Let U={a,b,c,d,e,f,g,ℎ,i,j}, A={a,b,f,g,i}, B={b,d,f,i,j}, C={c,e,f,g} then show that
[5 marks]A∪(B∩C) =(A∪B) ∩(A∪C) (ii) (A∩B∩C).
[ marks]Give an example of a relation which is Reflexive, Symmetric but not Transitive.
[5 marks]Define: Graph and Sub graph with an example.
[5 marks]Solve the equation: 2x2−5x+3
[5 marks](2−8i)(7+8i) Express the complex number in the form of a+ib. 1+i
[5 marks]If A = {2,3,4,5} and B= {4, 5, 9,25} and R:A →Bdefined by aRb, if b = a2. Find the domain and Range.
[5 marks]1 2 −3 If A = [−1 −4] and B = [ ] then find(AB)T.201 1 −1
[5 marks]1 2 Find the Inverse of the matrix A = [ 2 1 −1] −2 2 −1
[5 marks]If x = (−1, −2, 3), y = (−3, 7, 9), z = (−2, 1, 3) then find x ∙ (y + z)
[5 marks]Find the mean deviation about the mean for the following frequency distribution. Marks 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Student 3 7 12 15 8 3 205
[5 marks]Acard is drawn from a well-shuffled pack of 52 cards. Find the probability of
[ marks]getting a king card, (ii) getting a face card.
[ marks]Calculate the standard deviation of the following data: Size of the items 10 11 12 13 14 15 16 frequency 2 7 11 15 10 4 1
[5 marks]Aclass consists of 6 girls and 10 boys. If a committee of three is chosen at random from the class, find the probability that (i) three boys are selected and (ii) exactly two girls are selected.1
[5 marks]Design a Boolean function of AB + CD using logic gates.
[5 marks]State De Morgan’s Law. What is De Morgan’s Law in Boolean Algebra.
[5 marks]Write the truth table for the compound proposition p∨(q∧r) ↔[(p∨q)∧(p∨r)].
[5 marks]State Boolean Algebra with an example.
[5 marks]