PTU Punjab Technical University B-Tech May 2019 Question Papers 4th Semester Computer Science Engineering (CSE)
www.FirstRanker.com
Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech.(CSE) (2011 Batch) (Sem.?4)
MATHEMATICS ? III
Subject Code : BTCS-402
M.Code : 56605
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying T EN marks each and students
have to attempt any T WO questions.
SECTION?A
Answer briefly :
1.
Find the Fourier series expansion of the periodic function f (x) = x, ?2 < x < 2.
2
(s 1)
2.
Find inverse Laplace transform of
.
4
(s 2)
3.
Find Laplace transform of (t ? 2)2 e3t.
4.
Eliminate the arbitrary constants a and b from z = ax + by + a2b2, to obtain the partial
differential equation governing it.
5.
Find general solution of linear partial differential equation 2yz p + zx q = 3xy
www.FirstRanker.com
6.
Show that the function f (z) z is a continuous at the point z = 0 but differentiable at
z = 0.
7.
Define Eigen Values and Eigen vectors of a square matrix.
8.
The number of emergency admissions each day to a hospital is found to have Poisson
distribution with mean 4. Find the probability that on a particular day there will be no
emergency admissions.
9.
Obtain the approximate value of y (1.2) for the initial value problem
y = ? 2xy2, y (1) = 1 using Euler's method.
10.
Derive the expression of moment generating function about origin of a normal
distribution.
1 | M-56605
(S2)-178
www.FirstRanker.com
www.FirstRanker.com
www.FirstRanker.com
SECTION?B
11. Obtain the Fourier series expansion of the function f (x) = 4 ? x2, ?2 x 2 and hence
2
1
1
1
show that
1
.....
2
2
2
12
2
3
4
12. Using Laplace transform, solve the initial value problem
y + y = t, y (0) = 1, y(0) = 0.
13. Find the solution of the given homogeneous partial differential equation
(D 4 ? 2 D 2 D 2 + D4)z = 0.
14. Using Gauss Seidel iteration method, solve 4x + 2z = 6, 5y + 2z = ?3, 5x + 4y + 10z = 11.
15. Find the approximate values of y(x) at the given points using Runge-Kutta method of
fourth order for the initial value problem y
x y , y (0.4) 0.41 and given is h = 0.2
and x [0.4, 0.8].
SECTION?C
16. i) State and prove second shifting property of Laplace transformation.
ii) Show that the function u (x, y) = 2x + y3 ? 3x2y is harmonic. Find its conjugate
harmonic function v (x, y) and the corresponding analytic function f (z).
dy
17. i) Solve
2
5x
y 2 0 given is y(4) = 1 for y(4.1) and y(4.2), taking h = 0.1 using
dx
Modify Euler methods.
ii) A continuous rwww.FirstRanker.com
andom variable X is normally distributed with mean 16 and standard
deviation 5. Find the probability that X 25 and 0 X 16.
18. i) The heights of 8 males participating in an athletic event are found to be 175cm,
168cm, 165cm, 170cm, 167cm, 160cm, 173cm and 168cm. Can we conclude that the
average height is greater than 165cm? Test at 5% level of significance.
ii) Two random samples of sizes 9 and 7 gave the sum of squares of deviations from
their respective means as 175 and 95 respectively. Can they be regarded as drawn
from normal populations with the same variance?
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.
2 | M-56605
(S2)-178
www.FirstRanker.com
This post was last modified on 04 November 2019