Match List-I with List-II, List-I, List-II, (A) f(x) = cases x^10-1 &, x ≤ 1 \ x^2 &, x 1 cases, (I) is continuous at all points of domain, (B) g(x) = [x], [x] denotes the greatest integer function, (II) is continuous at x = 0, (C) h(x) = cases ( x)/x &, x

Question

Match List-I with List-II | List-I | List-II | |---|---| | (A) $$f(x) = \begin{cases} x^{10}-1 & , x \leq 1 \ x^2 & , x > 1 \end{cases}$$ | (I) is continuous at all points of domain | | (B) $$g(x) = [x]$$, $$[x]$$ denotes the greatest integer function | (II) is continuous at $$x = 0$$ | | (C) $$h(x) = \begin{cases} \dfrac{\sin x}{x} & , x < 0 \ x+1 & , x \geq 0 \end{cases}$$ | (III) is discontinuous at $$x = -2$$ | | (D) $$p(x) = \begin{cases} \dfrac{x}{\left\vert x ight\vert} & , x < 0 \ -1 & , x \geq 0 \end{cases}$$ | (IV) is discontinuous at $$x = 1$$ | Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

List-I	List-II
(A) $f(x) = \begin{cases} x^{10}-1 & , x \leq 1 \\ x^2 & , x > 1 \end{cases}$	(I) is continuous at all points of domain
(B) $g(x) = [x]$ , $[x]$ denotes the greatest integer function	(II) is continuous at $x = 0$
(C) $h(x) = \begin{cases} \dfrac{\sin x}{x} & , x < 0 \\ x+1 & , x \geq 0 \end{cases}$	(III) is discontinuous at $x = -2$
(D) $p(x) = \begin{cases} \dfrac{x}{\left\vert x \right\vert} & , x < 0 \\ -1 & , x \geq 0 \end{cases}$	(IV) is discontinuous at $x = 1$

Solution

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