A) \[\frac{1}{2}<\alpha <\frac{1}{\sqrt{2}}\]
B) \[-\frac{1}{\sqrt{2}}<\alpha <\frac{1}{\sqrt{2}}\]
C) \[\alpha >\frac{1}{2}\]
D) \[0<\alpha <\frac{1}{2}\]
Correct Answer: A
Solution :
| Point\[(\alpha ,\,\,\alpha )\] will lie is shaded region | |
| it \[{{a}^{2}}+{{a}^{2}}-1<0\] | |
| \[\Rightarrow \] \[2{{a}^{2}}-1<0\] | |
| \[\Rightarrow \] \[-\frac{1}{2}<\alpha <\frac{1}{\sqrt{2}}\] | ?(1) |
| and \[\alpha +\alpha >1\] \[\Rightarrow \] \[\alpha >\frac{1}{2}\] | ?(2) |
 | |
| \[\therefore \] common solution of (1) and (2) is: | |
| \[\frac{1}{2}<\alpha <\frac{1}{\sqrt{2}}\] | |
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