Let A, B, C be three points whose position vectors respectively are =1+4j+3K b=2i+aj+4k,R c=31-2j+5k If a is the smallest positive integer for which a, b, c are noncollinear, then the length of the median, in AABC, through A is: 82 (a) 2 62 (b) 2 (c) (d) 66 2 2 16. The probability that a relation R from {x,y} to{x,y} is both symmetric and transitive, is equal to 9 (b) 16 11 (c) 16 13 (d) 16 The number of values of aN such that the variance of 3, 7, 12, a, 43 -a is a natural number 5 (a) 16 17. is: (a) 0 18. (b) 2 (c) 5 (d) infinite From the base of a pole of height 20 meter, the angle of elevation of the top of tower is 60. The pole subtends an angle 30 at the top of the tower. Then the height of the tower is: (a) 153 (b) 203 Negation of the Boolean statement (pvq)=((r)vp) is equivalent to 19. (a) p^(q)^ 20. (b) (p)^(q)^r (c) 20+103 (c) (p)^q^ (d) 30 (d) ^^() Let n5 be an integer. If 9 - 8n - 1 = 64 and 6"-5n-1 = 25, then a - is equal to (a) 1 + "C (8 5) + "C3 (8 5) + ... + "Cn (8-1 - 5-1) - (b) 1+C (8-5)+"C (8 -5 ) + ... + "C (8"-2 -5n-2) n (c) C3 (8-5)+"C4 (82-52) +...+ "Cn (8n-2-5n-2) (d) "C (8-5)+C (82-5) +...+"C (8-3-5-3) 4