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Applied Mathematics 4 - Dec 18
Information Technology (Semester 4)
Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
Find (i) $\bar x$, $\bar y$ (ii) correlation coefficient of r
x=0,1,2 and p(0) = $3k^3$, p(1)=$4k-10k^2$, p(2) = $5k-1$
Find (i) k (ii) p (0 $\lt $x $\leq$2)
(i) Eulerian circuit but not a Hamiltonian circuit
(ii) Hamiltonian circuit but not an Eulerian circuit
(1) V = {a,b,c,d} ,E ={(a,b),(a,d), (b,d), (c,d),(c,b),(c,d)}
(2) V' ={1,2,3,4} ,E' = {(1,2),(2,3) ,(3,1),(3,4),(4,1), (4,2)}
i) in the first 800 burning hours?
ii) Between 800 and 1200 burning hours?
(ii) Find the Legendre's symbol of $(\frac{19}{23})$.
x | 12 | 9 | 8 | 10 | 11 | 13 | 7 |
---|---|---|---|---|---|---|---|
y | 14 | 8 | 6 | 9 | 11 | 12 | 3 |
(ii) Show that any connected graph with ‘n-1’ edges is a tree.
(ii) Ten individuals are chosen at random from a population and their heights are found to be in inches 63, 63, 64, 65, 66,69, 69, 70, 70,71. Discuss the suggestion that the mean height of the universe is 65 inches.
(ii) Express the expression (x +y) (x + z) (x’y)’ in the sum-of-product form.