1. If A (-2, 2, 3) and B(13, -3, 13) are two points. Find the locus of a point P which moves in such a way that 3PA = 2PB. [4M]

2. Find the ratio in which the join the A(2, 1, 5) and B(3, 4, 3) is divided by the plane 2x + 2y – 2z = 1. Also, find the coordinates of the point of division. [4M]

3. Find the centroid of triangle, mid-points of whose sides are (1, 2, -3), (3, 0, 1) and (-1, 1, -4). [4M]

4. Prove that : [4M]

5. [4M]

6. Prove that : [4M]

7. Solve: [4M]

8. Prove that : [4M]

9. Let A = {1, 2, 3} and B = {x : x∈N , x is prime less than 5}. Find A×B andB×A . [2M]10. A relation R is defined on the set Z of integers as follows:

( x , y )∈R⇔ x2+ y2=25Express R as the sets of ordered Paris and hence find their respective domains. [2M]

11. Find the domain of the function f (x) defined by

f ( x )=√4−x2+ 1

√ x2−1 [2M]

12. Find the domain and range of [4M]

13. Find the domain and range of the following f ( x )= 1

2−sin 3 x [4M]

14. Evaluate: [2M]

15. Evaluate: [3M]

16. Differentiate [3M]

17. Find the derivative using first principle [3M]18. Differentiate the following functions with respect to x [3M]

19. If and are in the ratio 2:1, find the value of n. [3M]20. A gentleman has 6 friends to invite. In how many ways can he send invitation card to them, if he has

three servants to carry the cards? [4M]

21. How many different signals can be given using any number of flags from 5 flags of different colours?[3M]

22. In how many ways can 9 examination papers be arranged so that the best and the worst papers are never together? [3M]

23. How many different words can be formed from the letters of the word ‘GANESHPURI’? in how many of these words: [6M]

(i) The letter G always occupies the first place?(ii) The letters P and I respectively occupy first and last place?(iii) The vowels are always together?(iv) The vowels always occupy even places?

24. A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when,

[6

(i) At least two ladies are included; (ii) At most two ladies are included; [6M]

25. If the letter of the word ‘MOTHER’ are written in all possible orders and these words are written out as in a dictionary, find the rank of the word ‘MOTHER’ [4M]

26. The mid-points of the sides of an triangles are (2, 1), (-5, 7) and (-5, -5). Find the equations of the sides of the triangle.

[4M]27. Find the image of the point (-8, 12) with respect to the line mirror 4x + 7y + 13 = 0.

[4M]28. Find the equation of the internal bisector of angle BAC of the triangle ABC whose

vertices A, B, C are (5, 2), (2, 3) and (6, 5) respectively. [4M]

29. In a lottery of 50 tickets numbered 1 to 50, two tickets are simultaneously. Find the probability that:

(a) Both the tickets drawn have prime numbers,

(b) None of the tickets drawn has prime number,

(c) One ticket has prime number. [4M]

30. Check whether the following probabilities P(A) and P(B) are consistently defined :

i) P(A) = 0.5, P(B) = 0.7, P = 0.6

ii) P(A) = 0.5, P(B) = 0.4, P = 0.8 [2M]

31. The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with

probability 0.2, then find [2M]