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

Questions asked in this paper

1. Q1 Q.No.01 is compulsory
2. Q2 Solve any three from Q. No. 02 to 6 marks
3. Q3 Numbers to the right indicate full marks
4. Q4 Use of statistical tables is allowed
5. Q1 Solve If find the sum and product of Eigen values A
   • b) Integrate the function f(z) = z* from A(O, 0) to 1) along straight line AB. 5
   • c) Find the Z-Transform of (k) = a* ,k <0. 5
   • d) A transmission channel has a per-digit error probability p = 0.01. Calculate the 5 probability of more than | error in 10 received digits using Poisson distribution Find the Eigenvalues and Eigenvectors of the 5
   • b) Find the Z-Transform of Cos + a) k=0. 6
   • c) Use the dual simplex method to solve the LPP Evaluate dz Where C is acircle
   • b) Verify Caley-Hamilton theorem and hence find A~* and A* where A =
   • c) Solve the LPP by Big -M method ) Find inverse Z transform of F(z) = for i) |z| < 1, ii) 1< |z| <3
   • b) The following data represent the marks obtained by 12 students in two tests, one held before the coaching and the other after the coaching Do the data indicate that the coaching was effective in improving the performance of the students?
   • c) Find all possible Laurent’s series expansions of the function f(z) = about z indicating the region of convergence in each case. 8
   • a) Determine all basic solutions to the following problem
   • b) Using Normal distribution, find the probability of getting 55 heads in the toss of 100 6 Cc) Solve the NLPP
   • a) Show that the given matrix is diagonalizable and hence find diagonal form and transforming matrix where A = | 1 3 2 |. 6
   • b) Of the 64 off springs of a certain cross between guinea pigs 34 were red, 10 were 6 black and 20 were white. According to the generic model these numbers should be in the ratio 9 : 3: 4. Use 2- test to check whether the data are consistent with the model
   • c) Max. Z = 4x, + 6x, — — x27 — x3” , Subject to x, + x2 < 2 and 2x, + 3x. < 8

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