Consider f(x) = log_{[x]} [x] where [.] is the greatest integer function and {x} is fractional part function.

**1. f(x) is**

(A) a one-one function

(B) a many-one function

(C) a odd function

(D) a periodic function

**2. Consider the inequality f(x) < 2. Number of solutions of this inequality in x ∈ (1, 2) is/are**

(A) 0

(B) 1

(C) 3

(D) infinitely many