Question

Let [x] denote the greatest integer function. Then match List-I with List-II:

• A. (A)-(I),(B)-(II),(C)-(III),(D)-(IV)
• B. (A)-(I),(B)-(III),(C)-(II),(D)-(IV)
• C. (A)-(II),(B)-(I),(C)-(III),(D)-(IV)
• D. (A)-(II),(B)-(IV),(C)-(III),(D)-(I)

Answer 1

Answer: (C)

(A)-(II),(B)-(I),(C)-(III),(D)-(IV)

Answer 2

For each function in List-I , analyze its behavior and match it with List-II :

For (A) $|x - 1| + |x - 2|$: The modulus function $|x - 1| + |x - 2|$ is continuous everywhere because modulus functions are inherently continuous. Match: (A) → (II).

For (B) $x - |x|$: The function $x - |x|$ is differentiable at $x = 1$. This is because $|x|$ is well-defined and continuous for all $x$. Match: (B) → (I).

For (C) $x - [x]$: The greatest integer function $[x]$ causes a lack of differentiability at all integers. Hence $x - [x]$ is not differentiable at $x = 1$. Match: (C) → (III).

For (D) $x|x|$: The function $x|x|$ is quadratic in behavior for both $x>0$ and $x<0$. Hence, it is differentiable everywhere except at $x = 0$. Match: (D) → (IV).

$(A) – (II), (B) – (I), (C) – (III), (D) – (IV)$.