Computer Engineering Sem 4 Engineering Mathematics IV Question Paper PDF 2026 - Mumbai University | munotes
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Questions asked in this paper
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Q2 Attempt any three questions from Q.2to Q.6
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Q3 Use of statistical tables permitted
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Q4 Figures to the right indicate full marks
- J. (z — z*)dz, where C is the upper half of circle |z| = 1 IfA=|0 1 find the Eigen values of A? — 2A +I
- c) State whether the following statement is true or false with reasoning: “The line of regression between x and y are parallel to the line of regression between 2x 5
- d) Find the dual of the following L.P.P. 5
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Q2 a) f c dz , where c is the circle |z|=2. Show that the matrix 4] 1s non-derogatory 6 marks
- c) For a normal variate X with mean 2.5 and standard deviation 3.5 , find the 8
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Q3 a) Find the expectation of number of failures preceding the first success in an infinite series of independent trials with constant probabilities p and q of success and failure respectively 6 marks
- b) Solve the following L.P.P. by simplex method Expand f(z) = about Z = 0 indicating the region of convergence [8] in each case 6
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Q4 a) A biased coin is tossed n times. Prove that the probability of getting even number of heads is 0.5[1 + 6 marks
- b) Calculate the coefficient of correlation between X and Y from the following data. Show that the matrix 3 4] is diagonalizable. the transforming matrix M and the diagonal form D 6
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Q5 a) Can it be concluded that the average life-span of an Indian is more than 70 years, if a random sample of 100 Indians has an average life span of 71.8 years with standard deviation of 8.9 years? 6 marks
- c) Using the Kuhn — Tucker conditions, solve the following N.L.P.P. 8
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Q6 a) Adie was thrown 132 times and the following frequencies were observed. Test the hypothesis that the die is unbiased 6 marks
- b) If two independent random samples of sizes 15 and 8 have respectively the following means and population standard deviations, Test the hypothesis that = at 5% level of significance 6
- b) Using Penalty (Big-M) method solve the following L.P.P. Subject to 2x; +xX2 <2 8
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