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

Questions asked in this paper

1. Q1 (a) Find the remainder when is divided by 7. 5 marks
   • (b) The probability distribution function of random variable X is 5
   • (c) Calculate rank correlation coefficient from the following data. 5
   • (d) Draw the Hasse diagram of Poset A ={2,3,6,12,24,36,72} under the relation of divisibility. Is it Lattice? 5
2. Q2 (a) If x is a Poisson variate such that P(x=2) =9P(x=4)+90P(x=6) then Find mean of x
   • (b) Consider (3,4) parity check code .For each of the following received words determine whether an error will be detected ?
   • (1) 0010 (ii) 1001 1101 Gv) 1111 6
   • (c) Using Sieve of Eratosthenes find the prime number upto 150. 4
   • (ii) What is the remainder when following sum divided by 4? Prove that a graph ‘G’ remains connected after removing an edge ‘e’ from ‘G’ iff ‘e’ is in some circuit of G. (06) 4
   • (b) Marks obtained by students in an examination follow normal distribution . If 30% of students got below 35 marks and 10% got above 60 marks, Find mean and standard
   • (c) Investigate the association between the darkness of eye colour in father and son from the following data Colour of the father's eye 8
3. Q4 (a) Using Euclid 's Algorithm find x and y satisfying the following. 6 marks
   • (b) Let L= {1,2,3,5,6,10,15,30} with divisibilty relation. Then show that L is a
   • (c) Give an example of a graph which has 8
   • (1) Eulerian circuit but not a hamiltonian circuit
   • (2) Hamiltonian circuit but not an Eulerian circuit
   • (3)Both
   • (4)None of these two
4. Q5 (a) Fit Binomial Distribution to the following data 6 marks
   • (b) Nine items of a sample had the following values 45,47, 47, 49, 53,51 Does the mean of 9 items differ significantly from assumed population mean 47.5?
5. Q6 (a) Given 6y =5x +90 , 5x = 8y +30, = 16 Find (i) x and y (ii) r (iii) 6 marks
   • (b) Prove that set of cube root of unity is a group under multiplication of complex
   • (c) (i) Prove that 111733 + 333111 js divisible by 7. 4
   • (ii) mod(23) 4

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