79987 Let \(f(x)=\left\{\begin{array}{cl}\frac{\sin (x-[x])}{x-[x]} & , x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & ,|x|\lt 1 \\ 1 & , \text { otherwise }\end{array}\right.\) where \([t]\)denotes greatest integer \(\leq \mathrm{t}\). If \(\mathrm{m}\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \((m, n)\) is :

79988 Let \(\mathbf{f}: \mathbf{R} \rightarrow \mathbf{R}\) be defined as
\(\mathbf{f}(\mathbf{x})=\left[\begin{array}{cc}{\left[\mathbf{e}^{\mathbf{x}}\right],} & \mathbf{x}\lt \mathbf{0} \\ \mathbf{a e}^{\mathbf{x}} \mid[\mathbf{x}-\mathbf{1}], & \mathbf{0} \leq \mathbf{x}\lt \mathbf{1} \\ \mathbf{b}+[\sin (\boldsymbol{\pi} \mathbf{x})], & \mathbf{1} \leq \mathbf{x}\lt \mathbf{2} \\ {\left[\mathbf{e}^{-\mathbf{x}}\right]-\mathbf{c},} & \mathbf{x} \geq \mathbf{2}\end{array}\right.\)
where \(a, b, c \in \mathbb{R}\) and \([t]\) denotes greatest integer less than or equal to \(t\). Then, which of the following statements is true?

79989 Let \(f(x)= \begin{cases}\frac{x^{3}+x^{2}-16 x+20}{(x-2)^{2}} , \text { if } x \neq 2 . \\ b, \text { if } x=2\end{cases}\)
If \(f(x)\) is continuous for all \(x\), then \(b\) is equal to

79990 if \([x]\) denotes the greatest integer \(\leq x\), then the value of \(\lim _{x \rightarrow 0}|x|^{[\cos x]}\) is

79987 Let \(f(x)=\left\{\begin{array}{cl}\frac{\sin (x-[x])}{x-[x]} & , x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & ,|x|\lt 1 \\ 1 & , \text { otherwise }\end{array}\right.\) where \([t]\)denotes greatest integer \(\leq \mathrm{t}\). If \(\mathrm{m}\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \((m, n)\) is :

79988 Let \(\mathbf{f}: \mathbf{R} \rightarrow \mathbf{R}\) be defined as
\(\mathbf{f}(\mathbf{x})=\left[\begin{array}{cc}{\left[\mathbf{e}^{\mathbf{x}}\right],} & \mathbf{x}\lt \mathbf{0} \\ \mathbf{a e}^{\mathbf{x}} \mid[\mathbf{x}-\mathbf{1}], & \mathbf{0} \leq \mathbf{x}\lt \mathbf{1} \\ \mathbf{b}+[\sin (\boldsymbol{\pi} \mathbf{x})], & \mathbf{1} \leq \mathbf{x}\lt \mathbf{2} \\ {\left[\mathbf{e}^{-\mathbf{x}}\right]-\mathbf{c},} & \mathbf{x} \geq \mathbf{2}\end{array}\right.\)
where \(a, b, c \in \mathbb{R}\) and \([t]\) denotes greatest integer less than or equal to \(t\). Then, which of the following statements is true?

79989 Let \(f(x)= \begin{cases}\frac{x^{3}+x^{2}-16 x+20}{(x-2)^{2}} , \text { if } x \neq 2 . \\ b, \text { if } x=2\end{cases}\)
If \(f(x)\) is continuous for all \(x\), then \(b\) is equal to

79990 if \([x]\) denotes the greatest integer \(\leq x\), then the value of \(\lim _{x \rightarrow 0}|x|^{[\cos x]}\) is

79987 Let \(f(x)=\left\{\begin{array}{cl}\frac{\sin (x-[x])}{x-[x]} & , x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & ,|x|\lt 1 \\ 1 & , \text { otherwise }\end{array}\right.\) where \([t]\)denotes greatest integer \(\leq \mathrm{t}\). If \(\mathrm{m}\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \((m, n)\) is :

79988 Let \(\mathbf{f}: \mathbf{R} \rightarrow \mathbf{R}\) be defined as
\(\mathbf{f}(\mathbf{x})=\left[\begin{array}{cc}{\left[\mathbf{e}^{\mathbf{x}}\right],} & \mathbf{x}\lt \mathbf{0} \\ \mathbf{a e}^{\mathbf{x}} \mid[\mathbf{x}-\mathbf{1}], & \mathbf{0} \leq \mathbf{x}\lt \mathbf{1} \\ \mathbf{b}+[\sin (\boldsymbol{\pi} \mathbf{x})], & \mathbf{1} \leq \mathbf{x}\lt \mathbf{2} \\ {\left[\mathbf{e}^{-\mathbf{x}}\right]-\mathbf{c},} & \mathbf{x} \geq \mathbf{2}\end{array}\right.\)
where \(a, b, c \in \mathbb{R}\) and \([t]\) denotes greatest integer less than or equal to \(t\). Then, which of the following statements is true?

79989 Let \(f(x)= \begin{cases}\frac{x^{3}+x^{2}-16 x+20}{(x-2)^{2}} , \text { if } x \neq 2 . \\ b, \text { if } x=2\end{cases}\)
If \(f(x)\) is continuous for all \(x\), then \(b\) is equal to

79990 if \([x]\) denotes the greatest integer \(\leq x\), then the value of \(\lim _{x \rightarrow 0}|x|^{[\cos x]}\) is

79987 Let \(f(x)=\left\{\begin{array}{cl}\frac{\sin (x-[x])}{x-[x]} & , x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & ,|x|\lt 1 \\ 1 & , \text { otherwise }\end{array}\right.\) where \([t]\)denotes greatest integer \(\leq \mathrm{t}\). If \(\mathrm{m}\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \((m, n)\) is :

79988 Let \(\mathbf{f}: \mathbf{R} \rightarrow \mathbf{R}\) be defined as
\(\mathbf{f}(\mathbf{x})=\left[\begin{array}{cc}{\left[\mathbf{e}^{\mathbf{x}}\right],} & \mathbf{x}\lt \mathbf{0} \\ \mathbf{a e}^{\mathbf{x}} \mid[\mathbf{x}-\mathbf{1}], & \mathbf{0} \leq \mathbf{x}\lt \mathbf{1} \\ \mathbf{b}+[\sin (\boldsymbol{\pi} \mathbf{x})], & \mathbf{1} \leq \mathbf{x}\lt \mathbf{2} \\ {\left[\mathbf{e}^{-\mathbf{x}}\right]-\mathbf{c},} & \mathbf{x} \geq \mathbf{2}\end{array}\right.\)
where \(a, b, c \in \mathbb{R}\) and \([t]\) denotes greatest integer less than or equal to \(t\). Then, which of the following statements is true?

79989 Let \(f(x)= \begin{cases}\frac{x^{3}+x^{2}-16 x+20}{(x-2)^{2}} , \text { if } x \neq 2 . \\ b, \text { if } x=2\end{cases}\)
If \(f(x)\) is continuous for all \(x\), then \(b\) is equal to

79990 if \([x]\) denotes the greatest integer \(\leq x\), then the value of \(\lim _{x \rightarrow 0}|x|^{[\cos x]}\) is