Download PTU B-Tech ECE 2020 Dec 3rd Sem 76448 Mathematics Iii Question Paper

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Roll No. LTI [ 1] Total No. of Pages : 02
Total No. of Questions : 18

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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 Laplace of (cos t) u₁ (t)
2. Find L(t²e^t)
3. Find a₀ if f(x)= x², where x ? (-2,2).
4. Discuss behavior of Fourier series near a point of discontinuity of
   

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   f(x) =
   -p < x < 0
   -1, 0 < x < p
5. Find Z {sin(n+1) ?}
6. Find relationship between Laplace and Fourier Transform.

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7. Two cards are drawn one after the other from a well shuffled deck of 52 cards. Find the probability that both are spade, if the first card is not replaced.
8. If X is Poisson variate satisfies P (X=1)=0.5 P (X =2), find mean and variance.
9. Define F-test
10. Discuss method to fit Parabola.

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SECTION-B

1. State convolution theorem and find L^-1(1/(s² - 16)²)
2. Find the Fourier sine series of the function f(x) =sin 3x, 0 < x < p.
3. Solve difference equation y_n+2 — 2y_n+1 +y_n =n, y₀=1, y₁=1.
4. In a distribution, 12% of the item are under 30 and 85% are under 60. Find the mean and standard deviation of the distribution.

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5. Two independent sample have 28 and 19 pair of observations with correlation co-efficient 0.55 and 0.75 respectively. Are these values consistent with the hypothesis that both the samples are drawn from the same population?

SECTION-C

1. Using Laplace transform to solve the initial value problem u_t = u_xx, 0 < x <1, t> 0, subject to u (x, 0)=0, u_t (x, 0) = sin 3px, u (0, t) =sin t, u (1,t)=0.
2. Using convolution find F^-1[1/(6+5i)]
3. Find correlation coefficient of the following bivariate frequency distribution data :

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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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