Domain, Co-domain and Range of Function
Sets, Relation and Function

117361 The minimum value of \(\cos \theta+\sin \theta+\frac{2}{\sin 2 \theta}\) for \(\theta \in(0, \pi / 2)\), is

1 \(2+\sqrt{2}\)
2 2
3 \(1+\sqrt{2}\)
4 \(2 \sqrt{2}\)
Sets, Relation and Function

117362 Let \(f: R \rightarrow R\) be defined as \(f(x)=\) \(\frac{x^2-x+4}{x^2+x+4}\). Then, range of the function \(f(x)\) is

1 \(\left[\frac{3}{5}, \frac{5}{3}\right]\)
2 \(\left[\frac{5}{3}, \frac{3}{5}\right]\)
3 \(\left(-\infty \frac{3}{5}\right) \cup\left(\frac{5}{3}, \infty\right)\)
4 \(\left[-\frac{5}{3},-\frac{3}{5}\right]\)
Sets, Relation and Function

117363 If \(\log _{0.3}(x-1)\lt \log _{0.09}(x-1)\), then \(x\) lies in the interval

1 \((2, \infty)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 None of these
Sets, Relation and Function

117364 If \(x\) is real then the range of \(\frac{x^2+2 x+1}{x^2+2 x+7}\) is

1 \([0,1)\)
2 \((-\infty, 0) \cup(1, \infty)\)
3 \((0,1)\)
4 \(\mathrm{R}\)
Sets, Relation and Function

117365 If \([x]\) denotes the greatest integer not exceeding \(x\), then the values of \(x\) satisfying \([x]^2-7[x]+\) \(\mathbf{1 2} \leq \mathbf{0}\)

1 \(1 \leq x\lt 4\)
2 \(3 \leq x\lt 5\)
3 \(-5\lt \mathrm{x} \leq-3\)
4 \(2 \leq x \leq 4\)
Sets, Relation and Function

117361 The minimum value of \(\cos \theta+\sin \theta+\frac{2}{\sin 2 \theta}\) for \(\theta \in(0, \pi / 2)\), is

1 \(2+\sqrt{2}\)
2 2
3 \(1+\sqrt{2}\)
4 \(2 \sqrt{2}\)
Sets, Relation and Function

117362 Let \(f: R \rightarrow R\) be defined as \(f(x)=\) \(\frac{x^2-x+4}{x^2+x+4}\). Then, range of the function \(f(x)\) is

1 \(\left[\frac{3}{5}, \frac{5}{3}\right]\)
2 \(\left[\frac{5}{3}, \frac{3}{5}\right]\)
3 \(\left(-\infty \frac{3}{5}\right) \cup\left(\frac{5}{3}, \infty\right)\)
4 \(\left[-\frac{5}{3},-\frac{3}{5}\right]\)
Sets, Relation and Function

117363 If \(\log _{0.3}(x-1)\lt \log _{0.09}(x-1)\), then \(x\) lies in the interval

1 \((2, \infty)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 None of these
Sets, Relation and Function

117364 If \(x\) is real then the range of \(\frac{x^2+2 x+1}{x^2+2 x+7}\) is

1 \([0,1)\)
2 \((-\infty, 0) \cup(1, \infty)\)
3 \((0,1)\)
4 \(\mathrm{R}\)
Sets, Relation and Function

117365 If \([x]\) denotes the greatest integer not exceeding \(x\), then the values of \(x\) satisfying \([x]^2-7[x]+\) \(\mathbf{1 2} \leq \mathbf{0}\)

1 \(1 \leq x\lt 4\)
2 \(3 \leq x\lt 5\)
3 \(-5\lt \mathrm{x} \leq-3\)
4 \(2 \leq x \leq 4\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

117361 The minimum value of \(\cos \theta+\sin \theta+\frac{2}{\sin 2 \theta}\) for \(\theta \in(0, \pi / 2)\), is

1 \(2+\sqrt{2}\)
2 2
3 \(1+\sqrt{2}\)
4 \(2 \sqrt{2}\)
Sets, Relation and Function

117362 Let \(f: R \rightarrow R\) be defined as \(f(x)=\) \(\frac{x^2-x+4}{x^2+x+4}\). Then, range of the function \(f(x)\) is

1 \(\left[\frac{3}{5}, \frac{5}{3}\right]\)
2 \(\left[\frac{5}{3}, \frac{3}{5}\right]\)
3 \(\left(-\infty \frac{3}{5}\right) \cup\left(\frac{5}{3}, \infty\right)\)
4 \(\left[-\frac{5}{3},-\frac{3}{5}\right]\)
Sets, Relation and Function

117363 If \(\log _{0.3}(x-1)\lt \log _{0.09}(x-1)\), then \(x\) lies in the interval

1 \((2, \infty)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 None of these
Sets, Relation and Function

117364 If \(x\) is real then the range of \(\frac{x^2+2 x+1}{x^2+2 x+7}\) is

1 \([0,1)\)
2 \((-\infty, 0) \cup(1, \infty)\)
3 \((0,1)\)
4 \(\mathrm{R}\)
Sets, Relation and Function

117365 If \([x]\) denotes the greatest integer not exceeding \(x\), then the values of \(x\) satisfying \([x]^2-7[x]+\) \(\mathbf{1 2} \leq \mathbf{0}\)

1 \(1 \leq x\lt 4\)
2 \(3 \leq x\lt 5\)
3 \(-5\lt \mathrm{x} \leq-3\)
4 \(2 \leq x \leq 4\)
Sets, Relation and Function

117361 The minimum value of \(\cos \theta+\sin \theta+\frac{2}{\sin 2 \theta}\) for \(\theta \in(0, \pi / 2)\), is

1 \(2+\sqrt{2}\)
2 2
3 \(1+\sqrt{2}\)
4 \(2 \sqrt{2}\)
Sets, Relation and Function

117362 Let \(f: R \rightarrow R\) be defined as \(f(x)=\) \(\frac{x^2-x+4}{x^2+x+4}\). Then, range of the function \(f(x)\) is

1 \(\left[\frac{3}{5}, \frac{5}{3}\right]\)
2 \(\left[\frac{5}{3}, \frac{3}{5}\right]\)
3 \(\left(-\infty \frac{3}{5}\right) \cup\left(\frac{5}{3}, \infty\right)\)
4 \(\left[-\frac{5}{3},-\frac{3}{5}\right]\)
Sets, Relation and Function

117363 If \(\log _{0.3}(x-1)\lt \log _{0.09}(x-1)\), then \(x\) lies in the interval

1 \((2, \infty)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 None of these
Sets, Relation and Function

117364 If \(x\) is real then the range of \(\frac{x^2+2 x+1}{x^2+2 x+7}\) is

1 \([0,1)\)
2 \((-\infty, 0) \cup(1, \infty)\)
3 \((0,1)\)
4 \(\mathrm{R}\)
Sets, Relation and Function

117365 If \([x]\) denotes the greatest integer not exceeding \(x\), then the values of \(x\) satisfying \([x]^2-7[x]+\) \(\mathbf{1 2} \leq \mathbf{0}\)

1 \(1 \leq x\lt 4\)
2 \(3 \leq x\lt 5\)
3 \(-5\lt \mathrm{x} \leq-3\)
4 \(2 \leq x \leq 4\)
Sets, Relation and Function

117361 The minimum value of \(\cos \theta+\sin \theta+\frac{2}{\sin 2 \theta}\) for \(\theta \in(0, \pi / 2)\), is

1 \(2+\sqrt{2}\)
2 2
3 \(1+\sqrt{2}\)
4 \(2 \sqrt{2}\)
Sets, Relation and Function

117362 Let \(f: R \rightarrow R\) be defined as \(f(x)=\) \(\frac{x^2-x+4}{x^2+x+4}\). Then, range of the function \(f(x)\) is

1 \(\left[\frac{3}{5}, \frac{5}{3}\right]\)
2 \(\left[\frac{5}{3}, \frac{3}{5}\right]\)
3 \(\left(-\infty \frac{3}{5}\right) \cup\left(\frac{5}{3}, \infty\right)\)
4 \(\left[-\frac{5}{3},-\frac{3}{5}\right]\)
Sets, Relation and Function

117363 If \(\log _{0.3}(x-1)\lt \log _{0.09}(x-1)\), then \(x\) lies in the interval

1 \((2, \infty)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 None of these
Sets, Relation and Function

117364 If \(x\) is real then the range of \(\frac{x^2+2 x+1}{x^2+2 x+7}\) is

1 \([0,1)\)
2 \((-\infty, 0) \cup(1, \infty)\)
3 \((0,1)\)
4 \(\mathrm{R}\)
Sets, Relation and Function

117365 If \([x]\) denotes the greatest integer not exceeding \(x\), then the values of \(x\) satisfying \([x]^2-7[x]+\) \(\mathbf{1 2} \leq \mathbf{0}\)

1 \(1 \leq x\lt 4\)
2 \(3 \leq x\lt 5\)
3 \(-5\lt \mathrm{x} \leq-3\)
4 \(2 \leq x \leq 4\)