A) 2
B)
C) 4
D) 1
Correct Answer: B
Solution :
\[\frac{1}{\sqrt{2k}}\int\limits_{0}^{\pi /3}{\frac{\tan \theta }{\sqrt{\sec \theta }}d\theta =\frac{1}{\sqrt{2k}}\int\limits_{0}^{\pi /3}{\frac{\sin \theta }{\sqrt{\cos \theta }}}}d\theta \]\[=\left. -\frac{1}{\sqrt{2k}}2\sqrt{\cos \theta } \right|_{0}^{\pi /3}\]\[=-\frac{\sqrt{2}}{\sqrt{k}}\left( \frac{1}{\sqrt{2}}-1 \right)\] \[\Rightarrow \] \[k=2.\]
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