Find the area of the parallelogram whose diagonals are represented by the vectors

OR

Find the angle between the vectors

and

Find:

OR

Find:

Form the differential equation of all circles which touch the x-axis at the origin.

If A and B are two independent events, prove that A′ and B are also independent.

One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from the first bag to the second bag, and then a ball is drawn from the second bag. Find the probability that the ball is drawn is red.

OR

If P(A) = 0.6, P(B) = 0.5 and P(A|B) = 0.3, then find P (Α∪ B).