Kcet 2025 Limits Continuity And Differentiability PYQ with Solution

Question

Match the following: In the following, [\mathrm{x}] denotes the greatest integer less than or equal to x . Column - I Column - II (a) x | x | x | x | x|x| (i) continuous in (-1, 1) (b) | x | | x | sqrt(|x|) (ii) differentiable in (-1, 1) (c) x + [ x ] x + [ x ] x+[x] (iii) strictly increasing in (-1, 1) (d) | x − 1 | + | x + 1 | | x − 1 | + | x + 1 | |x-1|+|x+1| (iv) not differentiable at, at least one point in (-1, 1)

Accepted Answer

C

Limits Continuity And Differentiability

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Column - I		Column - II
(a)	$x \| x \|$	(i)	continuous in (-1, 1)
(b)	$\sqrt{\| x \|}$	(ii)	differentiable in (-1, 1)
(c)	$x + [x]$	(iii)	strictly increasing in (-1, 1)
(d)	$\| x - 1 \| + \| x + 1 \|$	(iv)	not differentiable at, at least one point in (-1, 1)