Computer Engineering Sem 4 Engineering Mathematics IV Question Paper PDF 2026 - Mumbai University | munotes

Questions asked in this paper

• (4) Figures to the right indicate full marks

1. Q1 a)IfA= then find the Eigen values of A? + + 5 marks
   • b) Evaluate + iy) the path (i)y = x, (ii) y = x? 5
   • c ) Write the dual of the following problem 5
   • d) A certain drug administered to 12 patients resulted in the following change in their Blood Can we conclude that drug increase the Blood Pressure?
   • J. Where c is
   • (b) Verify Cayley-Hamilton theorem and find A~* for A = Hence, find 2A? — A? —
   • (c) Solve by Simplex Method 8
2. Q3 a) Based on the following data determine if there is a relation between literacy and (Given that Critical value of chi-square | d. f and 5% L.O:S is 3.841
   • b) Obtain Laurent’s series expansion of f(z) = 6
   • c) Using the method of Lagrangian multipliers solve the following N.L.P.P 8
3. Q4 a) Using the method of Lagrange’s multipliers solve the following N.L.P.P 6 marks
   • b) Find the inverse Z-transform of if ROCis (i) 6
   • c) Show that the matrix A = 7 is diagonalizable. Find the transforming matrix and the diagonal matrix. [8]
4. Q5 a) Find * = 6 marks
   • b) Find the Eigen values and Eigen Vectors of the following matrix. 6
   • c) Solve by the dual Simplex Method 8
5. Q6 a) Find Z{2* cos(3k + 2)},k = 0. 6 marks
   • b) If the heights of 500 students is normally distributed with mean 68 inches and standard deviation 4 inches, estimate the number of students having heights (i) greater than 72 inches
   • (ii) less than 62 inches (iii) between 65 and 71 inches 6
   • c) Using Kuhn Tucker conditions, solve the following NLPP 8

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