Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CSE/IT (Computer Science And Engineering/ Information Technology) 2020 March 4th Sem BTCS402 Mathematics Iii Previous Question Paper
Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Computer Science Engineering / Information Technology / ECE)
(Sem.?4)
MATHEMATICS ?III / ENGINEERING MATHEMATICS ?III
Subject Code : BTCS402
M.Code : 56605
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
Write briefly :
1) Define periodic functions.
2) State the sufficient condition for the existence of Laplace transforms.
3) Define analytic and conjugate functions of a complex variable.
4) Define Homgenous linear partial differential equation.
5) Define critical region of the testing.
6) Define Eigen value and eigen vector of a matrix.
7) Define Binomial and Poisson distributions.
8) Write the Laplace transform of t
2
sin 2t.
9) Write the difference between chi-square and t-distributions.
10) Differentiate between Euler?s and modified Euler?s method for solving the ordinary
differential equation.
SECTION-B
11) Obtain the Fourier series of x sin x as a cosine series in (0, ?). Hence show that
1 1 1 2
.....
1.3 3.5 5.7 4
? ?
? ? ? ? ? .
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1 | M-56605 (S2)-2693 & 2797
Roll No. Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Computer Science Engineering / Information Technology / ECE)
(Sem.?4)
MATHEMATICS ?III / ENGINEERING MATHEMATICS ?III
Subject Code : BTCS402
M.Code : 56605
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
Write briefly :
1) Define periodic functions.
2) State the sufficient condition for the existence of Laplace transforms.
3) Define analytic and conjugate functions of a complex variable.
4) Define Homgenous linear partial differential equation.
5) Define critical region of the testing.
6) Define Eigen value and eigen vector of a matrix.
7) Define Binomial and Poisson distributions.
8) Write the Laplace transform of t
2
sin 2t.
9) Write the difference between chi-square and t-distributions.
10) Differentiate between Euler?s and modified Euler?s method for solving the ordinary
differential equation.
SECTION-B
11) Obtain the Fourier series of x sin x as a cosine series in (0, ?). Hence show that
1 1 1 2
.....
1.3 3.5 5.7 4
? ?
? ? ? ? ? .
2 | M-56605 (S2)-2693 & 2797
12) Using the Laplace transform, prove that
0
log
at bt
e e b
dt
t a
?
? ?
?
?
?
.
13) Solve the following equation by Gauss elimination method :
2x + y + z = 10 ; 3x + 2y + 3z = 18 ; x + 4y + 9z = 16
14) The theory predicts the proportion of beans, in the four groups A, B, C and D should be
9:3:3:1. In an experiment among 1600 beans, the numbers in the four groups were 882,
313, 287 and 118. Does the experimental result support the theory ? (The table value of
?
2
for 3 d.f. at 5% level of significance is 7.81).
15) Show that f (z) = xy
2
(x + iy) + (x
2
+ y
4
), z ?0 and f (z) = 0, z = 0 is not analytic at z = 0,
although C-R equations are satisfied at the origin.
SECTION-C
16) a) Marks obtained by a number of students are assumed to be normal distributed with
mean 50 and variance 36. If 4 students are taken at random, what is the probability
that exactly two of them will have marks over 65? Given that
2
0
( ) z dz ?
?
= 0.4772
where z is N (0, 1).
b) The intelligence quotients (IQ) of 16 students from B.Tech. IInd year showed a mean
of 107 and a standard deviation of 10, while the IQs of 14 students from B.Tech. Ist
year showed a mean of 112 and a standard deviation of 8. Is there a significant
difference between the IQs of the two groups at significance levels of 0.05? Given
that critical value of 28 degree of freedom with 5% level of significance is 2.05.
17) Find the largest eigen value and the corresponding eigen vector of the matrix
2 1 0
1 2 1
0 1 2
? ? ?
? ?
? ?
? ?
? ? ?
? ?
.
18) Solve the following by Euler?s modified method :
, (0) 1
dy
x y y
dx
? ? ?
at x = 0.3 with step size 0.1.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 21 March 2020