In the following, [x] denotes the greatest integer less than or equal to x. `{:(,"Column I",,"Column II"),(A.,x|x|,p.,"continuous in (-1, 1)"),(B.,sqrt|x|,q.,"differentiable in (-1, 1) "),(C.,x+[x],r.,"strictly increasing (-1, 1)"),(D.,|x-1|+|x+1| " in (-1,1)",s.,"not differentiable atleast at one point in (-1, 1)"):}`

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

1.	In the following, [x] denotes the greatest integer less than or equal to x. `{:(,"Column I",,"Column II"),(A.,x\|x\|,p.,"continuous in (-1, 1)"),(B.,sqrt\|x\|,q.,"differentiable in (-1, 1) "),(C.,x+[x],r.,"strictly increasing (-1, 1)"),(D.,\|x-1\|+\|x+1\| " in (-1,1)",s.,"not differentiable atleast at one point in (-1, 1)"):}`
Answer» Correct Answer - `(A) to p,q,r,s; (B) to p, s; (D) to p, s ` 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 `rArr` not differentiable at x = 0. D. `\|x-1\|+\|x+1\|=2" in "(-1, 1)` `rArr ` The function is continuous and differentiable in (-1, 1) .