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

Questions asked in this paper

1. Q1 [a] Given two lines of regression lines 6y = 5x +90, 15x = 8y + 130. [c] A random discrete variable x has the probability density function given [5] [d] Show that G = {1, —i} is a group under usual multiplication of [5] 5 marks
2. Q2 [a] Find gcd (2378, 1769) using Euclidean Algorithm. Also find x and y such that 2378x + 1769y = gcd(2379,1769) [b] Give an example of a graph which has [6] 6 marks
   • (i) Eulerian circuit but not a Hamiltonian circuit
   • (ii) Hamiltonian circuit but not an Eulerian circuit
   • (iii) Both Hamiltonian circuit and Eulerian circuit [c] Show that is a lattice. Draw its Hasse diagram. [8]
3. Q3 [a] Derive mgf of Binomial distribution and hence find its mean and variance. [b] It was found that the burning life of electric bulbs of a particular brand [6] was normally distributed with the mean 1200 hrs and the S.D. of 90 hours, Estimate the number of bulbs in a lot of 2500 bulbs having the burning life: (4) more than 1300 hours (ii) between 1050 and 1400 hours 6 marks
   • (i) Find inverse of (mod 77) using Euler’s theorem. 8
   • (11) Find the Jacobi’s symbol of (=)
4. Q4 [a] Calculate the coefficient of correlation between x and y from the [b] Let G be a group of all permutations of degree 3 on 3 symbols 1,2 & 3. [6] Let H ={I, (1. 2)} be a subgroup of G. find all the distinct left cosets of H in G and hence index of H 6 marks
   • Q.P. Code: 37497 [c] The average marks scored by 32 boys is 72 with standard deviation of [8] 8 while that for 36 girls is 70 with standard deviation of 6. Test at 5% LOS whether the boys perform better than the girls
   • (11) A random sample of 15 items gives the mean 6.2 and variance 10.24 Can it be regarded as drawn from a normal population with mean 5.4 [b] Given L = 10, 20}with divisibility relation. Verify that (L,<) [6] is a distributive but not complimented Lattice [c] () Draw a complete graph of 5 vertices. [8]
   • (11) Give an example of tree. (sketch the tree)
5. Q6 [a] Show that + 333111 is divisible by 7. [b] The following table gives the number of accidents [6] Find whether the accidents are uniformly distributed over a week [c] () Write the following permutation as the product of disjoint cycles [8] 6 marks
   • (ii) Simplify as sum of product (A+B) (A+B’)

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