Q. Let P, Q and R be sets let Δ denote the symmetric difference operator defined as PΔQ = (P U Q) - (P ∩ Q). Using Venn diagrams, determine which of the following is/are TRUE? PΔ (Q ∩ R) = (P Δ Q) ∩ (P Δ R) P ∩ (Q ∩ R) = (P ∩ Q) Δ (P Δ R)

View solution

Q. What is the cardinality of the set of integers X defined below? X = {n | 1 ≤ n ≤ 123, n is not divisible by either 2, 3 or 5} ?

View solution

Q. Let A = {a, b, c, d }, B = { p, q, r, s } denote sets. R : A –> B, R is a function from A to B. Then which of the following relations are not functions ?

(i) { (a, p) (b, q) (c, r) }
(ii) { (a, p) (b, q) (c, s) (d, r) }
(iii) { (a, p) (b, s) (b, r) (c, q) }

View solution

Q. Let A = { 1,2,3,4,…….∞ } and a binary operation ‘+’ is defined by a + b = ab ∀ a,b ∈ A. Which of the following is true ?

View solution

Q. The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is

View solution

Q. An n x n array v is defined as follows:

v[i, j] = i-j for all i, j, 1 <= i <= n, 1 <= j <= n

The sum of the elements of the array v is

View solution

Q. X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true?

View solution

Q. E1 and E2 are events in a probability space satisfying the following constraints:

Pr(E1) = Pr(E2)
Pr(EI U E2) = 1
E1 and E2 are independent

The value of Pr(E1), the probability of the event E1 is

View solution

Q. A polynomial p(x) satisfies the following:

p(1) = p(3) = p(5) = 1
p(2) = p(4) = -1

The minimum degree of such a polynomial is

View solution

Q. A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following state­ments is true?

View solution

Q. Let a, b, c, d be propositions. Assume that the equivalences a ↔ (b V-b) and b ↔ c hold. Then the truth value of the formula (a ∧ b) → (a ∧ c) ∨ d) is always

View solution

Q. Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false?

View solution

Q. Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?

View solution

Q. Consider the following statements:

S1: The sum of two singular n × n matrices may be non-singular
S2: The sum of two n × n non-singular matrices may be singular.

Which of the following statements is correct?

View solution

Q. Let f(n) = n^2Logn and g(n) = n (logn)^10 be two positive functions of n. Which of the following statements is correct?

View solution

Q. How many 4-digit even numbers have all 4 digits distinct?

View solution

Q. Let f: A→B be a function, and let E and F be subsets of A. Consider the following statements about images.

S1: f (E ∪ F) = f (E) ∪ f (F)
S1: f (E ∩ F) = f (E) ∩ f (F)

Which of the following is true about S1 and S2?

View solution

Q. Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?

View solution

Q. Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r,u) and d(r,v) be the lengths of the shortest paths from r to u and v respectively in G. If u is visited before v during the breadth-first traversal, which of the following statements is correct?

View solution

Q. How many undirected graphs (not necessarily connected) can be constructed out of a given set V = {v1, v2, ... vn} of n vertices?

View solution