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

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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

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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?

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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

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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?

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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?

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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?

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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?

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

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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?

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

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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?

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

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Q. The trapezoidal rule for integration give exact result when the integrand is a polynomial of degree:

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Q. The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is

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Q. If X, then Y unless Z" is represented by which of the following formulae in propositional logic? ("¬" is negation "^" is conjunction, and "→" is implication)

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Q. The decimal value 0.25

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Q. Maximum number of edges in a n - node undirected graph without self loops is

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Q. The Newton-Raphson iteration Xn + 1 = (Xn/2) + 3/(2Xn) can be used to solve the equation

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Q. Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is :

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