Properties of Functions and Graphs
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Sets, Relation and Function

116874 If \(\boldsymbol{f}: \mathrm{R} \rightarrow \mathrm{R}\) be the signum function and \(\mathrm{g}: \mathrm{R}\)
\(\rightarrow R\) be the greatest integer function, then \(\sin \left\{\pi\left((\mathbf{f o g})\left(\frac{1}{2}\right)\right)\right\}\) is equal to

1 1
2 \(\frac{\sqrt{3}}{2}\)
3 0
4 \(\frac{1}{\sqrt{2}}\)
CG PET- 2016
Sets, Relation and Function

116876 The graph of the function \(y=\cos x \cos (x+2)-\cos ^2(x+1)\) is a

1 straight line passing through the point \(\left(0,-\sin ^2 1\right)\) and parallel to \(x\)-axis
2 straight line passing through the origin
3 parabola with vertex \(\left(0,-\sin ^2 1\right)\)
4 None of the above
SCRA-2014
Sets, Relation and Function

116878 Let \(\mathbf{f}(\mathbf{x})=2 \mathbf{x}+\tan ^{-1} \mathbf{x}\) and \(\mathbf{g}(\mathbf{x})=\log _{\mathrm{e}}\) \(\left(\sqrt{1+x^2}+x\right), x \in[0,3]\). Then

1 \(\min \mathrm{f}^{\prime}(\mathrm{x})=1+\max \mathrm{g}^{\prime}(\mathrm{x})\)
2 there exist \(0\lt \mathrm{x}_1\lt \mathrm{x}_2\lt 3\) such that \(\mathrm{f}(\mathrm{x})\lt \) \(\mathrm{g}(\mathrm{x}), \forall \mathrm{x} \in\left(\mathrm{x}_1, \mathrm{x}_2\right)\)
3 \(\max \mathrm{f}(\mathrm{x})>\max g(\mathrm{x})\)
4 there exists \(x \in[0,3]\) such that \(\mathrm{f}^{\prime}(\mathrm{x})\lt \mathrm{g}^{\prime}(\mathrm{x})\)
Shift-I
Sets, Relation and Function

116879 The function \(f(x)=\sqrt{\frac{1}{\sqrt{x}}-\sqrt{x+1}}\) is defined for

1 \(0\lt x \leq \frac{\sqrt{5}-1}{2}\)
2 \(\frac{-1-\sqrt{5}}{2}\lt x\lt 0\)
3 \(0\lt x\lt \frac{\sqrt{3}-1}{2}\)
4 \(\frac{-1-\sqrt{3}}{2}\lt x\lt 0\)
AMU-2006
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Sets, Relation and Function

116874 If \(\boldsymbol{f}: \mathrm{R} \rightarrow \mathrm{R}\) be the signum function and \(\mathrm{g}: \mathrm{R}\)
\(\rightarrow R\) be the greatest integer function, then \(\sin \left\{\pi\left((\mathbf{f o g})\left(\frac{1}{2}\right)\right)\right\}\) is equal to

1 1
2 \(\frac{\sqrt{3}}{2}\)
3 0
4 \(\frac{1}{\sqrt{2}}\)
CG PET- 2016
Sets, Relation and Function

116876 The graph of the function \(y=\cos x \cos (x+2)-\cos ^2(x+1)\) is a

1 straight line passing through the point \(\left(0,-\sin ^2 1\right)\) and parallel to \(x\)-axis
2 straight line passing through the origin
3 parabola with vertex \(\left(0,-\sin ^2 1\right)\)
4 None of the above
SCRA-2014
Sets, Relation and Function

116878 Let \(\mathbf{f}(\mathbf{x})=2 \mathbf{x}+\tan ^{-1} \mathbf{x}\) and \(\mathbf{g}(\mathbf{x})=\log _{\mathrm{e}}\) \(\left(\sqrt{1+x^2}+x\right), x \in[0,3]\). Then

1 \(\min \mathrm{f}^{\prime}(\mathrm{x})=1+\max \mathrm{g}^{\prime}(\mathrm{x})\)
2 there exist \(0\lt \mathrm{x}_1\lt \mathrm{x}_2\lt 3\) such that \(\mathrm{f}(\mathrm{x})\lt \) \(\mathrm{g}(\mathrm{x}), \forall \mathrm{x} \in\left(\mathrm{x}_1, \mathrm{x}_2\right)\)
3 \(\max \mathrm{f}(\mathrm{x})>\max g(\mathrm{x})\)
4 there exists \(x \in[0,3]\) such that \(\mathrm{f}^{\prime}(\mathrm{x})\lt \mathrm{g}^{\prime}(\mathrm{x})\)
Shift-I
Sets, Relation and Function

116879 The function \(f(x)=\sqrt{\frac{1}{\sqrt{x}}-\sqrt{x+1}}\) is defined for

1 \(0\lt x \leq \frac{\sqrt{5}-1}{2}\)
2 \(\frac{-1-\sqrt{5}}{2}\lt x\lt 0\)
3 \(0\lt x\lt \frac{\sqrt{3}-1}{2}\)
4 \(\frac{-1-\sqrt{3}}{2}\lt x\lt 0\)
AMU-2006
NEET DIGITAL LIBRARY
Sets, Relation and Function

116874 If \(\boldsymbol{f}: \mathrm{R} \rightarrow \mathrm{R}\) be the signum function and \(\mathrm{g}: \mathrm{R}\)
\(\rightarrow R\) be the greatest integer function, then \(\sin \left\{\pi\left((\mathbf{f o g})\left(\frac{1}{2}\right)\right)\right\}\) is equal to

1 1
2 \(\frac{\sqrt{3}}{2}\)
3 0
4 \(\frac{1}{\sqrt{2}}\)
CG PET- 2016
Sets, Relation and Function

116876 The graph of the function \(y=\cos x \cos (x+2)-\cos ^2(x+1)\) is a

1 straight line passing through the point \(\left(0,-\sin ^2 1\right)\) and parallel to \(x\)-axis
2 straight line passing through the origin
3 parabola with vertex \(\left(0,-\sin ^2 1\right)\)
4 None of the above
SCRA-2014
Sets, Relation and Function

116878 Let \(\mathbf{f}(\mathbf{x})=2 \mathbf{x}+\tan ^{-1} \mathbf{x}\) and \(\mathbf{g}(\mathbf{x})=\log _{\mathrm{e}}\) \(\left(\sqrt{1+x^2}+x\right), x \in[0,3]\). Then

1 \(\min \mathrm{f}^{\prime}(\mathrm{x})=1+\max \mathrm{g}^{\prime}(\mathrm{x})\)
2 there exist \(0\lt \mathrm{x}_1\lt \mathrm{x}_2\lt 3\) such that \(\mathrm{f}(\mathrm{x})\lt \) \(\mathrm{g}(\mathrm{x}), \forall \mathrm{x} \in\left(\mathrm{x}_1, \mathrm{x}_2\right)\)
3 \(\max \mathrm{f}(\mathrm{x})>\max g(\mathrm{x})\)
4 there exists \(x \in[0,3]\) such that \(\mathrm{f}^{\prime}(\mathrm{x})\lt \mathrm{g}^{\prime}(\mathrm{x})\)
Shift-I
Sets, Relation and Function

116879 The function \(f(x)=\sqrt{\frac{1}{\sqrt{x}}-\sqrt{x+1}}\) is defined for

1 \(0\lt x \leq \frac{\sqrt{5}-1}{2}\)
2 \(\frac{-1-\sqrt{5}}{2}\lt x\lt 0\)
3 \(0\lt x\lt \frac{\sqrt{3}-1}{2}\)
4 \(\frac{-1-\sqrt{3}}{2}\lt x\lt 0\)
AMU-2006
Join With Us for More Updates
Sets, Relation and Function

116874 If \(\boldsymbol{f}: \mathrm{R} \rightarrow \mathrm{R}\) be the signum function and \(\mathrm{g}: \mathrm{R}\)
\(\rightarrow R\) be the greatest integer function, then \(\sin \left\{\pi\left((\mathbf{f o g})\left(\frac{1}{2}\right)\right)\right\}\) is equal to

1 1
2 \(\frac{\sqrt{3}}{2}\)
3 0
4 \(\frac{1}{\sqrt{2}}\)
CG PET- 2016
Sets, Relation and Function

116876 The graph of the function \(y=\cos x \cos (x+2)-\cos ^2(x+1)\) is a

1 straight line passing through the point \(\left(0,-\sin ^2 1\right)\) and parallel to \(x\)-axis
2 straight line passing through the origin
3 parabola with vertex \(\left(0,-\sin ^2 1\right)\)
4 None of the above
SCRA-2014
Sets, Relation and Function

116878 Let \(\mathbf{f}(\mathbf{x})=2 \mathbf{x}+\tan ^{-1} \mathbf{x}\) and \(\mathbf{g}(\mathbf{x})=\log _{\mathrm{e}}\) \(\left(\sqrt{1+x^2}+x\right), x \in[0,3]\). Then

1 \(\min \mathrm{f}^{\prime}(\mathrm{x})=1+\max \mathrm{g}^{\prime}(\mathrm{x})\)
2 there exist \(0\lt \mathrm{x}_1\lt \mathrm{x}_2\lt 3\) such that \(\mathrm{f}(\mathrm{x})\lt \) \(\mathrm{g}(\mathrm{x}), \forall \mathrm{x} \in\left(\mathrm{x}_1, \mathrm{x}_2\right)\)
3 \(\max \mathrm{f}(\mathrm{x})>\max g(\mathrm{x})\)
4 there exists \(x \in[0,3]\) such that \(\mathrm{f}^{\prime}(\mathrm{x})\lt \mathrm{g}^{\prime}(\mathrm{x})\)
Shift-I
Sets, Relation and Function

116879 The function \(f(x)=\sqrt{\frac{1}{\sqrt{x}}-\sqrt{x+1}}\) is defined for

1 \(0\lt x \leq \frac{\sqrt{5}-1}{2}\)
2 \(\frac{-1-\sqrt{5}}{2}\lt x\lt 0\)
3 \(0\lt x\lt \frac{\sqrt{3}-1}{2}\)
4 \(\frac{-1-\sqrt{3}}{2}\lt x\lt 0\)
AMU-2006
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here