Discuss the methods of representing the sets.
[5 marks]Which of the following relations are functions? Give reasons and also find the domain and range of the function.
[5 marks]f = {(1, 3), (1, 5), (2, 3), (2, 5)} (ii) g = {(2, 1), (5, 1), (8, 1), (11, 1)}
[ marks]Express the sum, difference, product, and quotient of the following complex numbers as a complex number. Z = −2 + i1 Z = 1 − 2i2
[5 marks]Find the determinant of the given matrix:
[5 marks]If (cid:1)={1,2,3}, (cid:2)={2,3,4}, (cid:3)={1,3,4} and (cid:4)= {2,4,5} , then verify that ((cid:1)×(cid:2)) ∩ ((cid:3)×(cid:4)) = ((cid:1)∩(cid:3)) × ((cid:2)∩(cid:4)).
[5 marks]Explain the matrix operations with suitable example.
[5 marks]Find the sample variance of the data set 2, 6, 12, 15.
[5 marks]Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards.
[5 marks]Differentiate between the Permutation and Combination.
[5 marks]Simplify the Boolean function F = AB + (AC)′ + AB′C(AB + C).
[5 marks]Acoin is tossed, and a die is rolled. What is the probability that the coin shows the head and the die shows 3?
[5 marks]Explain the absolute measures of dispersion with suitable example. Page 1 of
[2 marks]Draw the truth table of the given Boolean expression: A . ¬ (B + (C.D)).
[5 marks]Solve the given quadratic equation: 3x2 - 5x +2 = 0.
[5 marks]Prove the De - Morgan’s law using the truth table.
[5 marks]Define the terms: Graph, Sub graph, Complete Graph, Regular Graph and Bipartite Graph.
[5 marks]Find the in degree, Out degree and total degree for the given graph: Page 2 of
[2 marks]