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) Find all the basic solutions to the following problem:
   • (b) Evaluate )de, where is upper half of the circle | | =]. 05
   • (c) Ten individual are chosen at random from a population & heights are found to be 63, 63, 64, 65, 66, 69, 69, 70, 70, 71.inches. Discuss the suggestion that the height of universe is 05
   • (d) If find A'” 05 Evaluate dz, where is the circle |z 06
   • (b) test was administered to_5 persons and after they were trained. The results ate Test whether there is any change in I.Q. after the training programme, use 1% LOS
   • (c) Solve the following LPP using Simplex Method
2. Q3 (a) Find the Eigen values and Eigen vectors of the following matrix
   • (b) Ifthe height of 500 students is normally distributed with mean 68 inches and standard deviation 4 inches. Find the expected number of students having heights between 65 & Obtain Taylor’s and Laurent’s expansions of (z ) z=0 08
3. Q4 (a) A machine is claimed to produce nails of mean length 5 cms & standard of 0.45 cm. A random sample of 100 nails gave 5.1 as their average length. Does the performance of the machine justify the claim? Mention the level of significance you apply
   • (b) Using the Residue theorem, Evaluate 06
   • (c) (i) manufacturing process 5% of the tools produced turnout to be defective Find the probability that in a sample of 40 tools at most 2 will be defective
   • (ii) A random variable x has the probability distribution 04+04 P(X =x,) X Find the moment generating function of x
4. Q5 (a) Check whether the following matrix is Derogatory or Non-Derogatory:
   • (b) an industry 200 workers employed for a specific job were classified according to their performance & training received to test independence of training received & performance. The data are summarized as follows Performance Not good 06 Use y’ -test for independence at 5% level of significance & write your conclusion
   • (c) Use the dual simplex method to solve the following L.P.P
5. Q6 (a) Show that the matrix A satisfies Cayley-Hamilton theorem and hence find
   • (b) random variable has the probability density function given below
   • (c) Using Kuhn-Tucker conditions, solve the following NLPP

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