Properties of Functions and Graphs
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Sets, Relation and Function

117005 If \(f(x)=\frac{4^x}{4^x+2}\), then \(f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+f\left(\frac{96}{97}\right)\) is equal to

1 1
2 48
3 -48
4 -1
Rajasthan PET-2012
Sets, Relation and Function

117006 The solution of equation \(9^x-2^{x+\frac{1}{2}}=2^{x+\frac{3}{2}}-3^{2 x-1}\) is

1 \(\log _{\mathrm{e}}\left(\frac{9}{\sqrt{8}}\right)\)
2 \(\log _9\left(\frac{9}{\sqrt{8}}\right)\)
3 \(\log _{(9 / 2)}\left(\frac{9}{\sqrt{8}}\right)\)
4 None of these
Rajasthan PET-2006
Sets, Relation and Function

117007 Which one of the following is an even function?

1 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+\mathrm{a}^{-\mathrm{x}}}{\mathrm{a}^{\mathrm{x}}-\mathrm{a}^{-\mathrm{x}}}\)
2 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+1}{\mathrm{a}^{\mathrm{x}}-1}\)
3 \(f(\mathrm{x})=\mathrm{x} \frac{\mathrm{a}^{\mathrm{x}}-1}{\mathrm{a}^{\mathrm{x}}+1}\)
4 \(f(\mathrm{x})=\log _{\mathrm{e}}\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Rajasthan PET-2003
Sets, Relation and Function

117008 If \(\boldsymbol{f}(\boldsymbol{\theta})=\tan \theta\), then the value of \(\frac{\boldsymbol{f}(\boldsymbol{\theta})-\boldsymbol{f}(\phi)}{\boldsymbol{1}+\boldsymbol{f}(\boldsymbol{\theta}) \boldsymbol{f}(\phi)}\) is

1 \(f(\theta)+f(\phi)\)
2 \(f(\theta-\phi)\)
3 \(f\left(\frac{\theta}{\phi}\right)\)
4 \(\theta-\phi\)
Rajasthan PET-2003
Sets, Relation and Function

117009 The sum of the real solutions of equation \(2|\mathbf{x}|^2+\mathbf{5 1}=|\mathbf{1}+\mathbf{2 0 x}|\) is

1 5
2 24
3 0
4 None of these
Manipal UGET-2020
Join With Us for More Updates
Sets, Relation and Function

117005 If \(f(x)=\frac{4^x}{4^x+2}\), then \(f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+f\left(\frac{96}{97}\right)\) is equal to

1 1
2 48
3 -48
4 -1
Rajasthan PET-2012
Sets, Relation and Function

117006 The solution of equation \(9^x-2^{x+\frac{1}{2}}=2^{x+\frac{3}{2}}-3^{2 x-1}\) is

1 \(\log _{\mathrm{e}}\left(\frac{9}{\sqrt{8}}\right)\)
2 \(\log _9\left(\frac{9}{\sqrt{8}}\right)\)
3 \(\log _{(9 / 2)}\left(\frac{9}{\sqrt{8}}\right)\)
4 None of these
Rajasthan PET-2006
Sets, Relation and Function

117007 Which one of the following is an even function?

1 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+\mathrm{a}^{-\mathrm{x}}}{\mathrm{a}^{\mathrm{x}}-\mathrm{a}^{-\mathrm{x}}}\)
2 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+1}{\mathrm{a}^{\mathrm{x}}-1}\)
3 \(f(\mathrm{x})=\mathrm{x} \frac{\mathrm{a}^{\mathrm{x}}-1}{\mathrm{a}^{\mathrm{x}}+1}\)
4 \(f(\mathrm{x})=\log _{\mathrm{e}}\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Rajasthan PET-2003
Sets, Relation and Function

117008 If \(\boldsymbol{f}(\boldsymbol{\theta})=\tan \theta\), then the value of \(\frac{\boldsymbol{f}(\boldsymbol{\theta})-\boldsymbol{f}(\phi)}{\boldsymbol{1}+\boldsymbol{f}(\boldsymbol{\theta}) \boldsymbol{f}(\phi)}\) is

1 \(f(\theta)+f(\phi)\)
2 \(f(\theta-\phi)\)
3 \(f\left(\frac{\theta}{\phi}\right)\)
4 \(\theta-\phi\)
Rajasthan PET-2003
Sets, Relation and Function

117009 The sum of the real solutions of equation \(2|\mathbf{x}|^2+\mathbf{5 1}=|\mathbf{1}+\mathbf{2 0 x}|\) is

1 5
2 24
3 0
4 None of these
Manipal UGET-2020
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

117005 If \(f(x)=\frac{4^x}{4^x+2}\), then \(f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+f\left(\frac{96}{97}\right)\) is equal to

1 1
2 48
3 -48
4 -1
Rajasthan PET-2012
Sets, Relation and Function

117006 The solution of equation \(9^x-2^{x+\frac{1}{2}}=2^{x+\frac{3}{2}}-3^{2 x-1}\) is

1 \(\log _{\mathrm{e}}\left(\frac{9}{\sqrt{8}}\right)\)
2 \(\log _9\left(\frac{9}{\sqrt{8}}\right)\)
3 \(\log _{(9 / 2)}\left(\frac{9}{\sqrt{8}}\right)\)
4 None of these
Rajasthan PET-2006
Sets, Relation and Function

117007 Which one of the following is an even function?

1 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+\mathrm{a}^{-\mathrm{x}}}{\mathrm{a}^{\mathrm{x}}-\mathrm{a}^{-\mathrm{x}}}\)
2 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+1}{\mathrm{a}^{\mathrm{x}}-1}\)
3 \(f(\mathrm{x})=\mathrm{x} \frac{\mathrm{a}^{\mathrm{x}}-1}{\mathrm{a}^{\mathrm{x}}+1}\)
4 \(f(\mathrm{x})=\log _{\mathrm{e}}\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Rajasthan PET-2003
Sets, Relation and Function

117008 If \(\boldsymbol{f}(\boldsymbol{\theta})=\tan \theta\), then the value of \(\frac{\boldsymbol{f}(\boldsymbol{\theta})-\boldsymbol{f}(\phi)}{\boldsymbol{1}+\boldsymbol{f}(\boldsymbol{\theta}) \boldsymbol{f}(\phi)}\) is

1 \(f(\theta)+f(\phi)\)
2 \(f(\theta-\phi)\)
3 \(f\left(\frac{\theta}{\phi}\right)\)
4 \(\theta-\phi\)
Rajasthan PET-2003
Sets, Relation and Function

117009 The sum of the real solutions of equation \(2|\mathbf{x}|^2+\mathbf{5 1}=|\mathbf{1}+\mathbf{2 0 x}|\) is

1 5
2 24
3 0
4 None of these
Manipal UGET-2020
NEET DIGITAL LIBRARY
Sets, Relation and Function

117005 If \(f(x)=\frac{4^x}{4^x+2}\), then \(f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+f\left(\frac{96}{97}\right)\) is equal to

1 1
2 48
3 -48
4 -1
Rajasthan PET-2012
Sets, Relation and Function

117006 The solution of equation \(9^x-2^{x+\frac{1}{2}}=2^{x+\frac{3}{2}}-3^{2 x-1}\) is

1 \(\log _{\mathrm{e}}\left(\frac{9}{\sqrt{8}}\right)\)
2 \(\log _9\left(\frac{9}{\sqrt{8}}\right)\)
3 \(\log _{(9 / 2)}\left(\frac{9}{\sqrt{8}}\right)\)
4 None of these
Rajasthan PET-2006
Sets, Relation and Function

117007 Which one of the following is an even function?

1 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+\mathrm{a}^{-\mathrm{x}}}{\mathrm{a}^{\mathrm{x}}-\mathrm{a}^{-\mathrm{x}}}\)
2 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+1}{\mathrm{a}^{\mathrm{x}}-1}\)
3 \(f(\mathrm{x})=\mathrm{x} \frac{\mathrm{a}^{\mathrm{x}}-1}{\mathrm{a}^{\mathrm{x}}+1}\)
4 \(f(\mathrm{x})=\log _{\mathrm{e}}\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Rajasthan PET-2003
Sets, Relation and Function

117008 If \(\boldsymbol{f}(\boldsymbol{\theta})=\tan \theta\), then the value of \(\frac{\boldsymbol{f}(\boldsymbol{\theta})-\boldsymbol{f}(\phi)}{\boldsymbol{1}+\boldsymbol{f}(\boldsymbol{\theta}) \boldsymbol{f}(\phi)}\) is

1 \(f(\theta)+f(\phi)\)
2 \(f(\theta-\phi)\)
3 \(f\left(\frac{\theta}{\phi}\right)\)
4 \(\theta-\phi\)
Rajasthan PET-2003
Sets, Relation and Function

117009 The sum of the real solutions of equation \(2|\mathbf{x}|^2+\mathbf{5 1}=|\mathbf{1}+\mathbf{2 0 x}|\) is

1 5
2 24
3 0
4 None of these
Manipal UGET-2020
Join With Us for More Updates
Sets, Relation and Function

117005 If \(f(x)=\frac{4^x}{4^x+2}\), then \(f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+f\left(\frac{96}{97}\right)\) is equal to

1 1
2 48
3 -48
4 -1
Rajasthan PET-2012
Sets, Relation and Function

117006 The solution of equation \(9^x-2^{x+\frac{1}{2}}=2^{x+\frac{3}{2}}-3^{2 x-1}\) is

1 \(\log _{\mathrm{e}}\left(\frac{9}{\sqrt{8}}\right)\)
2 \(\log _9\left(\frac{9}{\sqrt{8}}\right)\)
3 \(\log _{(9 / 2)}\left(\frac{9}{\sqrt{8}}\right)\)
4 None of these
Rajasthan PET-2006
Sets, Relation and Function

117007 Which one of the following is an even function?

1 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+\mathrm{a}^{-\mathrm{x}}}{\mathrm{a}^{\mathrm{x}}-\mathrm{a}^{-\mathrm{x}}}\)
2 \(f(\mathrm{x})=\frac{\mathrm{a}^{\mathrm{x}}+1}{\mathrm{a}^{\mathrm{x}}-1}\)
3 \(f(\mathrm{x})=\mathrm{x} \frac{\mathrm{a}^{\mathrm{x}}-1}{\mathrm{a}^{\mathrm{x}}+1}\)
4 \(f(\mathrm{x})=\log _{\mathrm{e}}\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Rajasthan PET-2003
Sets, Relation and Function

117008 If \(\boldsymbol{f}(\boldsymbol{\theta})=\tan \theta\), then the value of \(\frac{\boldsymbol{f}(\boldsymbol{\theta})-\boldsymbol{f}(\phi)}{\boldsymbol{1}+\boldsymbol{f}(\boldsymbol{\theta}) \boldsymbol{f}(\phi)}\) is

1 \(f(\theta)+f(\phi)\)
2 \(f(\theta-\phi)\)
3 \(f\left(\frac{\theta}{\phi}\right)\)
4 \(\theta-\phi\)
Rajasthan PET-2003
Sets, Relation and Function

117009 The sum of the real solutions of equation \(2|\mathbf{x}|^2+\mathbf{5 1}=|\mathbf{1}+\mathbf{2 0 x}|\) is

1 5
2 24
3 0
4 None of these
Manipal UGET-2020