BSc IT Sem III ATKT APPLIED MATHEMATICS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt of the following: 15 marks
   • a. Find the adjoint of the given matrix and hence find Inverse if exist
   • b. Find the Characteristic values and characteristic vectors of the given matrix
   • c. Discuss the consistency of the following systems of equations and solve them
   • e. Solve the equation x’
   • f. Prove that (1 x x)" (cos nx/2 + i sin nx/2)
2. Q2 Attempt of the following: 15 marks
   • a. Solve the Differential Equation (1 - 2xy — x3) dy - (1 + y* + dx =0 Solve the Differential Equation x*dy/dx = 3x? — 2xy + 1
   • c. Solve the following Equation sec x dy/dx = y + sin x
   • d. Solve the following Equation + p(2y +2) =0 Find the Complementary and Particular Solution of the equation (D? + D? + D + 1 )y Find the General Solution of the equation + 3D)y = cos x Attempt any three of the following: 15
   • b. Find the inverse Laplace transform for the function Laplace transformation of the function
   • d. Obtain the Laplace transform of each of the given function
   • e. Find Inverse Laplace Transformation by convolution theorem for
   • f. | Using Laplace transform method solve the following differential equations with the
3. Q4 Attempt of the following: Change the order of integration and evaluate i dxdy 15 marks
   • f. Change to polar coordinates and evaluate f
4. Q5 Attempt any three of the following: 15 marks
   • Q.P. Code: 53636
   • f. Define error function. Evaluate

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