of the differences, x – y.  Use the

Wilcoxon statistic to test the null hypothesis H0 : m = 0 against the alternative

hypothesis H1 : m > 0 at an approximate a = 0.05 significance level.

 

X Y
35.4

28.8

10.6

16.7

14.6

8.8

17.9

17.8

9.3

23.6

15.6

24.3

23.8

22.4

23.5

24.1

22.5

17.5

16.9

11.7

8.3

7.9

20.7

26.8

20.6

25.1

 33.6

31.9

10.5

15.6

14.0

13.9

8.7

17.6

8.9

23.6

13.7

24.7

25.3

21.0

24.5

21.9

21.7

17.9

14.9

17.5

11.7

10.2

17.7

24.1

20.4

21.9

(20)

(OR)

  1. A certain size bag is designed to hold 25 pounds of potatoes. A former fills such bags in the field.  Assume that the weight X of potatoes in a bag is N (m,9).  We shall test the null hypothesis Ho : m = 25 against the alternative hypothesis H1 : m < 25.  Let X1,X2 , X3, X4 be a random sample of size 4 from this distribution, and let the critical region for this test be defined by , where  is the observed value of .

(a) What is the power function of this test?.  In particular, what is the significance

level of this test?  (b) If the random sample of four bags of potatoes yielded the values

= 21.24,  = 24.81 , = 23.62, = 26.82,would you accept or reject Ho using this test?  (c) What is the p-value associated with the  in part (b) ?                                             (20)

 

  1. (d) Let X equal the yield of alfalfa in tons per acre per year. Assume that X is N (1.5, 0.09).

It is hoped that new fertilizer will increase the average yield.  We shall test the null

hypothesis Ho: m = 1.5 against the alternative hypothesis H1: m > 1.5.  Assume that the

variance continues to equal s2 = 0.09 with the new fertilizer.  Using , the mean of a

random sample of size n, as the test statistic, reject Ho if  ≥ c.  Find n and c so that

the power function bf(m)  =  P ( ≥ c) is such that

a  =  bf (1.5)  =  0.05  and  bf (1.7)  =  0.95.                                                                (14)

 

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Loyola College B.Sc. Statistics Nov 2003 Basic Sampling Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – NOVEMBER 2003

ST  4500 / STA 504 – BASIC SAMPLING THEORY

01.11.2003                                                                                                           Max:100 marks

9.00 – 12.00

SECTION-A

Answer ALL the questions.                                                                              (10×2=20 marks)

 

  1. Explain sampling frame and give two examples.
  2. If there are two unbiased estimators for a parameter then show that one can construct, uncountable number of unbiased estimators.
  3. If T is an estimator for , then show that MSE (T)  =  V(T)  +  [B(T)]2 .
  4. Explain Lottery method for drawing random numbers.
  5. Show that probability of including the ith population unit (i =  1, 2, …, N) when a SRSWOR of size n is drawn from a population containing N units is .
  6. Find the probability of selecting ith population unit in cumulative total method.
  7. Examine whether the estimator is unbiased for the population total under PPSWR.
  8. Show that the sample mean under SRSWOR is more efficient than under SRSWR.
  9. Explain Linear Systematic Sampling Scheme.
  10. When do we use Neyman allocation?

 

SECTION-B

Answer any FIVE questions.                                                                           (5×8=40 marks)

 

  1. Examine the validity of the following statement using a proper illustration :

“property of unbiasedness depends on the sampling scheme under use”.

  1. Prove that, under usual notations, in SRSWOR, P[yi =
  2. What is PPS sampling? Describe cumulative total method?
  3. Deduce expressions for , V() and v () under SRSWR using the expressions for , V() and v () available under PPSWR.
  4. Prove that is an unbiased estimator for population mean under stratified random sampling.  Derive .
  5. Derive the formula for Neyman allocation.
  6. Prove that the sample mean coincide with the population mean in Centered Systematic Sampling, when there is linear trend in the population.
  7. a) List all possible Balanced Systematic Samples if N = 40,  n= 8.
  8. b) List all possible Circular Systematic Samples if N = 7, n = 3.

 

 

 

 

SECTION-C

Answer any TWO questions.                                                                           (2×20=40 marks)

 

  1. a) Describe the principal steps involved in the planning and execution of a survey. (14)
  2. b) Let denote the sample mean of only distinct units under SRSWR. Find E

and V .                                                                                                     (6)

  1. a) A population contains 5 units and it is known that Compare

with .  Find the values of a for which

is less efficient than .                                                 (12)

  1. b) Show that Lahiri’ s method of selection is a PPS selection. (8)
  2. a) Show that an unbiased estimator of V() is

(10)

  1. b) Derive values of nh such that Co + is minimum for a given value of

.                                                                                                                                  (10)

  1. a) Compare and assuming Nh is large for all h = 1,2, …., L.

(12)

  1. b) A sampler has 2 strata. He believes that S1 and S2 can be taken as equal. For a given

cost c = c1 n1 + c2 n2,   show that   =   .                      (8)

 

 

 

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Loyola College B.Sc. Statistics Nov 2003 Applied Stochastic Process Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.Sc., DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2003

ST-5400/STA400 – APPLIED STOCHASTIC PROCESS

12.11.2003                                                                                                           Max:100 marks

1.00 – 4.00

 

SECTION-A

Answer ALL questions.                                                                                   (10×2=20 marks)

 

  1. Define a stochastic process with an example.
  2. Define Bernoulli process with an example.
  3. Give an example of a continuous time, discrete space stochastic process.
  4. When do you say a process has stationary independent increments?
  5. Define a Markov Chain.
  6. Explain a doubly stochastic matrix.
  7. Define the periodicity of a state i of a Markov Chain.
  8. When the state i is said to be recurrent?
  9. Explain the one dimensional random walk with an example.
  10. Define a Martingale.

 

SECTION-B

 

Answer any FIVE  questions.                                                                          (5×8=40 marks)

 

  1. Let {Xn, n=0, 1, 2, …} be a sequence of iid r.v’s with common distribution P(Xo = i) = pI, iÎS, pI>0, . Prove that {Xn, n = 0. 1,2, ….} is a Markov chain.
  2. Prove that the state i of a Markov chain is recurrent iff .
  3. Show that the state ‘0’ of a one-dimensional symmetric random walk is recurrent.
  4. Explain a counting process with an example.
  5. Explain a Poisson process with an example.
  6. If {X1 (t), t Î (o, ¥,} and {X2 (t), t Î (o, ¥,} one two independent Poisson processes with parameters l1 and l2, Show that the distribution of X1 (t) / (X1 (t) + X2(t) = n follows B

.

  1. Explain in detail the generalization of a Poisson process.
  2. Let {Xt, t Î T} be a process with stationary independent increments when T – 0,1,2….. show that the process is a Markov process.

 

 

 

 

 

SECTION-C

Answer any TWO  questions.                                                                          (2×20=40 marks)

 

  1. a) Show that a communication is an equivalence relation.
  2. b) Let{Xn, n ≥ 0} be a Markov Chain with state space S = {0,1,2,3,4} and transition

probability matrix      p=.     Find the equivalence classes.

  1. Show that for a Poisson process with distribution of x(t) is given by P{x(t) = m} =

 

  1. Explain the two dimensional symmetric random walk. Also prove that the state ‘0’ is recurrent.
  2. a) Let Yo­ = 0 andY1, Y2 .. be iid r.r’s with E(Yk) = 0 and E(Yk2) = s2 ” k = 1,2, ….

Let Xn = .  Show that {Xn, n≥ 0 } is a martingale w.r.t {Yn, n ≥ 0}.

  1. b) Write short notes on Renewal process.

 

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Loyola College B.Sc. Statistics Nov 2003 Applied Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034

B.Sc. DEGREE EXAMINATION  –  STATISTICS

Fifth  SEMESTER  – NOVEMBER 2003

ST 5502/STA 507 APPLIED STATISTICS

07.11.2003                                                                                        Max: 100 Marks

1.00 – 4.00

 

SECTION –A                                                         

Answer ALL the questions.  Each carries TWO marks.                   (10 ´ 2 = 20 Marks)

  1. Distinguish between weighted and unweighted Index numbers.
  2. What do you mean by splicing of Index numbers?
  3. How do you eliminate the effect of trend from time series and measure seasonal variations?
  4. Distinguish between seasonal variations and cyclical fluctuations.
  5. Given the data: rxy =0.6 rxz = 0.4, find the value of ryz so that Ryz , the coefficient of multiple correlation of x on y and z, is unity.

 

  1. Explain briefly the significance of the study of multiple correlation in statistical analysis.

 

  1. Define Vital statistics. What is the importance of these statistics?
  2. What are crude and standardised death rates? Why is comparison on the basis of standardised death rates more reliable?

 

  1. Write a short rote on De-Facto and De-Jure enumeration.
  2. Give that the complete expectation of life at ages 35 and 36 for a particular group are respectively 21.39 and 20.91 years and that the number living at age 35 is 41,176, find the number that attains the age 36.

 

SECTION – B

Answer any FIVE questions.  Each carries eight marks.                (5 ´ 8 = 40 Marks)

 

  1. An enquiry into the budget of the middle class families in a certain city in

India gave the following information.

 

Expenses on Food Fuel Clothing  Rent Misc.
40% 10% 18% 20% 12%
Prices (2001) (in Rs.)

 

 2250 600 1000 1500 700
Price (2003) 2500 900 1100 1600 800

 

What changes in cost of living figures of 2003 as compared with that

of 2001 are seen?

 

 

 

 

 

 

  1. Obtain the trend of bank clearance by the method of moving averages by

assuming a 5 -yearly cycle:

 

Year 1991 92 93 94 95 96
Bank clearance

(in crores)

 53 79 76 66 69 94
Year 1997 98 99 2000 01 02
Bank clearance

(in crores

 105 87 79 104 97 92

 

Also, draw original and trend lines on the graph and compare them.

 

  1. Production of a certain commodity is given below:

 

Year 1999 2000 2001 2002 2003
Production (in lakh tons) 7 9 10 7 5

 

Fit a parabolic curve of second degree to the production.

Estimate the production for 2004.

 

  1. The following means, standard deviations and correlations are found for

X1= seed hay crop in kgs. per acre, X2 = spring rainfall in inches,

X3 = Accumulated temperature above 42°F.

 

r12  = 0.8

r13  = – 0.4

r23   = – 0.56

 

Number of years of data = 25

Find the regression equation for hay crop on spring rainfall

and accumulated temperature.

 

  1. a) It is possible to get: r12 = 0.06, r23 = 0.8 and r13 =  -5 from a set of

experimental data?                                                                                     (3)

  1. If all the correlation coefficients of zero order on a set of p variates are

equal to  then show that every partial correlation coefficient of the sth

order is                                                                                             (5)

 

  1. a) Given the age returns for the two ages x = 9 years and x +1 = 10 years with

a few life-table values as l9 = 75,824, l10 = 75,362, d10 = 418 and

T10 = 49,53,195. Give the complete life-table for the ages of persons.       (5)

  1. b) In what way, does the construction   of an abridged life-table differ

from a complete life-table?                                                                          (3)

 

 

 

 

 

 

  1. What are the current research developments and landmarks in

agricultural statistics?

 

  1. Explain in detail the different methods of measuring National Income.

 

 

SECTION – C         

Answer any TWO questions.  Each carries twenty marks.      (2 ´ 20 = 40 Marks)

 

  1. a) Using the following data, construct Fisher’s Ideal Index number

and show how it satisfies  Time Reversal and Factor Reversal tests:

 

 

Commodity

 Base year Current year
Price Quantity Price Quantity
A 6 50 10 56
B 2 100 2 120
C 4 60 6 60
D 10 30 12 24
E 8 40 12 36

(12)

  1. What are Index numbers? How are they constructed? Discuss the

applications of Index numbers.                                                                 (8)

 

  1. Calculate the seasonal variation indices by the method of link relatives for

the following figures.

 

Year Quarterly cement  production in 1000 tons
Q1 Q2 Q3 Q4
1998 45 54 72 60
1999 48 56 63 56
2000 49 63 70 65
2001 52 65 75 73.5
2002 63 70 84 66
  1. For the following set of data:
  2. Calculate the multiple correlation coefficientand the partial correlation coefficient .
  3. Test the significance of both population multiple correlation coefficient and partial population correlation coefficient at 5% level of significance.

 

Y 10 17 18 26 35 8
X1 8 21 14 17 36 9
X2 4 9 11 20 13 28

 

(10+10)

 

 

 

 

 

 

 

 

  1. The population and its distribution by sex and number of births in a

town in 2001 and survival rates are given in the table below.

 

Age group Males Females Male births Females births Survival rate
15  -19 6145 5687 65 60 0.91
20 – 24 5214 5324 144 132 0.90
25 – 29 4655 4720 135 127 0.84
30 – 34 3910 3933 82 81 0.87
35 – 39 3600 2670 62 56 0.85
40 – 44 3290 3015 12 15 0.83
45 – 49 2793 2601 3 3 0.82

 

 

From the above data, calculate

 

  1. i) Crude Birth Rate
  2. ii) General fertility  rate

iii)   Age specific fertility  rate

  1. iv) Total fertility rate
  2. v) Gross reproduction rate and
  3. vi) Net reproduction rate; assuming no mortality.           (2 +2 + 4 + 2 + 5 +5)

 

 

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Loyola College B.Sc. Plant Biology and Biotechnology April 2003 Animal Diversity Question Paper PDF Download

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LOYOLA  COLLEGE (AUTONOMOUS), CHENNAI-600 034.

B.Sc. DEGREE  EXAMINATION  – PLANT BIOLOGY AND BIOTECHNOLOGY

THIRD SEMESTER  – APRIL 2003

ZO 3100/ZOO 100 – ANIMAL DIVERSITY

07.04.2003

9.00 -12.00                                                                                          Max : 100 Marks

 

 

PART – A               (10 ´ 2 = 20 Marks)

I  Answer ALL the questions.

 

  1. What is rosetellum?
  2. Write the dental formula of man and rabbit.
  3. What is alternation of generation? Give an example.
  4. What are extra embryonic membranes?
  5. Mention the types of chordate eggs.
  6. Comment on Pecten.
  7. Write a note on bipinnaria larva.
  8. What is synsacrum?
  9. What is greengtand?
  10. write about the structure and function of radula.

 

 

              PART – B                    (4 ´ 10 = 40 Marks)

 

II   Answer any FOUR of the following

 

  1. Describe the reproductive system in leech.
  2. Explain the lifecycle of Ascaris.
  3. Describe the reproductive system in rat.
  4. Explain the water vascular system in starfish.
  5. Explain the nervous system of Pila
  6. What is amoebic dysentry? How is it prevented and controlled?

 

 

PART – C                                      (2 ´ 20 = 40 Marks)

 

III   Answer any TWO of the following.

 

  1. DescribeGive in detail the lifecycle of Taenia solium
  2. Write an essay on migration of birds and flight adaptations.
  3. Write an essay on the appendages of prawn.
  4. Describe in detail the lifecycle of plasmodium vivax.

 

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Loyola College B.Sc. Plant Biology and Biotechnology April 2003 Plant Diversity-I Question Paper PDF Download

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Loyola college (autonomous), chennai – 600 034

b.sc. degree examination – plant biology and bitechnology

first semester – april 2003

PB  1500/  pbB  500  plant  diVeRsitY -i

05.04.2003                                                                             Max.:   100 Marks

1.00 – 4.00

 

PART – A                                        (5 ´ 1 = 5 Marks)

I Choose the correct answer:

  1. The Principal pigment of cyanophyta is:
  2. a) Phycoerythrin b) Phycocyanin   c)  Fucoxanthin         d) Chlorophyll
  3. When the ascocarp is a completely closed structure, it is called
  4. a) Perithecuium b) apothecium   c) Parathecium           d) Cleistothecium
  5. Which of the following is involved with spore dispersal in mosses.
  6. a) Operculum b)  apophysis      c)  elaters                   d) seta
  7. The stem and petiole of pteridophytes are covered with numerous

brownish scale like structures called

  1. a) Root hairs b) Hairs                c) Ramenta            d) scales
  2. Ovules are not found enclosed in ovary of
  3. a) Algae and fungi   b) Bryophyta         c) Gymnosperms        d) Angiosperms

II State true or false                                                                            (5 ´ 1 = 5 Marks)

  1. Free floating, microscopic algae are referred as phytoplanktons.
  2. Fungi are autotrophic in their mode of nutrition.
  3. In bryophytes, the sporophyte is independent of the gametophyte.
  4. Lycopodium species are commonly known as horse tail.
  5. Vegetative reproduction in Cycas is by means of bulbils.

III   Complete the following                                                           (5 ´ 1 = 5 Marks)

  1. In Rhodophyta, flagella are completely _____________.
  2. The characteristic spores produced by basidiomycetes are ____________.
  3. In primitive Pteridophytes, the  ___________has elongated neck with several

neck canal cells.

 

  1. In ______________, the sori are formed in a sporocarp.
  2. The type of embryo development in Cycas is __________.

IV   Answer the following in 2 or 3 sentences                (5 ´ 1 = 5 Marks)

  1. Distinguish between colonial and filamentous algae.
  2. Write down any two general features of bryophytes.
  3. Define heterospory.

 

 

 

 

  1. Write about the structure of protocorm.
  2. Write notes on ovuliferous scale of Pinus.

PART – B                  (5 ´ 8  = 40 Marks)

Answer any FIVE questions, choosing not more than three from each section. Each  within 350 words.

                                                            Section – I 

  1. Bringout the salient features of phaeophyta and chlorophyta in the form

of tabular column

  1. Explain any two types of life cycle patterns seen in fungi.
  2. Explain the structure of mature sporophyte of  Anthoceros .
  3. Draw diagrams only:  a) Cyanophycean cell   b) Basidocarp of Polyporus
  4. c) Moss plant body.

SECTION – II

  1. List the characteristics of Filicophyta.
  2. Distinguish between Eusporangium and Leptosporangium.
  3. Draw a well labelled diagram of Cycas ovule and discuss its structure.
  4. Describe the internal structure of Pinus

PART – C                             (2 ´ 20 = 40 Marks)

Answer the following, Each with in 1500 words. Draw necessary diagrams. Necessary diagrams.

  1. a) Explain the following.
  2. i) Habitats of algae ii) ascocarps in fungi   iii) sex organs of bryophytes.

 

  1. b) Write short notes on
  2. pigments and cell wall composition in any five algal divisions
  3. ii) asexual spores in fungi iii) adaptations in bryophytes

 

  1. a) Explain the following
  2. types of protosteles in pteridophytes
  3. Sexual reproduction in pteridophytes
  • Altered and unaltered fossils

(OR)

  1. Write notes on
  2. External features of  Gnetum
  3. Reproductive features of Gymnosperms

iii)         Economic importance of  Gymnosperms.

 

 

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Loyola College B.Sc. Plant Biology and Biotechnology April 2003 Agricultural Entomology Question Paper PDF Download

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LOYOLA  COLLEGE (AUTONOMOUS), CHENNAI-600 034.

B.Sc. DEGREE  EXAMINATION  – PLANT BIOLOGY AND BIOTECHNOLOGY

fourth SEMESTER  – APRIL 2003

ZO 4200/ZOO 200 – agricultural entomology             

24.04.2003

9.00 -12.00                                                                                         Max : 100 Marks

 

 

PART – A                           (10 ´ 2 = 20 Marks)

I      Answer ALL the questions.

 

  1. Differenciate Holometabola and Hemimetabola.
  2. What is a termatorium?
  3. Name four pests of sugarcane (with scientific names)
  4. What are repellants? Give two examples.
  5. What is meant by ‘Biological control of insect pests’? Give 2 Egs.
  6. List the different types of mouth parts in insects.
  7. What is royal jelly?
  8. What are fumigants? Give two examples.
  9. What is card labelling and pinning technique?
  10. Comment on light traps.

 

 

PART – B                            (4 ´ 10 = 40 Marks)

II     Answer any FOUR of the following.

 

  1. Give the outline classification of insects.
  2. Describe the lifecycle of Helicoverpa armigera and add its control measures.
  3. Write a note on pests of groundnut and their prevention.
  4. Give an account on pests of coconut and their control measures.
  5. Give an account of cotton pests of India.
  6. Describe briefly on locusts and their control.

 

 

Part – c                           (2 ´ 20 = 40 Marks)

III   Answer any TWO of the following  

 

  1. Write an essay on ‘Integrated pest Management’.
  2. a) Give an account on pests of paddy and their control measures
  3. Discuss briefly on the stored pests and their prevention methods.
  4. Explain the types of insect pests and the causes for insects assuming pest status.
  5. Write an essay on termites and their control measures.

 

 

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Loyola College B.Sc. Plant Biology and Biotechnology Nov 2003 Animal Diversity Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034

B.Sc. DEGREE EXAMINATION – plant biology and biotechnology

third SEMESTER  – NOVEMBER 2003

                   ZO  3100/ ZOO  100  animal diversity

06.11.2003                                                                                        Max: 100 Marks

9.00  – 12.00

 

PART – A                            

I   Answer ALL the following questions                                  (10 ´ 2 = 20 Marks)

 

  1. Write the dental formula of man and rabbit.
  2. What is synsacrum?
  3. What is scolex?
  4. Comment on Pecten.
  5. Give the structure and function of plume feathers.
  6. What is measly pork?
  7. Mention the types of chordate eggs.
  8. What is a trophozoite?
  9. Comment on Tornaria larva.
  10. What are extra embryonic membranes?

PART – B

 

II  Answer any FOUR of the following                                   (4 ´ 10 = 40 Marks)

 

  1. What is amoebic dysentery? How is it prevented and controlled?
  2. Describe the reproductive system of leech.
  3. Describe the arterial system of rat.
  4. Explain the vascular system in starfish.
  5. Describe the life cycle of Ascaris.
  6. Explain the cranial nerves of frog.

 

PART – C                                           

III  Answer  any TWO of the following                                   (2 ´ 20 = 40 Marks)

  1. Illustrate the appendages of prawn.
  2. Explain in detail the lifecycle of Taenia solium.
  3. Explain the different types of respiration in frog.
  4. Describe the lifecycle of plasmodium vivax.

 

 

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Loyola College B.Sc. Physics April 2003 Mathematics For Physics Question Paper PDF Download

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LOYOLA COLLEGE (Autonomous), chennai – 600 034

B.Sc.  degree examination – physics

third semester -april 2003

 Mt  3100/ MAT 100 mathematics for physics

28.04.2003                                                                                     Max.: 100 Marks

9.00 – 12.00

 

PART – A                                       (10 ´ 2 = 20 Marks)

  1. Define Laplace transform of f(t) and prove that L(e–at) = .
  2. Find .
  3. Prove that the mean of the Poisson distribution Pr =, r = 0, 1, 2, 3 ….. is equal to m.
  4. Mention any two significance of the normal distribution.
  5. Find the .
  6. Find L (1+ t)2 .
  7. Find L-1.
  8. Write down the real part of sin .
  9. Prove that in the R.H. xy = c2, the subnormal varies as the cube of the ordinate.
  10. If y = log (ax +b), find y

 

PART – B                                          (5 ´ 8 = 40 Marks)

Answer any FIVE questions.  Each question carries EIGHT marks

  1. (a) Find L-1

           

  • Find L .
  1. Find L  .
  2. Define orthoganal matrix and prove that the matrix is orthoganal.
  3. Verify cayley-Hamilton theorem and hence find the inverse of
  4. (i)  Prove that
  • Find the sum to infinity of series

 

 

 

 

 

  1. (i) Find q approximately to the nearest minute if cos q =

(ii)   Determine a, b, c such that     .

 

  1. If cos (x + iy) = cos q + i sinq,  Show that cos 2x + cosh 2y =2.

 

  1. What is the rank of .

 

PART – C                                      (2 ´ 20 = 40 Marks)

Answer any TWO questions. Each question carries twenty marks.

 

  1. (a) If y = .

 

  • Find the angle of intersection of the cardioids r = a(1+cosq) and r = b(1-cosq).
  1. (a) Certain mass -produced articles of which 0.5 percent are defective, are packed

in  cartons each containing 130 article.  What Proportion of cartons are free

from defective articles, and what proportion contain 2 or more defectives

(given e-2.2 = 0.6065)

 

  • Of a large group of men 5 percent are under 60 inches in height and 40 percent are between 60 and 65 inches. Assuming a normal distribution find the mean height and standard deviation.

 

  1. (a) Find the sum to infinity of the series

 

  • From a solid sphere, matter is scooped out so as to form a conical cup, with vertex of the cup on the surface of the sphere, Find when the volume of the cup is maximum.

 

  1. a) Prove that sin5q =
  2. b) Prove that sin4q cos2q =

 

 

 

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Loyola College B.Sc. Physics Nov 2003 Physics For Chemistry Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

FOURTH SEMESTER – NOVEMBER 2003

PH 4201 / PHY 201 PHYSICS FOR CHEMISTRY

 

08.11.2003                                                                                                                                     100 Marks

1.00 – 4.00

 

SECTION – A

 

Answer ALL questions                                                                                          (2 x 10 = 20 marks)

 

  1. What is a polarimeter?
  2. What is diffraction?
  3. Give expressions for the combined capactiance of three capacitors connected in (I) series (ii) parallel.
  4. State Lenz’s law.
  5. Define half-life period of a radioactivity substance
  6. State Pauli’s exclusion principle.
  7. List any four characteristics of an operational amplifier.
  8. Sketch an half-adder.
  9. What is Crystal lattice?
  10. Define packing factor.

 

SECTION – B

 

Answer any FOUR questions                                                                    (7.5 x 4 = 30 marks)

 

  1. Discuss in detail polarisation by reflection.
  2. Derive an expression for the energy stored by a charged capacitor.
  3. Explain the binding energy of a nucleus and derive an expression for the same.
  4. With a need sketch derive an expression for the gain of an inverting amplifier using an operational amplifiers.
  5. Tabulate the main characteristics of the seven crystal systems.

 

SECTION – C

 

Answer any FOUR questions:                                                                 (12.5 x 4 = 50 marks)

 

  1. Explain how a plane transmission grating can be used to determine the wave length of a spectral line.
  2. Explain with necessary theory how a Carey-Foster bridge may be used to compare two nearly equal resistances.
  3. State Bohr’s postulates of hydrogen atom model. Obtain expressions for the radius and energy of the nth
  4. Realise operational amplifier as
  • adder (b) differentiator (c) integrator
  1. How are lattice parameter of a crystal found using Bragg’s x-ray spectrometer?

 

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Loyola College B.Sc. Physics Nov 2003 Materials Science Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

FIFTH SEMESTER – NOVEMBER 2003

PH 5402 / PHY 402 – MATERIALS SCIENCE

 

12.11.2003                                                                                           Max.   : 100 Marks

1.00 – 4.00

 

PART – A

 

Answer all the questions                                                                            (10 x 2 = 20 marks)

 

  1. How will you classify the engineering materials on the basis of the major areas of applications?
  2. Write a note on the structure-property relationships in materials.
  3. Discuss the steps involved in the formation of Burger’s circuit for dislocation.
  4. Determine the Miller indices of a plane that makes intercepts of 4x, y and 2z.
  5. Give the formula for measuring the Young’s modulus of composite materials.
  6. Explain the phenomenon of “work hardening” of engineering materials.
  7. What is the principle of the NDT method based on photoelastic phenomenon.
  8. How does the intrinsic break down of a dielectric material take place?
  9. Calculate the relative dielectric constant of a barium titanate crystal, which, when inserted in

a parallel plate condenser of area 8 mm X 8 mm and distance of separation of 1. 8 mm gives a capacitance of 0.05 mF

 

  1. List the advantages of scanning electron microscopie (SEM).

 

PART – B

 

Answer any FOUR questions                                                                              (4 x 7.5 = 30)

 

  1. Discuss, how the physical properties of materials are influenced by the variation in bonding character.
  2. What is meant by a symmetry operation? Explain the different types of symmetry elements of a crystalline solid.
  3. What are true stress and true strain? Using the tensile stress-strain curve for a ductile material, obtain the power relationship connecting s and e.
  4. Explain (I) electrical resistance (ii) tribolectric effect and (iii) thermoelectric effect techniques adopted for NDT.
  5. Give the theory of ferroelectrics as applied to Barium Titanate. Mention the applications of ferroelectric materials.

 

 

-2-

PART – C

 

Answer any FOUR questions                                                                           (4 x 12.5 = 50)

 

  1. What is meant by polarization?

Discuss the various polarization processes with necessary diagrams and hence obtain the expression for the total polarization of a material.

 

  1. Draw a schematic diagram of an Electron Microscope and explain its working.

 

  1. a) Discuss the essential characteristics of covalent bonding with relevant examples.

(5 marks)

  1. Explain the necessary steps involved in the formation of ionic bond and obtain the expression for the potential energy of the system of bond forming atoms.       (7.5 marks)

 

  1. a) State and explain Bragg’s low of x-ray diffraction                                      (5 marks)

 

  1. Describe with a neat sketch, the powder XRD method of determining crystal structure.

 

  1. Discuss the atomic model of elastic behavior with necessary figure and derive the relations connecting y,

 

 

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Loyola College B.Sc. Physics Nov 2003 Geo Physics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

V SEMESTER – NOVEMBER 2003

PH 5400 / PHY 400 – GEO PHYSICS

 

07. 11. 03                                                                                                 Max.  : 100 Marks

1.00 – 4.00.

 

PART–A

 

Answer All questions                                                                               (10 x 2 = 20 marks)

 

  1. What is a P – wave? What is it’s velocity?
  2. State the generalised form of Snell’s law, with a ray diagram.
  3. Distinguish between surface waves and body waves with respect to their intensity variation with distances

 

  1. What are the quantities that can be measured using a Seismometer?
  2. Bring out the difference between focus and epicentre of an earth-
  3. Write down the Laplace’s and the Poisson’s equation obeyed by the gravitational potential.

 

  1. What is the cause of the main (magnetic) field of the earth according to the dynamo theory?

 

  1. Explain briefly, the Gauss method of determining the earth’s magnetic field
  2. Give the decay schemes of the radio nuclide K40.
  3. List the two possible sources of heat within the Earth.

 

PART–B

 

Answer any FOUR questions                                                               (4 x 7 ½ = 30 marks)

 

  1. Calculate the bulk modulus and the shear modulus of a material having the following properties.

Density  =  4000 kg / m3;  dilatational  velocity (a) = 10 km / s and        shear velocity (b) = 6 km / s.

 

  1. Outline the principle and the construction of the strain seismograph with a simple
  2. a) State the relation between the energy released and the magnitude of an earth-quake
  3. b) Compare the energies released in earth quakes of magnitudes M = 6 and M = 2.

-2-

 

  1. Explain the dynamo theory of earth’s magnetism with the help of the Faraday disc generator.

 

  1. Obtain an expression for the variation of temperature with depth below the surface of the earth.
PART–C

 

 

Answer any FOUR questions                                                             (4 x 12 ½ = 50 marks)

 

  1. a) Find an expression for the time of travel of a seismic wave due to refraction in the

outer layers of earth                                                                                   (6 ½ mark)

 

  1. b) Derive an expression for the gradient of density in terms of velocities of body

waves                                                                                                             (6 mark)

 

  1. Discuss the theory of a horizontal seismograph with a neat diagram and explain all

possible cases.

  1. Explain the working of (I) Hammond and Faller method (of measuring gravity) and
  2. ii) Worden gravimeter, with neat diagrams                                  (6 + 6 ½)

 

  1. Explain the theory of (I) Saturation magnetometer and (ii) alkali vapor

magnetometer.                                                                                                   (5 + 7 ½)

  1. Give the theory of radioactive dating of rocks and minerals using (i) the decay

scheme of Rb87 and (ii) the decay scheme of K40 .

 

 

 

 

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Loyola College B.Sc. Physics Nov 2003 Atomic & Nuclear Physics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

V SEMESTER – NOVEMBER 2003

PH 5500 / PHY 507 — atomic & nuclear physics

 

03-11-2003                                                                                                                                             100 Marks

1.00 – 4.00

 

PART – A

Answer All questions                                                                         (10 x 2 = 20 marks)

 

  1. State and explain Pauli’s exclusion Principle.
  2. What is normal Zeeman effect?
  3. An x-ray machine Produces 0.1Å x – rays. What accelerating voltage does it employ?
  4. What is Auger effect?
  5. Determine the ratio of the radii of the nuclei 13Al27 and 52Te125
  6. State Geiger-Nuttall Law.
  7. Mention the properties of the nuclear force.
  8. Explain latitude effects in Cosmic rays.
  9. What are slow neutrons and fast neutrons?
  10. Distinguish between Fluorescence and Phosphorescence.

 

PART – B

 

Answer any FOUR only                                                                (4 x 7 ½  = 30 marks)

 

  1. Explain Frank and Hertz method of determining critical potentials.

 

  1. a) Explain the origin of characteristic x-rays.            (3 ½  mark)

 

  1. b) A ray of ultraviolet light of wavelength 3000 Å falling on the surface of a material

whose work function is 2.28 eV ejects an electron.

What will be the velocity of the emitted electron?                             (4 mark)

 

  1. a) Show that the energy equivalent of 1 a m u is 931 MeV           (2 mark)

 

  1. What is meant by binding energy of the nucleus. Find the binding energy and binding energy per nucleon of  of mass 30.973763 amu

MH = 1.007825 amu and MN = 1.008665 amu.                            (5 ½ mark)

 

  1. What are elementary particles? How are they classified on the basis of their masses and interactions?

 

  1. a) Distinguish between nuclear fission and fusion           (2 mark)

 

  1. b) Explain with a neat diagram, the Bohr’s theory of Compound nucleus.

(5 ½ mark)

 

-2-

 

PART – C

 

Answer any FOUR only                                                               (4 x 12 ½ = 50 marks)

 

 

 

  1. a) Describe Thomson’s parobola method to measure the specific charge of positive ions.                                                      (8 ½ marks)

 

  1. In a Bainbridge mass spectrograph, singly ionised atoms of Ne20 pass into the deflection chamber with a velocity of 105 m/s. If  they are deflected by a magnetic field of flux density 0.08T, calculate the radius of their path and where Ne22 ions would fall if they had the same initial velocity.            (4 mark)

 

  1. a) Explain compton scattering and derive an expression for the wavelength of the Scattered beam                                                                            (8 ½ mark)
  2. b) Estimate the value of compton wavelengths when the scattered angles are (i) and (ii)                                                                                                   (4 mark)

 

  1. Give the origin of b – ray line and continuous spectrum. Outline the theory of b – disintegration.

 

  1. Describe the ‘liquid drop model’ of the nucleus. How can the semi – empirical mass formula can be derived from it? Mention the uses of this model.

 

  1. a) Derive the four factor formula for a thermal nuclear reactor.            ( 8 ½ mark)

 

  1. b) Calculate the power output of a nuclear reactor which consumes 10 kg of U – 235 per day, given that the average energy released per fission is 200 MeV.

(4 mark)

 

 

 

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Loyola College B.Sc. Mathematics April 2003 Mathematical Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FourTH SEMESTER – APRIL 2003

ST 4201 / sTA 201  –  MATHEMATICAL STATISTICS

 

28.04.2003

9.00 – 12.00                                                                                                     Max : 100 Marks

                                                                PART – A                                       (10´ 2=20 marks)

      Answer ALL the questions.

 

  1. Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight?
  2. The probability that a customer will get a plumbing contract is and the probability that he will get an electric contract is 4/9. If the probability of getting at least one is 4/5,determine the probability that he will get both.
  3. Consider 2 events A and B such that and . Verify whether the given statement is true (or) false. .
  4. Define i)  independent events and ii)  mutually exclusive events.
  5. State any four properties of a distribution function.
  6. The random variable X has the following probability function
X = x 0 1 2 3 4 5 6 7
P (X=x) 0 k 2k 2k 3k k2 2k2 7k2+k

Find k.

 

  1. Let f (x) =

0    ;   else where

Find E(X).

  1. Let X ~ B (2, p) and Y~B (4, p). If P , find P.
  2. Define consistent estimator.
  3. State Neyman – Pearson lemma.

 

 

                                                                PART – B                                         (5´ 8=40 marks)

      Answer any FIVE questions.

 

  1. A candidate is selected for three posts. For the first post three are three candidates, for the

second there are 4 and for the third there are 2. What are the chances of his getting

  1. i) at least one post and  ii)  exactly one post?
  2. Three boxes contain 1 white, 2 red, 3 green ; 2 white, 3 red, 1 green and 3 white, 1 red, 2 green balls. A box is chosen at random and from it 2 balls are drawn at random. The balls so drawn happen to be white and red. What is the probability that they have come from the second box?
  3. Find the conditional probability of getting five heads given that there are at least four heads, if a fair coin is tossed at random five independent times.
  4. Derive the mean and variance of hyper-geometric distribution.
  5. Let X be a random variable having the p.d.f

 

f(x) =

Find the m.g.f. of X and hence obtain the mean and variance of X.

  1. If X is B(n,p), show that E= p and E.
  2. Let X be  N(m,s2).  i)  Find b so that
  3. ii) If P (X < 89) =0.90 and P(X < 94) =0.95, find m and s2.
  4. If X and Y are independent gamma variates with parameters m and n respectively,

Show that  ~ .

 

 

 

                                                               PART – C                                         (2´20=40 marks)

Answer any TWO questions

  1. If the random variables x1 and x2 have the joint  p.d.f

f  (x1 ,x2) =

i ) find the conditional mean of X1 given  X2 and  ii)  the  correlation coefficient

between  X1 and X2.

  1. a)  Find all the odd and even order  moments of Normal distribution.
  2. Let (X,Y) have a bivariate normal distribution. Show that each marginal distribution

in normal.

  1. a) Derive the p.d.f of F- variate with (n1,n2) d.f.
  2. Find the g.f of exponential distribution.
  • a) Let X1, X2, …. Xn  be a  random sample of size n from N (q,1) . Show that the sample

mean is an unbiased estimator of the parameter q.

  1. Write a short note on:
  2. i) null hypothesis ii) type I and type II errors iii)    standard error
  3. iv) one -sided and two -sided tests.

 

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Loyola College B.Sc. Mathematics April 2003 Algebra Analytical Geometry, Calculus-II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.

B.Sc. DEGREE EXAMINATION – MATHEMATICS

SECOND SEMESTER – APRIL 2003

 

MT 2500 / MAT 501  –  ALGEBRA ANALYTICAL GEOMETRY, cALCULUS – II

 

23.04.2003

9.00 – 12.00                                                                                                    Max : 100 Marks

 

                                                                PART – A                                       (10´ 2=20 marks)

      Answer ALL questions. Each question carries TWO marks.

 

  1. Prove that
  2. Evaluate
  3. State cauchy’s root test for convergence of a given series.
  4. Show that
  5. If Y= show that
  6. Solve
  7. Solve where
  8. Evaluate
  9. Find the equation to the plane through the point (3,4,5) and parallel to the plane
  10. Find the equation of the sphere with centre (-1, 2, -3) and radius 3 units.

 

 

 

                                                                PART – B                                         (5´ 8=40 marks)

      Answer any FIVE questions. Each question carries EIGHT marks.

 

  1. If n =   prove that   .
  2. Evaluate .
  3. Sum the series .
  4. Sum the series .
  5. Solve .
  6. Solve .
  7. Test for convergence of the series .
  8. Find the perpendicular distance from P (3, 9, -1) to the line .

 

                                                               PART – C                                         (2´20=40 marks)

Answer any TWO questions. Each question carries TWENTY marks.

 

  1. a) Evaluate I =                                                                                           (10)
  2. b) Find the reduction formulae for In =                                                  (10)
  3. a) Solve by variation of parameter method.                                         (10)
  4. b) Solve (10)
  5. a) Sum the series (10)

 

  1. b) Sum the series (10)
  2. a) Show that the series  is convergent when k is greater than unity and

divergent when k is equal to or less than unity.                                                           (10)

  1. Find the equation of the sphere which passes through the circle

and touch the plane            (10)

 

 

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Loyola College B.Sc. Mathematics Nov 2003 General Physics II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHS / CHEMISTRY

II SEMESTER – NOVEMBER 2003

PH 203 / 205 / 403 – GENERAL PHYSICS  II

 

08.11.2003                                                                                                                              100 Marks

 1.00 – 4.00

 

PART – A

 

Answer All questions                                                                         (10 x 2 = 20 marks)

 

  1. What is a Zone plate?
  2. Give the geometry of a Nicol prism
  3. Define specific rotatory power of an optically active substance
  4. State Gauss’s law in differential form
  5. Three capacitors of capacitance values 1 mF, 2 mF and 3 mF are arranged in series. What is the effective capacitance?
  6. Define the ampere, the unit of current.
  7. Distinguish between amplitude and frequency modulations.
  8. What are the charge carriers in semiconductor devices?
  9. Give the truth table of the NAND gate
  10. List any four properties of X-rays.

 

PART – B

Answer any FOUR questions                                                        (4 x 7 ½  = 30 marks)

 

  1. Prove the rectilinear propagation of light by Fresnel’s theory of half-period zones
  2. Derive an expression for the loss of energy on sharing of charges between two capacitors.
  3. Find the magnetic field at any point due to an infinitely long wire carrying current.
  4. State and prove De Morgan’s theorems.
  5. Discuss the theory and production of X-rays with a neat diagram.

 

PART – C

Answer any FOUR questions                                                      (4 x 12 ½ = 50 marks)

 

  1. Explain the theory of production and of analysis of different types of polarized beams.
  2. Using Gauss’s law, determine the intensity of electric field due to (i) a charged sphere and (ii) a line charge.
  3. Derive an expression for the intensity of magnetic field along the axis of a current carrying circular coil.
  4. Explain the working of a two-stage RC coupled amplifier with a circuit diagram. Also explain the frequency response of the amplifiers.
  5. Discuss with necessary theory the working of Bragg spectrometer.

 

 

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