In the following [x] denotes the greatest integer less than or...

In the following

[x]

denotes the greatest integer less than or equal to

x

. Match the functions in Column I with the properties Column II. In the following [x] denotes the greatest integer less than or equal to x . Match the functions in Column I with the

In the following [x] denotes the greatest integer less than or equal to x . Match the functions in Column I with the

Options

AA-p, r; B-p, q, s; C-p; D-q, r
BA-p, s; B-p, r, s; C-p, s; D-q, r
CA-p, q, r; B-p, s; C-r, s; D-p, q
DA-r, s; B-q; C-p; D-p, q, s

Correct answer

C. A-p, q, r; B-p, s; C-r, s; D-p, q

Step-by-step solution

(A)

x|x|

is continuous, differentiable and strictly increasing in

(-1,1)

. (B)

\sqrt{|x|}

is continuous in

(-1,1)

and not differentiable at

x=0

. (C)

x+[x]

is strictly increasing in

(-1,1)

and discontinuous at

x=0

\Rightarrow

not differentiable at

x=0

. (D)

|x-1|+|x+1|=2

(-1,1)

The function is continuous and differentiable in

(-1,1)

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