Engineering BE Electronics and Telecommunication Sem 3 December 2022 2022 Engineering Mathematics III Question Paper - Mumbai University | munotes
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Questions asked in this paper
- (3)Figures to the right indicate full marks
(Time : 3 hours) [Total marks: 80
(1) Question is compulsory
(2) Answer any three question from Q 2
(3)Figures to the right indicate full marks
1(a) Find the Laplace Transform of sin 2t sin 3t . 05
1(b) Construct an analytic function whose imaginary part is v = cosxsinhy. 05
1(c ) Find Eigen values of —2A +I 05
1(d) Find the Fourier Series Expansion f(x) = x ,where x 05
2(a) Find the direction derivative of y,z) = sin(xy) + in the direction of the
vector v = i — 2j + 2k at the point P = (1, 1) 06
2(b) Find Fourier series of f(x) 7. 06
2(c ) Find Inverse Laplace Transform of (i) 08
3(a) Find Eigen Values and Eigen Vector of the following matrix 06
3(b). Find orthogonal trajectory of family of curve 3x*y —y? =c. 06
3(c ) Find the Fourier Series for f(x) in (0,27)where
Hence deduce that
4(a) Prove F = is both solenoidal and irrotational . 06
4(c) Show that the matrix
A= | -8 3 diagonalizable and find transforming matrix and Diagonal matrix . 08
5(a) Find the inverse Laplace Transform of by using convolution theorem. 06
5(b) Construct an analytic functionf(z) = u+ iv, where 06
5(c) Evaluate by using Green’s theorem
6(a) By using CHT theorem and find A= |-1 3 0 06
6(b) Obtain half range sine series in for f(x) = — x),
Hence show that
(1) Question is compulsory
(2) Answer any three question from Q 2
(3)Figures to the right indicate full marks
1(a) Find the Laplace Transform of sin 2t sin 3t . 05
1(b) Construct an analytic function whose imaginary part is v = cosxsinhy. 05
1(c ) Find Eigen values of —2A +I 05
1(d) Find the Fourier Series Expansion f(x) = x ,where x 05
2(a) Find the direction derivative of y,z) = sin(xy) + in the direction of the
vector v = i — 2j + 2k at the point P = (1, 1) 06
2(b) Find Fourier series of f(x) 7. 06
2(c ) Find Inverse Laplace Transform of (i) 08
3(a) Find Eigen Values and Eigen Vector of the following matrix 06
3(b). Find orthogonal trajectory of family of curve 3x*y —y? =c. 06
3(c ) Find the Fourier Series for f(x) in (0,27)where
Hence deduce that
4(a) Prove F = is both solenoidal and irrotational . 06
4(c) Show that the matrix
A= | -8 3 diagonalizable and find transforming matrix and Diagonal matrix . 08
5(a) Find the inverse Laplace Transform of by using convolution theorem. 06
5(b) Construct an analytic functionf(z) = u+ iv, where 06
5(c) Evaluate by using Green’s theorem
6(a) By using CHT theorem and find A= |-1 3 0 06
6(b) Obtain half range sine series in for f(x) = — x),
Hence show that
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