Other Bachelor Degree- DISCRETE MATHEMATICS FOR BIOINFORMATICIANS(Karunya University, Coimbatore-2012)
Saturday, 24 August 2013 10:28anudouglas
Karunya University
(Karunya Institute of Technology and Sciences)
(Declared as Deemed to be University under Sec.3 of the UGC Act, 1956)
Supplementary Examination – June 2012
Subject Title: DISCRETE MATHEMATICS FOR BIOINFORMATICIANS
Time: 3 hours
Subject Code: 09MA202 Maximum Marks: 100
Answer ALL questions
PART – A (10 x 1 = 10 MARKS)1. If n(A) =3, then the number of subsets of A is _______.
2. If P is true and Q is false, then the truth value of P is _______.
3. Write in terms of factorials.
4. What is the probability of impossible event?
5. State absorption laws in a lattice.
6. Draw a graph of four vertices containing an Euler circuit.
7. Write the Newton – Raphson formula.
8. State the normal equations to fit a straight-line y= ax+b.
9. Give the order of error in Trapezoidal rule
10. State Euler’s algorithm to solve
PART – B (5 x 3 = 15 MARKS)
11. Prove by mathematical induction, 1+2+3+......+ n = .
12. If A= {x,y,z}, write all permutation functions defined on A.
13. Show that the following Lattice is non- distributive.
14. Compute three approximations for the root of in the interval (2,2.5) by bisection method.
15. Find y(0.1) by Taylor series method, given
PART – C (5 x 15 = 75 MARKS)
16. a. Prove that (6)
b. A survey of 500 television watchers produced following information: 285 watch football games, 195 watch hockey games, 115 watch basketball games, 45 watch football and basketball games.,70 watch football and hockey game, 50 watch hockey and basket ball games and 50 do not watch any of the three games. How many people in the survey watch all three kinds of games? (9)
(OR)
[P.T.O]
17. a. Construct the truth table for (8)
b. Prove the following:
i) (7)
18. a. An urn contains 15 balls of which 8 are red and 7 are black. In how many ways can five balls be chosen so that (i) all five are black (ii) three are red and two are black (iii) all five are red? (8)
b. A box contains 6 red and 4 green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be green? (7)
(OR)
19. a. Solve the recurrence relation (10)
b. Find the number of distinguishable permutations of the letters in BOOLEAN. (5)
20. a. Prove that a Poset has atmost are greatest element and atmost one least element. (8)
b. Consider the Boolean polynomial Construct the truth table for the Boolean function f: B3 B determined by this polynomial. (7)
(OR)
21. Using the Labeling algorithm, find a maximum flow for the following network.
22. a. Solve the system of equations x+2y+z=3, 2x+3y+3z=10, 3x-y+2z=13 by Gauss- elimination method, (7)
b. Solve, by Gauss-Seidel method, 27x+6y-z=85, 6x+15y+2z=72, x+y+54z=110 (8)
(OR)
23. Find the value of y at x=21 and x=28 from the following data
| x: |
20 |
23 |
26 |
29 |
| y: |
0.3420 |
0.3907 |
0.4384 |
0.4848 |
24. a. Evaluate by using (i) Trapezoidal rule and (ii) Simpson’s rule. (9)
b. The population y of a certain town is given below. Find the rate of growth of the population. (6)
| x: |
1931 |
1941 |
1951 |
1961 |
1971 |
| y: |
40.62 |
60.80 |
79.95 |
10.356 |
132.65 |
25. Obtain the values of y at x=0.1, 0.2 using R.K. Method of (a) Second order and (b) fourth order for the differential equation given y(0) =1.
| Earning: ₹ 0.00/- |
