1. A JEE aspirant estimates that he will be successful with an 80% chance if he studies 10 hr/day with 60% chance if he studies 7hr/day and with 40% chance if he studies 4 hr/day. Further, he believes that he will study 10 hr, 7hr and 4 hr/day with probability 0.1, 0.2 and 0.7 respectively. Given that he is successful, the probability that he studies for 4 hr/day equals. 2. 14 (a) 19 1 (b) 4 x-2y-z=0] 7 (c) 12 (d) 25 If the system of equations Ax-y-z = 0} has a unique solution, then the range of is R-{a, x+y-z=0 b}. Then the value of (a + b) is: (a) 1 3. Let b1, b2, (b) 2 (c) 4 (d) 9 be a geometric sequence such that b + b = a and b = 2. Given that b2 0, then the value of b is: k=1 4. (a) 2-2 (b) 1+2 (c) 2+2 (d) 4-2 If M is a 3 3 matrix such that M = 0, then det ((I + M)50 - 50M) where I is an identity matrix of order 3, is equal to : (a) 3 5. (b) 50 (c) 2 (d) 1 The equation of the common tangent touching the circle (x-3) + y = 9 and the parabola y = 4x above the x-axis, is (a) 3y=3x+1 (b) 3y=-(x+3) (c) 3y=x+3 (d) 3y=-(3x+1)