JEE Advanced Model Paper 8 with solutions for online practice

Total number of functions from A to B is 34 = 81. The number of functions which do not contain x ory or z in its range is 24 . Therefore,the number of functions which contain exactly 2 elements in therange is 3 . 24 = 48
The number of functions which contain exactly one element in its range is 3.Hence,the total numberof onto functions is 81 - 48 + 3 = 36 ⇒ n(F) = 36.
Let f ∊ F. We now count the no.of ways in which f−1 consists of single element. We can choose pre image of x in 4 ways. The remaining 3 elements can be mapped onto {y,z} is 23 - 2 = 6 ways. f1 will consist of exactly one element in 4 × 6 = 24 ways. Thus, the probability of the require event is 24/36 = 2/3