Engineering B.E. (Computer Engineering) Sem 3 Engineering Mathematics III Dec 2022 Question Paper - Mumbai University | munotes
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Questions asked in this paper
- (4) Figures to the right indicate full marks
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Q1 @ Laplace transform of given that = (1/48) 5 marks
- (b) Spearman’s rank correlation coefficient for the following data: 5
- (C) Find inverse Laplace transform of 5
- (d) If f(z)= -4xy-3xy’) is analytic, find the values of p,q, and r Find Laplace transform of f(t) where 2<t<3 5
- (b) Two unbiased dice are thrown. If X represents sum of the numbers on the two dice. Write probability distribution of the random variable X and find mean, standard 6
- (c) Obtain Fourier series for f(x) = x sinx in the interval x < 8
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Q3 (a) Using Milne-Thompson’s method construct an analytic function f(z)=u+ iv in terms of z where u+v = e*(cosy+siny) + 6 marks
- (b) Using convolution theorem find the inverse Laplace transform of 6
- (c) parabola y= to the following data and estimate y when x=10 8
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Q4 (a) Find Laplace transform of e if 6 marks
- (b) Find half range sine series for f(x) =x-x?, O<x <1. Hence deduce that Findi) xandy, ili) Oy? and iv) angle between the regression lines Can the function u= r+ — be considered as real or imaginary part of an analytic [6] function? If yes, find the corresponding analytic function 6
- (b) unbiased coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails, find moment generating function of X and hence obtain the first moment about origin and the second moment about mean 6
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Q6 (a) Find inverse Laplace transform of using method of partial fractions. 6 marks
- (b) random variable X following probability density function f(x) forx>0 find k and variance 6
- (c) Find half range cosine series for f(x) =x, O<x <2. Hence deduce that. 1) 8
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