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Discmath F3
Discmath
| Question | Answer |
|---|---|
| If X = Floor(X) = Ceil(X) then : a) X is a fractional number b) X is a Integer c) X is less than 1 d) none of the mentioned | b) X is a Integer |
| A ceil function map a real number to : a) smallest previous integer b) greatest previous integer c) smallest following integer d) none of the mentioned | c) smallest following integer |
| A floor function map a real number to : a) smallest previous integer b) greatest previous integer c) smallest following integer d) none of the mentioned | b) greatest previous integer |
| If x, and y are positive numbers both are less than one ,then maximum value of ceil(x + y) is? a) 0 b) 1 c) 2 d) -1 | c) 2 |
| If x, and y are positive numbers both are less than one, then maximum value of floor(x + y) is? a) 0 b) 1 c) 2 d) -1 | b) 1 |
| State whether the given statement is true or false For some integer n such that x < n < x + 1, ceil(x) < n . a) True b) False | False |
| State whether the given statement is true or false For some number x, Floor(x) <= x <= Ceil(x). a) True b) False | True |
| State True or False. Let n be some integer greater than 1,then floor((n-1)/n) is 1. a) True b) False | False |
| Floor(2.4) + Ceil(2.9) is equal to : a) 4 b) 6 c) 5 d) none of the mentioned | c) 5 |
| Range of a function is : 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 set of natural numbers for which a function is defined d) none of the mentioned | b) the maximal set of numbers which a function can take values |
| State whether the given statement is true or false For an onto function range is equivalent to codomain. a) True b) False | True |
| A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m ≤ n then number of one one functions are : a) nCm x m! b) nCm x n! c) 0 d) none of the mentioned | a) nCm x m! |
| function is defined by mapping f:A->B such that A contains m elements and B contains n elements and m > n then number of bijections are : a) nCm x m! b) nCm x n! c) 0 d) none of the mentioned | c) 0 |
| A mapping f : X -> Y is one one if : a) f(x1) ≠ f(x2) for all x1, x2 in X. b) If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X. c) f(x1) = f(x2) for all x1, x2 in X. d) None of the mentioned | b) If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X. |
| An injection is a function which is : a) many-one b) one-one c) onto d) none of the mentioned | b) one-one |
| Set A has 3 elements and set B has 4 elements then number of injections defined from A to B are? a) 12 b) 24 c) 36 d) 48 | b) 24 |
| State whether the given statement is true or false Onto function are known as injection. a) True b) False | False |
| State True or False. A bijection is a function which is many-one and onto. a) True b) False | False |
| A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m>n then number of one one functions are : a) nCm x m! b) nCm x n! c) 0 d) none of the mentioned | c) 0 |
| A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are: a) r=1∑r=n nCr (-1)n-r rm b) r=1∑r=n nCr (-1)n-r rn c) r=1∑r=n nCr (-1)m-r rn d) None of the mentioned | a) r=1∑r=n nCr (-1)n-r rm |
| If f(x) = (x3 – 1) / (3x + 1) then f(x) is a) O(x2) b) O(x) c) O(x2 / 3) d) O(1) | a) O(x2) |
| The big-Omega notation for f(x) = 2x4 + x2 – 4 is a) x2 b) x3 c) x d) x4 | d) x4 |
| The domain of the function that assign to each pair of integers the maximum of these two integers is ___________ a) N b) Z c) Z + d) Z+ X Z+ | d) Z+ X Z+ |
| The function f(x) = x3 is bijection from R to R. Is it True or False? a) True b) False | True |
| The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False? a) True b) False | True |
| Which of the following is true? a) A graph may contain no edges and many vertices b) A graph may contain many edges and no vertices | b) A graph may contain many edges and no vertices |
| A graph with all vertices having equal degree is known as a __________ a) Multi Graph b) Regular Graph c) Simple Graph d) Complete Graph | b) Regular Graph |
| If a simple graph G, contains n vertices and m edges, the number of edges in the Graph G'(Complement of G) is ___________ a) (n*n-n-2*m)/2 b) (n*n+n+2*m)/2 | a) (n*n-n-2*m)/2 |
| two vertices connected with an edge | adjacent |
| What is the number of edges present in a complete graph having n vertices? a) (n*(n+1))/2 b) (n*(n-1))/2 | b) (n*(n-1))/2 |
| State True or False. Let f(x)=sin2(x) + log(x) then domain of f(x) is (-∞, ∞). a) True b) False | False |
| The big-O notation for f(n) = 2log(n!) + (n2 + 1)logn is a) n b) n2 c) nlogn d) n2logn | d) n2logn |
| Which of the following function f: Z X Z → Z is not onto? a) f(a, b) = a + b b) f(a, b) = a c) f(a, b) = |b| d) f(a, b) = a – b | c) f(a, b) = |b| |
| __________ bytes are required to encode 2000 bits of data. a) 1 b) 2 c) 3 d) 8 | b) 2 |
| In the given graph identify the cut vertices. A -> B -> C -> E ^ ^ < - --D | C and B |
| What is the maximum number of edges in a bipartite graph having 10 vertices? a) 24 b) 21 c) 25 d) 16 | c) 25 |
| Vertex that is not connected to any other vertex | Isolated vertex |
| Which of the following ways can be used to represent a graph? a) Adjacency List and Adjacency Matrix b) Incidence Matrix c) Adjacency List, Adjacency Matrix as well as Incidence Matrix d) No way to represent | a) Adjacency List and Adjacency Matrix |
| State whether the given statement is true or false Codomain is the subset of range. a) True b) False | False |
| The little-o notation for f(x) = xlogx is a) x b) x3 c) x2 d) xlogx | c) x2 |
| 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 | a) O(g(x)) |
| 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} | d) {x | 0 ≤ x ≤ 1} |
| Number of edges that have a specific vertex as an endpoint | Degree of Vertex |
| For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true? a) v=e b) v = e+1 | b) v = e+1 |
| Which of the following properties does a simple graph not hold? a) Must be connected b) Must be unweighted c) Must have no loops or multiple edges d) Must have no multiple edges | a) Must be connected |
| Which of the following statements for a simple graph is correct? a) Every path is a trail b) Every trail is a path | a) Every path is a trail |
| The big-theta notation for function f(n) = 2n3 + n – 1 is a) n b) n2 c) n3 d) n4 | c) n3 |
| 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-many b) One-to-one c) Many-to-many d) Many-to-one | b) One-to-one |
| The inverse of function f(x) = x3 + 2 is ____________ a) f -1 (y) = (y – 2) 1/2 b) f -1 (y) = (y – 2) 1/3 c) f -1 (y) = (y) 1/3 d) f -1 (y) = (y – 2) | b) f -1 (y) = (y – 2) 1/3 |
| THE GIVEN GRAPH IS REGULAR. | True |
| A connected planar graph having 6 vertices, 7 edges contains _____________ regions. a) 15 b) 3 c) 1 d) 11 | b) 3 |
| What is domain of function f(x) = x-1 for it to be defined everywhere on domain? a) (2, ∞) b) (-∞, ∞) – {0} c) [0, ∞) d) None of the mentioned | b) (-∞, ∞) – {0} |
| The big-theta notation for f(n) = nlog(n2 + 1) + n2logn is a) n2logn b) n2 c) logn d) nlog(n2) | a) n2logn |
| The big-O notation for f(n) = (nlogn + n2)(n3 + 2) is a) O(n2) b) O(3n) c) O(n4) d) O(n5) | d) O(n5) |
| An edge that connects a vertex to itself | loop |
| If f(x) = x2 + 4 then range of f(x) is given by a) [4, ∞) b) (-∞, ∞) – {0} c) (0, ∞) d) None of the mentioned | a) [4, ∞) |
| The big-omega notation for f(x, y) = x5y3 + x4y4 + x3y5 is a) x5y3 b) x5y5 c) x3y3 d) x4y4 | c) x3y3 |
| The value of ⌊1/2.⌊5/2⌋ ⌋ is ______________ a) 1 b) 2 c) 3 d) 0.5 | a) 1 |
| 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 | a) 6x + 9 |
| The big-O notation for f(x) = 5logx is a) 1 b) x c) x2 d) x3 | b) x |
| For the given graph(G), which of the following statements is true? a. G is a complete graph b) G is not a connected graph c) The vertex connectivity of the graph is 2 | c) The vertex connectivity of the graph is 2 |
| What is domain of function f(x)= x1/2 ? a) (2, ∞) b) (-∞, 1) c) [0, ∞) d) None of the mentioned | a) (2, ∞) |
| If f(x) = 2x then range of the function is : a) (-∞, ∞) b) (-∞, ∞) – {0} c) (0, ∞) d) None of the mentioned | c) (0, ∞) |
| In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices. | False |
| A path exist between each pair of vertices. | connected graph |
| Domain of a function is : 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 set of natural numbers for which a function is defined d) none of the mentioned | a) the maximal set of numbers for which a function is defined |
| State whether the given statement is true or false The range of function f(x) = sin(x) is (-∞, ∞). a) True b) False | False |
| If f(x) = 3x2 + x3logx, then f(x) is | b) O(x3) |
| What is range of function f(x) = x-1 which is defined everywhere on its domain? | a) (-∞, ∞) |
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pioneerxxXXxx