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

Questions asked in this paper

1. Q2 Attempt any three questions from Q.2to Q.6
2. Q3 Use of statistical tables permitted
3. 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 — 5
   • 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
4. Q2 a) f c dz , where c is the circle |z|=2. Show that the matrix non-derogatory 6 marks
   • c) For a normal variate X with mean 2.5 and standard deviation 3.5 , find the 8
5. 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
6. Q4 a) A biased coin is tossed n times. Prove that the probability of getting even number of heads is 0.5[1 + (q 6 marks
   • b) Calculate the coefficient of correlation between X and Y from the following data. Show that the matrix 3 4] is diagonalizable. Find the transforming matrix M and the diagonal form D 6
7. 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
8. 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. 8

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