Match List-I with List-II List-

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

Match List-I with List-II

List-I	List-II
(A) $f(x) = x. \sin x$	(I) is not continuous at $x = -3$
(B) $f(x)=\frac{\|x\|}{x},x≠0$ and $f(x) = 1$ at $x = 0$	(II) is continuous everywhere
(C) $f(x) = x-[x]$, $[x]$ denotes greatest integer function	(III) is not differentiable at $x = 1$
(D) $f(x) = e^{\|x-1\|}$	(IV) is not continuous at $x = 0$

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

List-I	List-II	Explanation
(A) f(x) = x·sinx	(II) is continuous everywhere	Product of continuous functions (x and sinx)
(B) f(x) = \|x\|/x, x ≠ 0; f(0) = 1	(IV) is not continuous at x = 0	Left limit = −1, right limit = 1, f(0) = 1 ⇒ discontinuous
(C) f(x) = x − [x]	(I) is not differentiable at x = −3	f(x) ={x}= fractional part function ⇒ not differentiable at all integers
(D) f(x) = e^\|x−1\|	(III) is not differentiable at x = 1	Non-differentiable at the corner point x = 1 (\|x−1\|)