If A = w , x , y , B = x , y , z and C = y , then verify that A ( B C ) = ( A B ) ( A C )05 .
[ marks]In the graph given below, write the degree of each vertex. Is it a simple graph? If not, write the type of the graph.
[5 marks]If and are the roots of x 2 − 2 x + 4 = 0 , find .
[5 marks]Find the complex conjugate and modulus of ( 2 + i3 ) (1 − − i 2 i ) .
[5 marks]Consider the following five relations on the set A={1,2,3,4}: R1 = (1 , 1 ) , (1 , 2 ) , ( 2 , 3 ) , (1 , 3 ) , ( 4 , 4 ) R2 = (1 , 1 ) , (1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) R3 = ( 1 , 3 ) , ( 2 , 1 ) , R4 , =05 the empty relation R = AA,the universal relation5
[ marks]Which of the relations are reflexive? Why?
[ marks]Which of the relations are not symmetric? Why?
[ marks]Which of the relations are not transitive? Why?
[ marks](i) For what value of k the vectors u and v are orthogonal? u =(2, 1, 3) and v = ( 1 , 7 , k ) .05 (ii) If u =(−1, 2, 3) and v=(2, 0, 4), find u+v and u−v.
[ marks]1 1 1 bc ac ab Expand | |.111 a b c
[5 marks]If f : R → R , f ( x ) = x 2 + 2 and g : R → R , g ( x ) = 3 x , can f o g and g o f be defined? If yes, find f o g ( x ) and g o f ( x )05 .
[ marks]1 −1 If possible find A+4B and B+C-2D , where A = [−3 2 −1] , −2 1 0 B = , C = −6 and D = −5 −3 − −2 05 .
[5 marks]Find standard deviation of the following data x05 f 2 7 11 15 10 4 1
[ marks]If Aand Bare two events such that P ( A ) =2 , P ( B ) =1 , P ( A B ) =1 and P ( A B ) =1 find (i) P ( A B ) (ii) P ( A ) (iii) P ( B )05 ( ) ( ) (iv) P AB (v)P AB
[ marks]Find the mean deviation about mean from the following data: Product output 145 155 165 175 185 195 Workers 4 6 10 18 9
[3 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.
[5 marks]State De Morgan’s theorem for Boolean algebra. Also, write the complement of the following Boolean functions.
[ marks]F = x y z + x y z (ii) F = ( x + y ) ( x + z ) ( y + z )05
[ marks]Express the Boolean function F = x + y z as a sum of minterms.
[5 marks]Prove that x + x y = x using the truth table.
[5 marks]Find the Boolean expression of the given logic circuit.
[5 marks]