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

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Roll No. Total No. of Pages : 02
Total No. of Questions : 18

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B.Tech. (ECE) (Sem.-5)
MATHEMATICS Ill
Subject Code : BTAMXXX18
M.Code : 78750
Time : 3 Hrs. Max. Marks : 60

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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

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Write briefly :

1. Find the Z-Transform of a^k.
2. Prove that L(e^at)=1/(s-a) if s>a.
3. State first shifting theorem in Laplace transformation.
4. State the formula to calculate the Fourier coefficients.

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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 heads (ii) at least two heads
8. Define Probability Density Function (P.D.F).
9. Determine the Binomial Distribution when mean is 9 and whose standard deviation is v2.

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10. Write a short note on Correlation.

SECTION-B

11. Calculate the coefficient of rank correlation from the data given as :

    Marks in Statistics	Marks in Company Law
    20	14
    30	5
    40	30
    50	32
    60	40
    70	45
    80	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) sin3t (ii) cos²t

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14. State and prove Convolution theorem for Fourier Transforms.
15. Evaluate L^-1 {log (1+1/s)}
16. Prove that x cos x = (p/4) sin(nx) for x ? (-p, p).

SECTION-C

17. Solve 6x (k+2)—x (k+1)—x(k)=0; x(0)=0;x (1)=1 by using Z-Transforms.

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18. Fit the curve y = a + bx² to the data :

    X	y
    10	8
    20	10
    30	15
    40	21
    50	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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