Engineering B.E. (Computer Engineering) Sem 3 Engineering Mathematics III May 2023 Question Paper - Mumbai University | munotes
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Questions asked in this paper
- (4) Figures to the right indicate full marks
(Time: 3 hours ) Max. Marks: 80
N.B. (1) Question No. is compulsory
(2) Answer any three questions from Q.2 to Q.6
(3) Use of Statistical Tables permitted
(4) Figures to the right indicate full marks
(a) Find the Laplace transform of [5]
(b) Find the constants a, b ,c, d, e if [5]
(c) Calculate the Spearman’s rank correlation coefficient R [5 ]
(d) Laplace transform of (=) . [5 ]
(a) Find the Laplace transform of sin 3u du [6]
(b) find the value of k if the function f(x)= kx? , Os x
Is a probability density function. find mean and variance. [6]
(c) Obtain the Fourier series to represent f (x) = x? in (0, )
Hence show that [8]
(a) Find the analytic function f (z) = u + iv such that [ 6 ]
(b) Using convolution theorem Find inverse Laplace transform of [ 6 ]
(c) Fit a second-degree parabolic curve to the following data
(a) Obtain the Fourier series to x) = 9-x? in(-3,3). [6]
(b) . Find the coefficients of regression and hence obtain the equation of the lines of
Regression for the following data
(c) Prove that J, dt = =. [8]
(a) Find the orthogonal trajectories of the family of curves 3 y*=c. [6]
(b) If X denotes the outcome when a fair die is tossed, find Moment generating function
Of X and hence find the mean and variance of X. [ 6 ]
(c) Obtain the half range cosine series of f(x )
Hence show that = [8 ]
Q6.(a) Find inverse Laplace transform of . [6]
(b) The probability density function of a random variable X is
(c) Verify Laplace equation for u = (r + cos find [8]
N.B. (1) Question No. is compulsory
(2) Answer any three questions from Q.2 to Q.6
(3) Use of Statistical Tables permitted
(4) Figures to the right indicate full marks
(a) Find the Laplace transform of [5]
(b) Find the constants a, b ,c, d, e if [5]
(c) Calculate the Spearman’s rank correlation coefficient R [5 ]
(d) Laplace transform of (=) . [5 ]
(a) Find the Laplace transform of sin 3u du [6]
(b) find the value of k if the function f(x)= kx? , Os x
Is a probability density function. find mean and variance. [6]
(c) Obtain the Fourier series to represent f (x) = x? in (0, )
Hence show that [8]
(a) Find the analytic function f (z) = u + iv such that [ 6 ]
(b) Using convolution theorem Find inverse Laplace transform of [ 6 ]
(c) Fit a second-degree parabolic curve to the following data
(a) Obtain the Fourier series to x) = 9-x? in(-3,3). [6]
(b) . Find the coefficients of regression and hence obtain the equation of the lines of
Regression for the following data
(c) Prove that J, dt = =. [8]
(a) Find the orthogonal trajectories of the family of curves 3 y*=c. [6]
(b) If X denotes the outcome when a fair die is tossed, find Moment generating function
Of X and hence find the mean and variance of X. [ 6 ]
(c) Obtain the half range cosine series of f(x )
Hence show that = [8 ]
Q6.(a) Find inverse Laplace transform of . [6]
(b) The probability density function of a random variable X is
(c) Verify Laplace equation for u = (r + cos find [8]
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