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 What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as circle and lines)? (a) 6 (b) 10 (c) 14 (d) 16 Answer =  Intersection among 4 lines =4^C_{2} = 6 points.  Intersection of 4 lines with circle, Each line can intersect the circle at most 2 times, giving 4 × 2 = 8 points. Total intersection = 6+8=14 points . . Option (c) is correct.

  Select the answer using the code given below. (a) Both I and II (b) Both II and III (c) Both I and III (d) All I, II and III Answer = Statement 1 :P cap Q is reflexive if P and Q are reflexive. +0 Correct : If (a, a) \in P and (a, a) \in Q then (a, a) in P cap Q Statement II :P cup Q is symmetric if P and Q are symmetric Correct: If (a, b) in P cup Q then (b, a) \in Q (b, a) \in P So (b, a) in P cup Q Statement III: POQ is transitive if P and Q are transitive. Correct: If (a, b) in P cap Q and (b, c) in P cap Q then (a, c) in P cap Q .. Option (d) is correct.

Answer = We have, the vertex A lies on the parabola y ^ 2 = 4kx Two points lying on the parabola are P(4k,4k) and Q(4k, - 4k) ... The coordinates of the vertex A are (0, 0) The correct option is (b).