BE/B.

tech-DEGREE EXAMINATIONS, APRL/MAY 2023

Fourth Semester
1901MA401/ENGINEERING MATHEMATIC-III
II-CIVIL (Regulation 2019)

UNIT-I

Q. No PART-A [CO#, BTL]

1. Write Dirichlet condition. [CO1, K2]
2. Define Fourier series. [CO1, K2]
3. Write the formula for sine and cosine series. [CO1, K2]
4. Write the half range cosine series in (0,l). [CO1, K2]
5. Define periodic function. [CO1, K2]
6. Find bn for f ( x )=x ∈(0 ,l) by using half range sine series. [CO1, K2]
7. Find b n for f ( x )=1−x∈ ( 0 , 1 ) . By using half range sine series. [CO1, K2]
8. Find a n for f ( x )=x ∈ ( 0 , 1 ) . By using half range cosine series. [CO1, K2]
9. Find a 0 for the Fourier series of the function f ( x )=x 2in 0< x <2 π [CO1, K2]
10. Find a 0 for the Fourier series of the function f ( x )=k , 0≤ x ≤ 2 π . [CO1, K2]

PART- B [CO#, BTL]

11. Find the Fourier series expansion of period 2 l for the function of f ( x )=(l−x )2 in the range [CO1, K2]
(0 , 2 l).
12. Find the half sine series of f ( x )=x ∈(0 ,l) [CO1, K2]

13.
{1−x 1 ≤ x ≤2
Find the half sine series for f ( x )=
x−1 0 ≤ x ≤ 1 [CO1, K2]

14. Find the half sine series for f ( x )=x 2 ∈(0 , π ) [CO1, K2]
15. Find the half Fourier sine series of f ( x )=1−x∈(0 , l) [CO1, K2]
16. Find half the cosine series for f ( x )=x ∈(0 ,1) [CO1, K2]

UNIT-II

Q. No PART-A [CO#, BTL]

1. Define critical region. [CO2, K2]
2. Define hypothesis. What are the two types of hypothesis. [CO2, K2]
3. Write level of significance. [CO2, K2]
4. Define significance value. [CO2, K2]
5. Write the formula for Z-test of difference proportions. [CO2, K2]
6. Define populations [CO2, K2]
7. Write some applications of ℵ 2 test. [CO2, K2]
8. Calculate expected frequency for 2x2 contingency table. [CO2, K2]
9. Write type I and type II error. [CO2, K2]
10. Define Test of significance. [CO2, K2]
 PART- B [CO#, BTL]
11 The mean of two samples of size 1000 &2000 are 170cm and 169cm can the sample one is more [CO2, K2]
efficient than sample two if there are drawn from the same population with standard deviation
10cm at 1% Los.(tabulated value = 2.326)

12 1000 students at college level were graded according to their IQ and their economic [CO2, K2]
conditions.What conclusion can you draw from the following data. .(tabulated value = 3.841)
Economic condition IQ level
Rich High Low
Poor 460 140
240 160
13 The average marks scored by 32 boys in 72 with a SD of 8 While that for 36 girls is 70 with a [CO2, K2]
SDof 6. Test at 1% level of significance whether the boys perform better than girls?
14 A group of 10 people on diet A and another group of 8 people on diet B recorded that the [CO2, K2]
following increases in weight.Find if the variance are significantly different.(tabulated value =
3.29)
Diet A 5 6 8 1 12 4 3 9 6 10
Diet B 2 3 6 8 10 11 2 8 - -
15 From the following information state whether the condition of the child is associated with the [CO2, K2]
condition of the house.
Condition of Condition of house Total
child clean dirty
clean 69 51 120
Fairly clean 81 20 101
dirty 35 44 79
total 185 115

16 A sample of 100 student is taken from large population the mean height of the students in this [CO2, K2]
sample is 160cm can it be reasonable regarded this sample is taken from the population of mean
165cm and standard deviation 10cm.

UNIT-III

PART [2 Marks Questions] [CO#, BTL]

1. Define complex Fourier transform. [CO3, K2]

2. Write convolution of two functions. [CO3, K2]
3. State convolution theorem. [CO3, K2]
4. Write the formula for Fourier transform. [CO3, K2]
5. Write the formula for Fourier sine transform. [CO3, K2]
6. Write the formula for Fourier cosine transform. [CO3, K2]
7. Find the Fourier transform of f(x) defined by f ( x )=1 , a< x< b [CO3, K2]
8. Find the Fourier cosine transform of e−ax , a> 0. [CO3, K2]
9. Find Fourier cosine transform of [CO3,K2]
10. 1 [CO3 ,K2]
Find the sine transform of f ( x )=
x
 [16 Marks Questions] [CO#, BTL]
1. 1
Find the Fourier transform of [CO3, K2]
√| x|
2.
{ 0 otherwise
cosx 0< x<1 [CO3, K2]
Find the Fourier transform of f(x) defined by f ( x )=
−ax
3. Find the cosine transform of f ( x )=e cosax . [CO3, K2]
4. Find the sine transform of f ( x )=e−x cosx. [CO3, K2]
5.
{
sinx 0 ≤ x ≤ a [CO3, K2]
Find the cosine transform of the function f ( x )=
0x>a
6.
{
sinx 0 ≤ x ≤ a [CO3, K2]
Find the sine transform of the function f ( x )=
0x>a

UNIT-IV

Q. No PART-A [CO#, BTL]

1. What are the basic principles of design of experiments. [CO2, K2]
2. 2. Write down the ANOVA table for two way classification. [CO2, K2]
3. 3. What do you mean by a one way classification. [CO2, K2]
4. 4. What are the uses of analytic variance. [CO2, K2]
5. 5. Explain the term Homogeneity [CO2, K2]
6. 6. What is ANOVA. [CO2, K2]
7. 7. What are the assumptions involved in ANOVA. [CO2, K2]
8. 8. Write down the ANOVA table for one way classification. [CO2, K2]
9. 9. Write down the ANOVA table for Latin square classification. [CO2, K2]
10. 10. Why a 2x2 Latin square is not possible? [CO2, K2]

11. Construct ANOVA table for given data.(ONE WAY) 12 [CO5, K2]
A 6 C 5 A 5 B 9
C 8 A 4 B 6 C 9
B 7 B 6 C 10 A 6

12 Carry out one way ANOVA analysis from the following data. The data gives the no.of mistakes 12 [CO5, K2
made in 5 successive days of 4 techniques working for a photographic lab.
Technicion-1 6 14 10 8 11
Technicion-2 14 9 12 10 14
Technicion-3 10 12 7 15 11
Technicion-4 9 12 8 10 11

13 The following data represents the no.of units production per day turned out by different workers 12 [CO5, K2
using 4 different machines.Test whether 5 men productivity is same for different type.
 A B C D
1 44 38 47 36
2 46 40 52 43
3 34 36 44 32
4 43 38 46 33
5 38 42 49 39
14 Perform two way ANOVA 12 [CO5, K2
A B C
1 45 43 51
2 47 46 52
3 48 50 55
4 42 37 49
15. Compare and contrast LSD and RBD. [CO5, K2

16. Preform Latin square design.

A 105 B 95 C 125 D 115
C 115 D 125 A 105 B 105
D 115 C 95 B 105 A 115
B 95 A 135 D 95 C 115

UNIT-V

PART [2 Marks Questions] [CO#, BTL]

1. What is the probability that card taken from a standard deck is an ace? [CO3, K2]
2. What is the probability that in a leap year select at random we have 53 Sunday? [CO3, K2]
3. Raja known to hit the target in 2 out of 5 shots stalin is known to hit the target in 3 out of 3 shots using [CO3, K2]
axioms of probability compute the probability of the target being hit when both try.
4. State Baye’s Theorem. [CO3, K2]
5. Define Discrete random variable. [CO3, K2]
6. Computer 5 if the continuous random variable x has the probability density functions. f (x) = k(1+x); [CO3, K2]
2<x<5.
7. Compute “C” if x has the PDF f(x) = (4x-2x2), 0<x<2. [CO3, K2]
8. Find the mean of the continuous random variable x has the probability density functions. [CO3, K2]

f(x) =
{2( x−1); 1<x<2
0; otherwise
9. Determine the first 3 moments of the random variable x has the following distribution. [CO3,K2]
x -2 1 3
P(x) ½ ¼ ¼
10. Write addition theorem. [CO3 ,K2]

PART B [12 Marks Questions] Marks [CO#, BTL]

1. Two dies are thrown simultaneously find the probability that, 12 [CO3, K2]
i. The sum of face is 7.|
ii. The sum of faces is a multiple of 5.
iii. Both faces are same.
iv. Face of first die is less than face of 2nd die.
2. A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn 12 [CO3, K2]
Is
i. A red face card
ii. Neither a club nor a spade
iii. Neither an ACE nor a kind of red.
iv. Neither a red nor a queen
v. Neither a red card nor a black king.
3. A random variable x which follows the probability distribution function. 12 [CO3, K2]
X 0 1 2 3 4 5 6 7 8
p(x) A 3a 5a 7a 9a 11a 13a 15a 17a
 i. Determine the value of a.
ii. Find p(x<3) ; p(x>3); p(0<x<5)
iii. Compute the cumulative distribution function.
4. The probability density function of a random variable x is f(x)= kx(2-x); o<x<2 12 [CO3, K2]
i. k
ii. mean
iii. variance
iv. rth moment.
v. variance
5. Let x be the number turns – up down when die is thrown find mean, variance and standard
deviation x. also find moment generating function.

Blooms Taxonomy Level(BTL):

K1: Remember K2: Understand K3: Apply
K4: Analyze K5: Evaluate K6: Create