Part-A : Answer All The Questions 1. Define an empty relation. 2. If a matrix has 5 elements, what are the possible orders it can have? 3. Define a negative vector. 4. Define Optimal solution in a linear programming problem. 5. Find the vector components of the vector with initial point (2,1) and terminal point (-5,7). 6. Define the objective function in a linear programming problem.
Part-B : Answer any TEN questions: 1. Find the equation of the plane with intercepts 2, 3 and 4 on X, Y and Z axes respectively. 2. Assume that each child born in a family is equally likely to be a boy or girl. If a family has two children, what is the conditional probability that both are girls, given that the youngest is a girl. 3. Find the equation of the line passing through (1, 2) and (3, 6) using determinants. 4. Two cards drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black
Part-C : Answer Any Ten Questions 1. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. 2. If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute that is AB=BA. 3. Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag-II
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