1. X3 Let f [1.) R be a differentiable function such that f(1): and 3 f(t)dtx f(x)- X [1, 0). Let e 3 denote the base of the natural logarithm. Then the value of f(e) is e +4 log 4+e (A) (B) 3 3 4e2 e2-4 (C) (D) 3 3 2. Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is 1 , then the probability that the experiment stops with head is 3 13 42 (A) (C) 21 (B) 5227 (D) 3. For any y = R, let cot (y) = (0, ) and tan(y) e tan-1 6y 9-y2 +cot-1 9-y 6y = (A) 23-3 (C) 43-6 2 3 2' 2 for 0 4. Let the position vectors of points P, Q, R and S be a +2)- 5k, b = 31 + 6j + 3k, c= = 5 d = 2 + j + k, respectively. Then which of the following statements is true? (A) The points P, Q, R and S are NOT coplanar b+2d (B) 3 is the position vector of a point which divides PR internally in the ratio 5:4 b+2d (C) is the position vector of a point which divides PR externally in the ratio 5:4 3 (D) The square of magnitude of the vector b xd is 95 + + 5 7k and