117409 If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) is

117410 The range of the real valued function \(f(x)=\) \(\frac{\mathbf{x}^2+\mathbf{x}+1}{\mathrm{x}}\) is

117411 Match the items of List-I with those of the items of List-II
| List-I | List-II |
| :--- | :--- |
| A. Range of $\sec ^{-1}\left[1+\cos ^2 x\right],[\cdot]$ denote greatest integer function | I. odd function |
| B. Domain of $f(x)$, where $f\left(x+\frac{1}{x}\right)=$ $x^2+\frac{1}{x^2}$ | II. $\left\{0, \frac{1}{2}\right\}$ |
| C. $\mathbf{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+$ $\mathrm{f}(\mathrm{y}) ; \mathrm{f}(\mathbf{1})=5$ | III. $\left\{\sec ^{-1} 5, \sec ^{-1} 4\right\}$ |
| D. $\sin ^{-1} x-\cos ^{-1} x+\sin ^{-}$ $1(1-x)=0 \Rightarrow x \in$ | IV.R |

117413 The domain of the function \(f(x)=\frac{1}{\sqrt{[x]^2-[x]-2}}\) is (Here \([x]\) denotes the greatest integer not exceeding the value of \([x]\)

117414 If \((x)\) denotes the greatest integer function, then the domain of the function \(f(x)=\) \(\sqrt{\frac{x-[x]}{\log \left(x^2-x\right)}}\), is

117409 If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) is

117410 The range of the real valued function \(f(x)=\) \(\frac{\mathbf{x}^2+\mathbf{x}+1}{\mathrm{x}}\) is

117411 Match the items of List-I with those of the items of List-II
| List-I | List-II |
| :--- | :--- |
| A. Range of $\sec ^{-1}\left[1+\cos ^2 x\right],[\cdot]$ denote greatest integer function | I. odd function |
| B. Domain of $f(x)$, where $f\left(x+\frac{1}{x}\right)=$ $x^2+\frac{1}{x^2}$ | II. $\left\{0, \frac{1}{2}\right\}$ |
| C. $\mathbf{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+$ $\mathrm{f}(\mathrm{y}) ; \mathrm{f}(\mathbf{1})=5$ | III. $\left\{\sec ^{-1} 5, \sec ^{-1} 4\right\}$ |
| D. $\sin ^{-1} x-\cos ^{-1} x+\sin ^{-}$ $1(1-x)=0 \Rightarrow x \in$ | IV.R |

117413 The domain of the function \(f(x)=\frac{1}{\sqrt{[x]^2-[x]-2}}\) is (Here \([x]\) denotes the greatest integer not exceeding the value of \([x]\)

117414 If \((x)\) denotes the greatest integer function, then the domain of the function \(f(x)=\) \(\sqrt{\frac{x-[x]}{\log \left(x^2-x\right)}}\), is

117409 If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) is

117410 The range of the real valued function \(f(x)=\) \(\frac{\mathbf{x}^2+\mathbf{x}+1}{\mathrm{x}}\) is

117411 Match the items of List-I with those of the items of List-II
| List-I | List-II |
| :--- | :--- |
| A. Range of $\sec ^{-1}\left[1+\cos ^2 x\right],[\cdot]$ denote greatest integer function | I. odd function |
| B. Domain of $f(x)$, where $f\left(x+\frac{1}{x}\right)=$ $x^2+\frac{1}{x^2}$ | II. $\left\{0, \frac{1}{2}\right\}$ |
| C. $\mathbf{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+$ $\mathrm{f}(\mathrm{y}) ; \mathrm{f}(\mathbf{1})=5$ | III. $\left\{\sec ^{-1} 5, \sec ^{-1} 4\right\}$ |
| D. $\sin ^{-1} x-\cos ^{-1} x+\sin ^{-}$ $1(1-x)=0 \Rightarrow x \in$ | IV.R |

117413 The domain of the function \(f(x)=\frac{1}{\sqrt{[x]^2-[x]-2}}\) is (Here \([x]\) denotes the greatest integer not exceeding the value of \([x]\)

117414 If \((x)\) denotes the greatest integer function, then the domain of the function \(f(x)=\) \(\sqrt{\frac{x-[x]}{\log \left(x^2-x\right)}}\), is

117409 If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) is

117410 The range of the real valued function \(f(x)=\) \(\frac{\mathbf{x}^2+\mathbf{x}+1}{\mathrm{x}}\) is

117411 Match the items of List-I with those of the items of List-II
| List-I | List-II |
| :--- | :--- |
| A. Range of $\sec ^{-1}\left[1+\cos ^2 x\right],[\cdot]$ denote greatest integer function | I. odd function |
| B. Domain of $f(x)$, where $f\left(x+\frac{1}{x}\right)=$ $x^2+\frac{1}{x^2}$ | II. $\left\{0, \frac{1}{2}\right\}$ |
| C. $\mathbf{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+$ $\mathrm{f}(\mathrm{y}) ; \mathrm{f}(\mathbf{1})=5$ | III. $\left\{\sec ^{-1} 5, \sec ^{-1} 4\right\}$ |
| D. $\sin ^{-1} x-\cos ^{-1} x+\sin ^{-}$ $1(1-x)=0 \Rightarrow x \in$ | IV.R |

117413 The domain of the function \(f(x)=\frac{1}{\sqrt{[x]^2-[x]-2}}\) is (Here \([x]\) denotes the greatest integer not exceeding the value of \([x]\)

117414 If \((x)\) denotes the greatest integer function, then the domain of the function \(f(x)=\) \(\sqrt{\frac{x-[x]}{\log \left(x^2-x\right)}}\), is

117409 If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) is

117410 The range of the real valued function \(f(x)=\) \(\frac{\mathbf{x}^2+\mathbf{x}+1}{\mathrm{x}}\) is

117411 Match the items of List-I with those of the items of List-II
| List-I | List-II |
| :--- | :--- |
| A. Range of $\sec ^{-1}\left[1+\cos ^2 x\right],[\cdot]$ denote greatest integer function | I. odd function |
| B. Domain of $f(x)$, where $f\left(x+\frac{1}{x}\right)=$ $x^2+\frac{1}{x^2}$ | II. $\left\{0, \frac{1}{2}\right\}$ |
| C. $\mathbf{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+$ $\mathrm{f}(\mathrm{y}) ; \mathrm{f}(\mathbf{1})=5$ | III. $\left\{\sec ^{-1} 5, \sec ^{-1} 4\right\}$ |
| D. $\sin ^{-1} x-\cos ^{-1} x+\sin ^{-}$ $1(1-x)=0 \Rightarrow x \in$ | IV.R |

117413 The domain of the function \(f(x)=\frac{1}{\sqrt{[x]^2-[x]-2}}\) is (Here \([x]\) denotes the greatest integer not exceeding the value of \([x]\)

117414 If \((x)\) denotes the greatest integer function, then the domain of the function \(f(x)=\) \(\sqrt{\frac{x-[x]}{\log \left(x^2-x\right)}}\), is