Information Technology Engineering Sem 4 Engineering Mathematics IV Question Paper PDF 2026 - Mumbai University | munotes
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Questions asked in this paper
- (4) Figures to the right indicate full marks
-
Q1 (a)Calculate the coefficient of correlation from the following data 5 marks
- (b) Evaluate the line integral f along the path y = x 5
- (c) Find the Eigen values of + 5A? — 3Awhere A = 2 0 | 5
- (d) The probability density function of a random variable x is Find i) k mean standard deviation of the distribution. 5
-
Q2 (a) If the probability of a bad reaction from a certain injection is 0.001, determine the chance that out of 2000 individuals more than two will get a bad reaction. 6
- (b)The equations of the two regression lines are find the means of x and y and the coefficient of correlation between x and y. 6
- (c) Is the matrix —3 diagonalizable? If so find the diagonal form and the transforming matrix . 8
-
Q3 (a) Find the Eigen values and the Eigen vectors of the 3 6 marks
- (b) Evaluate using Residue theorem where c is the circle|z| = 3
- (c) The weights of 1000 students were found to be normally distributed with mean 40 kgs and standard deviation 4 kgs. Find the expected number of students with weights 1) less than 36 kgs, ii) more than 45 kgs. 8
-
Q4 (a) Evaluate where c is |z| = 1 6 marks
- (b) A sample of 900 members is found to have mean of Can it be regarded as a truly random sample from alarge population with mean 3.25 cm and S.D. 1.61
- (c) Solve the following LPP using Simplex method 5.(a) Find the Laurent’s series for f (z) = about z = Oin the regions i) 1 < |z| < 2, 6
- (b) Binomial distribution to the following data and compare the theoretical 6 frequencies with the actual ones
- (c) Solve the following LPP using the Dual Simplex method 8
-
Q6 (a) Find 4” where A = 6 marks
- (b) Solve the following NLPP using Kuhn-Tucker conditions Subject to <6; and 6
- (c) A die was thrown 132 times and the following frequencies were observed Test the hypothesis that the die is unbiased. Use x? Test 8
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Information Technology Engineering Sem 4 Paper Path
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