Box 1 contains three cards bearing numbers 1, 2, 3, box 2 contains five cards bearing numbers 1, 2, 3, 4, 5 and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let x; be the number on the card drawn from the ith box, i = 1, 2, 3. 158. The probability that x + x + x3 is odd, is 53 57 105 105 29 105 (b) (c) 159. The probability that x, x and x3 are in arithmetic [JEE Advanced 2014, 3+3M] 11 7 105 105 progression, is 9 105 (a) (b) 10 105 (d) 160. If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls, is [JEE Main 2015, 4M] (a) 20() (b) 22) ()(3) (3) 12 11 10 55 (d) 55 3 161. The minimum number of times a fair coin needs to be tossed, so that the probability of getting atleast two heads is atleast 0.96, is [JEE Advanced 2015, 4M]