Except for the following questions, all the remaining questions have been asked in Set I and Set II.
SECTION - A
Q. 2. An urn contains 6 white, 4 black and 5 red balls. Two balls are drawn at random. Find the probability that
(i) both the balls are red
(ii) one ball is red, the other is black
(iii) one ball is white
Q. 4. Using properties of determinants, Prove that:
Q. 7. Evaluate:
Q. 13. Prove that the curves and cut at right angles if 8K2 =1.
Verify Lagrange's mean value theorem for the function
Q. 14. Evaluate:
Q. 18. Using matrix method solve the following system of linear equations:
SECTION - B
Q. 21 . Find x such that the four points A (3, 2, 1) B (4, x, 5) C (4, 2, -2) and D (6, 5, -1) coplanar.
SECTION - C
Q. 22. Three urns A, B and C contain 4 red and 6 white; 3 red and 5 white; and 2 red and 4 white balls respectively. An urn is chosen at random and a ball is drawn. If the ball drawn is fond to be red, find the probability that the ball was drawn from urn A.