JEE Mains Model Paper 15

Domain of cot−1x is R and

x

√x2−[x2]

is defined if x2 = [(x2)]
i.e. x2 is not integer (∵ x2 ≥ [x2])
Hence x2 ≠ non negative integer i.e. 0 or +ve integer
Hence domain = R - { √n ≥ 0 , n ∊ Z}
Thus correct answer is (D)