Discrete Mathematics . Question With 100 Correct And Verified Answers. Latesr 2024 Update. A+ Grade.

UNIT 1 1. The range of the function f(x) = (x2 - x) / (x2 +2x) is a) R b) R - {1 } c) R - {-1/2, 1} d) None of these 2. The range of the function f(x) = x+2 / x +2 , x ≠ -2 is a) { -1, 1} b) { -1, 0, 1} c) {1} d) ( 0, ∞) 3. The domain of the function f(x) = √5 x -- x2 -6 is a) (-3, -2) U (2, 3) b) [-3, -2)U [2, 3) c) [ -3, -2] U [2,3] d) None of these 4. Which one of the following is not a function? a) { (x, y): x , y € R, x2 =y} b) { (x , y): x, y € R, y2 = x} c) { (x , y): x, y € R, x = y3} d) { (x , y): x, y € R, y = x3} 5. The sequence of the binary digits representing the outcomes of parity checks in Hamming codes is known as _________________. a) Look-up entry b) Hamming distance c) Radix d) Syndrome 6. If 3 f(x) + 5 f(1/x) = 1/x -3 for all non zero x, then f(x) = a) 1/14 (3/x +5x - 6) b) 1/14 (- 3/x +5x -6) c) 1/14 (-3/x +5x +6) d) None of these 7. The domain of definition of f(x) = √ 4x - x² is a) R-[0, 4] b) R-(0,4) c) (0, 4) d) [0, 4] 8. If R= {(2, 1), (4, 7), (1,2),…}then write the linear relation between the components of the ordered pairs of the relation R. a) y = 3x +6 b) y =2x - 5 c) y = 3x - 5 d) y = 2x + 5 9. Let R be a relation from a set A to a set B, then a) R= A U B b) R =A ∩ B c) R A X B d) R B X A 10. If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is a) 2mn b) 2mn - 1 c) 2mn d) mn 11. The Hamming code is a method of _______. a) Error detection b) Error correction c) Error encapsulation d) (a) and (b) 12. If R is a relation from a set A = { 11, 12, 13 } to set B = {8, 10, 12 } defined by y =x -3 then write R-1 a) { (8, 13), (11, 10)} b) { (8, 11), (10, 13)} c) { (10, 11), (8, 12)} d) { (0) } 13. If R = { (x, y) : x, y €Z, x² +y² ≤ 4} is a relation on Z, then domain of R is a) { 0, 1, 2} b) {0, -1, -2} c) { -2, -1, 0, 2} d) None of these 14. „Hamming Code is used in a) Programming code b) Data communication c) AutoCAD d) None of the above. 15. Let A= { 1, 2, 3, 5}, B ={4, 6, 9} and R be a relation from A to B defined by R = {(x , y): x -y is odd}. Write R in the roster form. a) R = { 1,2,3,5,4,6,9} b) R = { (1, 4), (1, 6), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)} c) R = {(1, 2), (1,3),(1, 5), (2, 9), (3, 4), (3, 6), (5, 4), (5, 6)} d) None of these 16. Let A and B be two sets such that n(A) = 3 and n( B)= 2. If (x, 1), (y, 2), (z, 1) are in AXB, write A and B a) A = {x, y, 2} B = {1, z} b) A = {x, 1, z} B ={y, 2} b) 1 c) 2 d) 3 c) A = {1, 2, z} B = {x, y} d) A = {x, y, z} B = {1, 2} 17. Which of the following is true a) a {b, c, a} b) {a} €{a, b, c} c) {a, b} = {a, a, b, b, a} d) The set {x: x+8 = 8} is a null set 18. The Hamming distance between 100 and 001 is _____. a) 0 19. Which are subsets of which: A={ x : x satisfies x² -8 +12 =0}, B= {2,4,6}, C={2,4,6.8…}, D ={6} a) D⊂A⊂B⊂C b) A B D C c) C A B D d) B A C D 20. A set consisting of single element is called a) Null set b) Singleton set c) Infinite set d) Empty set 21. The set of animals living on earth is: a) Finite set b) Infinite set c) Empty set d) Null set 22. In a survey of 700 students in a college, 180 were listed as drinking Limca, 275 as drinking Mrinda and 95 were listed as both drinking Limca and Miranda. Find how many students were drinking neither Limca nor Miranda. a) 315 b) 390 c) 340 d) 350 23. A market research group conducted a survey of 2000 consumers and reported that 1720 consumers liked product A and 1450 consumers liked product B. What is the least number that must have liked both the products? a) 1200 b) 980 c) 769 d) 1170 24. In order that a code is „t‟ error correcting, the minimum Hamming distance should be: a) t b) 2t-1 c) 2t d) 2t+1 25. If X and Y are two sets such that n(X) =17, n(Y) =23 and n(XUY) =38, find n( X∩Y) a) 40 b) 2 c) 25 d) 1 26. A college awarded 38 medals in football, 15 in basket and 20 to cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, How many received medals in exactly two of the three sports? a) 9 b) 8 c) 6 d) 10 27. If A = { 1, 3, 5, 7}, B={2, 4, 6, 8, 10} and let R={ (1,8), (3, 6), ( 5, 2), (1, 4)} be a relation from A to B, then domain is a) {8, 6, 2} b) {1, 2, 4} c) {1, 3, 5} d) {6, 2, 4} 28. To guarantee the detection of up to 5 errors in all cases, the minimum Hamming distance in a block code must be _______. a) 5 b) 6 c) 11 d) None of the above 29. Let f: R→R be a function given by f(x) =x² + 1. Find f-1 {26} a) {25, 5} b) {5, 0} c) {1,5} d) {-5, 5} 30. Find the range of the function f(x) = x² -9/ x-3 a) R - {3} b) {0} c) R -{6} d) {6, 3}