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

The Correct Option is C

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).

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