Download PTU B.Tech 2021 Jan ECE 5th Sem 78750 Mathematics Iii Question Paper

Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January ECE 5th Sem 78750 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (ECE) (Sem.?5)
MATHEMATICS III
Subject Code : BTAMXXX18
M.Code : 78750
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Write briefly :
1.
Find the Z-Transform of ak.
2.
Prove that ( at
L e
)
if s > a.
s a
3.
State first shifting theorem in Laplace transformation.
4.
State the formula to calculate the Fourier coefficients.
5.
What are the Dirichlet's conditions for Fourier Series?
6.
State the shifting property in Z-Transform.
7.
A coin is tossed successively three times. Determine the probability of getting
(i) Exactly two head (ii) at least two heads
8.
Define Probability Density Function (P.D.F).
3
9.
Determine the Binomial Distribution when mean is 9 and whose standard deviation is
.
2
10. Write a short note on Correlation.
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SECTION-B
11. Calculate the coefficient of rank correlation from the data given as :
Marks in Statistics
20
30
40
50
60
70
80
Marks in Company Law
14
5
30
32
40
45
65
12. A die is thrown 10 times. If getting an even number is a success. What is the probability
of getting at least 6 successes?
13. Find the z-transform of (i) sin23t (ii) cos3t
14. State and prove Convolution theorem for Fourier Transforms.
15. Evaluate
1
s 1
L
log
s 1
SECTION-C
n
1
( 1)
16. Prove that x cos x =
sin x 2
sin nx for x (? ).
2
2
n2 n
1
17. Solve 6x (k + 2) ? x (k + 1) ? x (k) = 0 ; x (0) = 0 ; x (1) = 1 by using Z-Transforms.
18. Fit the curve y = a + bx2 to the data :
x
10
20
30
40
50
y
8
10
15
21
30
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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