VU Midterm Past Papers
129 solved midterm past paper MCQs for MTH202 (Discrete Mathematics) at Virtual University, each with the correct answer marked. Use them to learn the VU question style and test your recall. An independent study tool — not affiliated with VU.
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Q1. Range of function f(x)=e^x is ___________
Q2. Composite relation symbolically written as _______
Q3. If x=17(mod 5) which of the following integers are valid solution for x ?
Q4. Range of the relation {(0,1),(3,22),(90,34)}
Q5. Let A= {0,1,2} and R = {(0,2),(1,1),(2,0)} be a relation on A. The which of the following ordered pairs are needed to make it transitive?
Q6. Operation of subtraction is a binary operation on the set of __________
Q7. Let S=R and define the ‘square’ relation R= {(x,y)Ix^2=y^2}. The square relation is an _________ relation
Q8. Let A= {1,2}, then P(A)=__________
Q9. If a relation R is reflexive, anti symmetric and transitive then which of the following is not true for the inverse relation.
Q10. Let R be a binary relation on a set A,R is anti-symmetric iff ___________
Q11. The inverse relation R^(-1) from B to A is defined as ____________
Q12. Which of the following is always true for the matrix representation of a symmetric relation?
Q13. Let A= {1,2,3,4} and let R and S be transitive binary relations on A defined as; R= {(1,2), (1,3), (2,2), (3,3), (4,2), (4,3) and S={(2,1), (2,4), (3,3)} then RuS= {(1,2), (1,3), (2,1), (2,2), (2,4), (3,3), (4,2), (4,3)}
Q14. Let S=R and define the ‘ square’ relation R = {(x,y)Ix^2=y^2}. The square is an _________ relation.
Q15. If x=-10(mod 15). Which of the following integers are valid solution for x?
Q16. Let R be a binary relation on a set A. If R is anti symmetric then ______________
Q17. If A={1,2,3} is a set and R = {(1,2),(2,2),(2,1)} is a relation on A, R is
Q18. Let A={0,1} and B=(1). Let R and S be two binary relations on Cartesian product of A and B such that R={(0,1)} and S= {(1,1)}. Then R intersection S=_________________
Q19. A relation R is said to be ______ iff it is reflexive, antisymmetric and transitive.
Q20. Let X={1,2,3} and Y={7,8,9} and let f be function defined from X to Y such that f is onto then which of the following statement about f is true?
Q21. If a relation R={(1,2),(2,3),(3,4)(4,1)(2,2) is given then which of the following is true about this relation.
Q22. A set is called countable if , and only if, it is____________
Q23. Let f(x) = x^2-1 define function f from R to R and c=2 be any scalar, then c,f(x) is __________
Q24. The set Z of all integers is ___________
Q25. For (2x-3, 4y+2) = (1,10). What will be the value of x and y ?
Q26. Let f and g be the two functions from R to R defined by f(x) = IxI and g(x)= square root of x^2 for all xeR. Then______
Q27. If a set A has 15 elements then P(A) (power set of A) has ___________ elements.
Q28. For the relation below to be a function, x cannot be what values {(12,14),(13,5),(-2,7),(x,13)}?
Q29. Let the set A = {1,2,3,4}. Then the relation {(2,4),(4,2)} is ____________
Q30. For the following relation to be a function, x can not be what values? R={(2,4),(x,1), (4,2),(5,6)}.
Q31. The properties of being symmetric and being anti symmetric are ____________
Q32. The number of elements in AxB are ___________ if A is a set with ‘5’ elements and B is a set with ‘4’ elements.
Q33. R={(a,1)(b,2)(c,3)(d,4)} then the inverse of this relation is _____________
Q34. Logic gate NOT does not define a binary operation on (0,1) because ____________
Q35. How many real numbers exist between 1 and 5
Q36. The number pi is
Q37. The number square root 2 is
Q38. Range the relation {(0,1)(3,22),(90,34)}
Q39. Supherical coordinate 0 is related to the cylindrical coordinate as_____________
Q40. Operation of subtraction is a binary operation on the set________
Q41. Let A {1,2,3,4} and R={(1,2),(2,3),(3,3),(3,4)} be a relation on A. Then which one of the following ordered pair has made R not an irreflexive relation?
Q42. Input values of the function are called the ____________
Q43. Range of function f(x)=IxI will be
Q44. Which of the following is not a binary operation on the set of integers?
Q45. In the matrix representation of an irreflexive relation all the entries in the main diagonal are __________
Q46. If the partition set of A is {A1,A2} then
Q47. Let A= {a,b} then P(A) =
Q48. Which relations below are not functions?
Q49. In the directed graph of an antisymmetric relation there is _________ pair of arrows between two distinct elements of the set.
Q50. If a relation R= (1,1),(2,1)(2,2) is given then which of the following is not true about this relation
Q51. Let R and S be transitive relations on a set A then ________________
Q52. Let R={(1,2)(3,4)(5,6)(7,8)}. Domain of the inverse of the relation is _____________
Q53. Let A={1,2,3,4,5} and B={4,9,,16,17,25}. Then the relation R={(2,4),(3,9),(4,16),93,17)} The inverse of R is’
Q54. Let R be a relation on a set A. If R is symmetric then its compliment is __________
Q55. Which is not a binary operation on the set of natural numbers N?
Q56. If a relation R={(1,1)(2,1)(1,2)(2,2)} is given then which of the following is not true about this relation.
Q57. For any set A, the Cartesian product of A and A is known as ____________
Q58. Let A={p,q,r,s} and define a relation R on A by R={(p,p),(p,r),(q,r),(q,s),(r,s)} Then which one of the following is the correct statement about R:
Q59. A={1,2} B={3,4}, R={(1,3)(2,4)}. Then the complement of R is __________.
Q60. Domain of a relation symbolically written as____________.
Q61. Let X={2,4,5} and Y={1,2,4} and R be a relation from X to Y defined by R={(2,4)(4,1)(a,2)}. For what value of ‘a’ the relation R is a function?
Q62. Let A={1,2,3,4,5,6,7,8,9}, then which of the following sets represent the partition of the set A?
Q63. Let A={1,2,3} and B={2,4} then number of binary relations from A to B are _____________.
Q64. A relation R is said to be ________iff it is reflexive, antisymmetric and transitivde.
Q65. Let f be a function from X={2,4,5} to Y={1,2,4,6} defined as:f={(2,6),(4,2),(5,1)} . The range of f is _________
Q66. Let A={0,1,2} and R={(0,2),(1,1),(2,0)} be a relation on A. Then which of the following statement about R is true?
Q67. Let A={2,3,4} and B={2,6,8} and let R be the “divides” relation from A to B i.e for all (a,b) belong to (Cartesian product of A and B), a,R b iff a I b (a divides b). Then
Q68. Common ration in the sequence “4, 16, 64, 256,...” is.....
Q69. The word ‘algorithm’ refers to a step-by-step method for performing some action.
Q70. A predicate become ______ when its variables are given specific values
Q71. The sum of two irrational numbers must be an irrational number.
Q72. The sum of two irrational numbers need not be irrational number
Q73. The division by zero is allowed in mathematics.
Q74. The product of any two consecutive positive integers is divisible by 2
Q75. If ‘n’ is an odd integer then n^3+n is ________.
Q76. For integers a,b,c, If divides b and a divides c, then a divides (a+b).
Q77. Quotient remainder theorem states that for any positive integer d, there exist unique integer q and r such that ________ and 0<r<d
Q78. A rule that assigns a numerical value to each outcome in a simple space is called
Q79. If A and B are two disjoint (mutually exclusive) events then P(AB)=
Q80. How many ways are there to select five players from a 10 member tennis team to make a trip to a match to another school?
Q81. The expectation of x is equal to
Q82. If P(A intersection B) = P(A) P(B) THEN THE events A and B are called
Q83. A walk that starts and ends at the same vertex is called.
Q84. How many integers from 1 through 1000 are neither multiple of 3 nor multiple of 5
Q85. What is the probability of getting a number greater than 4 when a die is thrown?
Q86. Eater formula for graphs is___________.
Q87. X+a,x+3a,x+5a.....is an____________
Q88. Real valued function is a function that assigns _____ to each member of its domain.
Q89. Let X={1,2,3,4} and a function ‘f’ defined on X f(1)=1,f(2)=2,f(3)=3,f(4)=4 then ________
Q90. A constant function is surjective if and only if ____________
Q91. Cardinality means the total number of elements in a set.
Q92. If f(x)=2x and g(x)=x then g(f(x)) is _________.
Q93. Let f:R->R is one to one function then c,f, c is not equal 0 is also one to one function.
Q94. Let X={1,2,3,4} and a function ‘f’ defined from X to X by f(1)=1, f(2)=1, f(3)=1, f(4)=1 then which of the following is true?
Q95. Which of the following is not correct for a ‘sequence’?
Q96. F(x)=x^2 is not one to one function from R to R^+
Q97. Let f: R->R is one to one function then c,f c is not equal to is also one to one function.
Q98. Let f(x)=x+2 then f^-1(x) is________
Q99. Let f(x)=x^2+1 define functions f from R to R and c=2 be any scalar, then c,f(x) is __________.
Q100. A function F: R-> R defined by f(x) = square root x is a real valued function.
Q101. If g:R->R defined by g(x)=e^2 is a real valued function of a real variable.
Q102. A function F:R-> R defined by f(x) = log x is a real valued function
Q103. ½, then 3rd term of sequence is __________.
Q104. The process of defining an object in terms of smaller versions of itself is called recursion.
Q105. A set that is not countable is called ___________.
Q106. Let f: R->R is one to one function then c,f is also one to one function for _______.
Q107. Let f(x) = x+3 then f^-1(x) is __________-
Q108. Let f and g be two functions defined by f(x) = x+2 and g(x)= 2x+1. Then the composition of f and g is__________.
Q109. Number of one to one functions form X={a,b} to Y={u,v} are equal to ______
Q110. The flbonacci sequence is deined as F0=1, F1=1, Fk=Fk-1+Fk-2 for all integers k> 2 then which of the following is true for F2
Q111. x+a, x+3a, x+5a,...... is a/an______.
Q112. Inverse of a function may not be a function.
Q113. In the following sequence ak=K/(k+1), for k=1, a1 will be __________.
Q114. If f(x)=x and g(x)= -x are both one to one function then (f+g)(x) is also one to one function.
Q115. If f(x)=x and g(x)= -x are both one to one function then (f+g)(x) is not one to one function.
Q116. The function ‘f’ and ‘g’ are inverse of each other if and only if their composition gives_______.
Q117. Which of the following set is the domain of a sequence?
Q118. Let C is defined as the set of all countries in the world then C is a _________.
Q119. The composition of function is always
Q120. A set is countably infinite if, and only if, it has the same cardinality as the set of
Showing the first 120 of 129 MCQs.