Let set a = {1, 2} and c be {3, 4} thenaxb


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  1. Let set A = {1, 2} and C be {3, 4} then A X B (Cartesian product of set A and B) is?
    a) {(1, 3), (2, 4), (1, 4), (2, 3)}
    b) {(1, 3),(2, 4)}
    c) {1, 2, 3, 4}
    d) {(3, 1), (4, 1)}



  2. If set A has 4 elements and B has 3 elements then set n(A X B) is?
    a) 12
    b) 14
    c) 24
    d) 7



  3. If set A has 3 elements then number of elements in A X A X A are __________
    a) 27
    b) 9
    c) 6
    d) 19



  4. Which of the following statements regarding sets is false?
    a) A X B = B X A
    b) A X B ≠ B X A
    c) n(A X B) = n(A) * n(B)
    d) All of the mentioned



  5. If n(A X B) = n(B X A) = 36 then which of the following may hold true?
    a) n(A)=6, n(b)=6
    b) n(A)=9, n(B)=4
    c) n(A)=2, n(B)=18
    d) None of the mentioned



  6. Let the sets be A, B, C, D then (A ∩ B) X (C ∩ D) is equivalent to __________
    a) (A X C) ∩ (B X D)
    b) (A X D) U (B X C)
    c) (A X C) U ( B X D)
    d) None of the mentioned



  7. If A ⊆ B then A X C ⊆ B X C the given statement is true or false.
    a) True
    b) False



  8. If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is?
    a) 4096
    b) 2048
    c) 512
    d) 1024



  9. If set A X B=B X A then which of the following sets may satisfy?
    a) A={1, 2}, B={2, 1} A={1, 2, 3}, B={1, 2, 3, 4}
    b) A={1, 2, 3}, B={1, 2, 3, 4}
    c) A={1, 2, 3}, B={2, 3, 4}
    d) None of the mentioned



  10. If a set contains 3 elements then the number of subsets is?
    a) 8
    b) 3
    c) 12
    d) 6



  11. The set containing all the collection of subsets is known as _________
    a) Power set
    b) Subset
    c) Union set
    d) None of the mentioned



  12. If a set is empty then number of subsets will be _________
    a) 1
    b) 2
    c) 0
    d) 4



  13. If the number of subsets of a set are 4 then the number of elements in that sets are _________
    a) 2
    b) 3
    c) 1
    d) 4



  14. The number of subsets of a set can be odd or even.
    a) True
    b) False



  15. Let a set be A={1, 2, 3} then the number of subsets containing two elements will be _________
    a) 3
    b) 4
    c) 5
    d) 8



  16. Let the set be A= {a, b, c, {a,b}} then which of the following is false?
    a) {a} Є A
    b) a Є A
    c) {a, b} Є A
    d) b, c ЄA



  17. If A={1, 2, 3, 4}, then the number of the subsets of A that contain the element 2 but not 3, is?
    a) 4
    b) 16
    c) 8
    d) 24



  18. Let A(1), A(2), A(3),…….., A(100) be 100 sets such that number of elements in A(i)=i+1 and A(1) is subset of A(2), A(2)is subset of A(3),….., A(99) is subset of A(100). The number of elements in union of the all the sets are: n(A(1) U A(2) U A(3) …..U A(100)).
    a) 101
    b) 100
    c) 99
    d) 102



  19. A function is said to be ______________ if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f.
    a) One-to-one
    b) One-to-many
    c) Many-to-many
    d) Many-to-one



  20. The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
    a) True
    b) False



  21. The value of ⌊1/2.⌊5/2⌋ ⌋ is ______________
    a) 1
    b) 2
    c) 3
    d) 0.5



  22. Which of the following function f: Z X Z → Z is not onto?
    a) f(a, b) = |b|
    b) f(a, b) = a
    c) f(a, b) = a + b
    d) f(a, b) = a – b



  23. The domain of the function that assign to each pair of integers the maximum of these two integers is ___________
    a) Z+ X Z+
    b) Z
    c) Z +
    d) N



  24. Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ____________
    a) 6x + 9
    b) 6x + 7
    c) 6x + 6
    d) 6x + 8



  25. __________ bytes are required to encode 2000 bits of data.
    a) 2
    b) 1
    c) 3
    d) 8



  26. The inverse of function f(x) = x3 + 2 is ____________
    a) f -1 (y) = (y – 2) 1/3
    b) f -1 (y) = (y – 2) 1/2
    c) f -1 (y) = (y) 1/3
    d) f -1 (y) = (y – 2)



  27. The g -1({0}) for the function g(x)= ⌊x⌋ is ___________
    a) {x | 0 ≤ x ≤ 1}
    b) {x | 0 < x ≤ 1}
    c) {x | 0 < x < 1}
    d) {x | 0 ≤ x < 1}






  1. If f(x) = (x3 – 1) / (3x + 1) then f(x) is?
    a) O(x2)
    b) O(x)
    c) O(x2 / 3)
    d) O(1)



  2. If f(x) = 3x2 + x3logx, then f(x) is?
    a) O(x3)
    b) O(x2)
    c) O(x)
    d) O(1)



  3. The big-O notation for f(n) = (nlogn + n2)(n3 + 2) is?
    a) O(n5)
    b) O(3n)
    c) O(n4)
    d) O(n2)



  4. The big-theta notation for function f(n) = 2n3 + n – 1 is?
    a) n3
    b) n2
    c) n
    d) n4



  5. The big-theta notation for f(n) = nlog(n2 + 1) + n2logn is?
    a) n2logn
    b) n2
    c) logn
    d) nlog(n2)



  6. The big-omega notation for f(x, y) = x5y3 + x4y4 + x3y5 is?
    a) x3y3
    b) x5y5
    c) x5y3
    d) x4y4



  7. If f1(x) is O(g(x)) and f2(x) is o(g(x)), then f1(x) + f2(x) is?
    a) O(g(x))
    b) o(g(x))
    c) O(g(x)) + o(g(x))
    d) None of the mentioned



  8. The little-o notation for f(x) = xlogx is?
    a) x2
    b) x3
    c) x
    d) xlogx




  1. The big-O notation for f(n) = 2log(n!) + (n2 + 1)logn is?
    a) n2logn
    b) n2
    c) nlogn
    d) n



  2. The big-O notation for f(x) = 5logx is?
    a) x
    b) 1
    c) x2
    d) x3



  3. The big-Omega notation for f(x) = 2x4 + x2 – 4 is?
    a) x4
    b) x3
    c) x
    d) x2



  4. What is the domain of a function?
    a) the maximal set of numbers for which a function is defined
    b) the maximal set of numbers which a function can take values
    c) it is a set of natural numbers for which a function is defined
    d) none of the mentioned



  5. What is domain of function f(x)= x1/2?
    a) [0, ∞)
    b) (-∞, 1)
    c) (2, ∞)
    d) None of the mentioned



  6. What is the range of a function?
    a) the maximal set of numbers which a function can take values
    b) the maximal set of numbers for which a function is defined
    c) it is set of natural numbers for which a function is defined
    d) none of the mentioned



  7. What is domain of function f(x) = x-1 for it to be defined everywhere on domain?
    a) (-∞, ∞) – {0}
    b) (2, ∞)
    c) [0, ∞)
    d) None of the mentioned



  8. The cardinality of the set A = {1, 2, 3, 4, 6} is?
    a) 5
    b) 6
    c) Integer
    d) None of the mentioned



  9. For two equal sets there ___________
    a) Cardinality is same
    b) Cardinality is different
    c) May be same or different
    d) None of the mentioned



  10. If A is a subset of B then _______
    a) The cardinality of B is greater than A The cardinality of A is greater than B
    b) The cardinality of A is greater than B
    c) Can’t say
    d) None of the mentioned



  11. If there is a bijection between two sets A and B then _______
    a) Cardinality of B is equal to A
    b) Cardinality of B is greater than A
    c) Cardinality of A is greater than B
    d) None of the mentioned



  12. Let a set E ={0,2,4,6,8….} of non-negative even numbers and O = {1, 3, 5, 7, 9,…..} of non-negative odd numbers then?
    a) Cardinality of set E is equal to that of O
    b) Cardinality of set O is greater than that of E
    c) Cardinality of set E is greater than that of O
    d) None of the mentioned



  13. If for sets A and B there exists an injective function but not bijective function from A to B then?
    a) Cardinality of B is strictly greater than A
    b) Cardinality of A is strictly greater than B
    c) Cardinality of B is equal to A
    d) None of the mentioned



  14. If cardinality of (A U B) = cardinality of A+ cardinality of B. This means ____________
    a) A and B are disjoint
    b) B is a subset of A
    c) A is a subset of B
    d) None of the mentioned



  15. If A is a subset of B and B is a subset of C, then cardinality of A U B U C is equal to ____________
    a) Cardinality of C
    b) Cardinality of B
    c) Cardinality of A
    d) None of the mentioned



  16. An algorithm is a _________ set of precise instructions for performing computation.
    a) Finite
    b) Infinite
    c) Constant
    d) None of the mentioned



  17. Out of the following which property algorithms does not share?
    a) Constancy
    b) Finiteness
    c) Generality
    d) Input



  18. In ________ search each element is compared with x till not found.
    a) Sequential
    b) Binary l
    c) Merge
    d) None of the mentioned



  19. If the entire list is searched sequentially without locating x in linear search, the solution is __________
    a) 0
    b) -1
    c) 1
    d) 2



  20. To sort a list with n elements, the insertion sort begins with the __________ element.
    a) Second
    b) First
    c) Third
    d) Fourth



  21. __________ comparisons required to sort the list 1, 2, 3…….n using insertion sort.
    a) (n2 + n – 2) / 2
    b) (n3 + n – 2) / 2
    c) (n2 + n + 2) / 2

d) (n2 – n – 2) / 2



  1. The Worst case occurs in linear search algorithm when ____________
    a) Item is the last element in the array or is not there at all
    b) Item is not in the array at all
    c) Item is the last element in the array
    d) Item is somewhere in the middle of the array



  2. List obtained in third pass of selection sort for list 3, 5, 4, 1, 2 is ___________
    a) 1, 2, 3, 4, 5
    b) 1, 2, 4, 3, 5
    c) 1, 5, 4, 3, 2
    d) 3, 5, 4, 1, 2



  3. The operation of processing each element in the list is known as _________
    a) Traversal
    b) Merging
    c) Inserting
    d) Sorting



  4. The complexity of Bubble sort algorithm is _________
    a) O(n2)
    b) O(log n)
    c) O(n)
    d) O(n log n)



  5. An Algorithm is ___________
    a) A procedure for solving a problem
    b) A problem
    c) A real life mathematical problem
    d) None of the mentioned



  6. An algorithm in which we divide the problem into subproblem and then we combine the subsolutions to form solution to the original problem is known as _________
    a) Divide and Conquer
    b) Brute Force
    c) GreedyAlgorithm
    d) None of the mentioned



  7. An algorithm which uses the past results and uses them to find the new results is _________
    a) Dynamic programming algorithms
    b) Divide and Conquer
    c) Brute Force
    d) None of the mentioned



  8. A Complexity of algorithm depends upon _________
    a) Both Time and Space
    b) Space only
    c) Time only
    d) None of the mentioned



  9. An algorithm which tries all the possibilities unless results are satisfactory is and generally is time-consuming is _________
    a) Brute Force
    b) Divide and Conquer
    c) Dynamic programming algorithms
    d) None of the mentioned



  10. For a recursive algorithm _________
    a) a base case is not necessary
    b) a base case is necessary and is solved without recursion
    c) doesnot solve a base case directly
    d) none of the mentioned



  11. Optimization of algorithm means _________
    a) making that algorithm fast by time and compact by space
    b) making that algorithm slow by time and large by space
    c) making that algorithm fast by time and large by space
    d) making that algorithm slow by time and compact by space



  12. For an algorithm which is the most important characteristic that makes it acceptable _________
    a) Correctness and Precision
    b) Compact
    c) Fast
    d) None of the mentioned



  13. An algorithm: can be represented through _________
    a) all of the mentioned
    b) pseudo codes
    c) instructions in common language
    d) flow charts



  14. There are two algorithms suppose A takes 1.41 milli seconds while B takes 0.9 milliseconds, which one of them is better considering all other things the same?
    a) B is better than A
    b) A is better than B
    c) Both are equally good
    d) None of the mentioned



  15. Which of the following case does not exist in complexity theory?
    a) Null case
    b) Worst case
    c) Average case
    d) Best case



  16. The complexity of linear search algorithm is _________
    a) O(n)
    b) O(log n)
    c) O(n2)
    d) O(n log n)



  17. The Worst case occur in linear search algorithm when _________
    a) Item is the last element in the array or is not there at all
    b) Item is not in the array at all
    c) Item is the last element in the array
    d) Item is somewhere in the middle of the array




  1. The complexity of Fibonacci series is _________
    a) O(2n)
    b) O(log n)
    c) O(n2)
    d) O(n log n)



  2. The worst case occurs in quick sort when _________
    a) Pivot is the smallest element
    b) Pivot is the median of the array
    c) Pivot is the middle element
    d) None of the mentioned



  3. Which is used to measure the Time complexity of an algorithm Big O notation?
    a) all of the mentioned
    b) characterises a function based on growth of function
    c) upper bound on growth rate of the function
    d) describes limiting behaviour of the function




  1. If for an algorithm time complexity is given by O(1) then the complexity of it is ____________
    a) constant
    b) polynomial
    c) exponential
    d) none of the mentioned



  2. If for an algorithm time complexity is given by O(log2n) then complexity will be ___________
    a) none of the mentioned
    b) polynomial
    c) exponential
    d) constant



  3. If for an algorithm time complexity is given by O(n) then the complexity of it is ___________
    a) linear
    b) constant
    c) exponential
    d) none of the mentioned



  4. If for an algorithm time complexity is given by O((32)n) then complexity will be ___________
    a) exponential
    b) quardratic
    c) constant
    d) none of the mentioned



  5. The number of factors of prime numbers are ___________
    a) 2
    b) 3
    c) Depends on the prime number
    d) None of the mentioned



  6. How many prime numbers are there between 1 to 20?
    a) None of the mentioned
    b) 6
    c) 7
    d) 5



  7. Sum of two different prime number is a ____________
    a) Either Prime or Composite
    b) Composite number
    c) Prime number
    d) None of the mentioned



  8. Difference of two distinct prime numbers is?
    a) None of the mentioned
    b) Even and composite
    c) Odd and prime
    d) All of the mentioned



  9. If a, b, c, d are distinct prime numbers with an as smallest prime then a * b * c * d is a ___________
    a) Even number
    b) Odd number
    c) Prime number
    d) None of the mentioned



  10. If a, b are two distinct prime number than a highest common factor of a, b is ___________
    a)1
    b) 0
    c) 2
    d) ab



  11. {x: x is an integer neither positive nor negative} is ________
    a) Non- empty and Finite set
    b) Non-empty set
    c) Finite set
    d) Empty set



  12. {x: x is a real number between 1 and 2} is an ________
    a) Infinite set
    b) Finite set
    c) Empty set
    d) None of the mentioned



  13. Number of power set of {a, b}, where a and b are distinct elements.
    a) 4
    b) 3
    c) 2
    d) 5



  14. Which of the following is subset of set {1, 2, 3, 4}?
    a) All of the mentioned
    b) {1, 2, 3}
    c) {1}
    d) {1, 2}



  15. A = {∅,{∅},2,{2,∅},3}, which of the following is true?
    a) ∅ ⊂ A
    b) {2} ∈ A
    c) {{∅,{∅}} ∈ A
    d) 3 ⊂ A



  16. Subset of the set A= { } is?
    a) All of the mentioned
    b) {}
    c) ∅
    d) A



  17. {x: x ∈ N and x is prime} then it is ________
    a) Infinite set
    b) Finite set
    c) Empty set
    d) Not a set



  18. The complement of the set A is _____________
    a) U – A
    b) A – B
    c) A – U
    d) B – A



  19. The shaded area of figure is best described by?

    a) A ∩ B
    b) A U B
    c) A
    d) B



  20. The shaded area of figure is best described by?

    a) A U B -B
    b) A‘ (Complement of A)
    c) A ∩ B
    d) B



  21. If n(A)=20 and n(B)=30 and n(A U B) = 40 then n(A ∩ B) is?
    a) 10
    b) 30
    c) 40
    d) 20



  22. The shaded area of figure is best described by?

    a) B – (A ∩ B) – (C ∩ B)
    b) A‘ (Complement of A)
    c) A ∩ C ∩ B
    d) B’ (Complement of B)



  23. Let A: All badminton player are good sportsperson.
    B: All person who plays cricket are good sportsperson.
    Let X denotes set of all badminton players, Y of all cricket players, Z of all good sportsperson. Then which of the following statements is correct?
    a) Z contains both X and Y
    b) Z contains X and Y is outside
    c) X contains Y and Z
    d) None of the mentioned



  24. In the given figure the if n(A)=20,n(U)=50,n(C)=10 and n(A∩B)=5 then n(B)=?

    a) 35
    b) 20
    c) 30
    d) 10



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