\( \begin{array}{ll}\text { Comprehension } & : \theta \text { is said to be well behaved if it }\end{array} \) lies in interval \( \left[0, \frac{\pi}{2}\right] \). They are intelligent if they make domain of \( f+g \) and \( g \) equal. The values of \( \theta \) for which \( h(\theta) \) is defined are handsome. Let
\[
\begin{array}{l}
f(x)=\sqrt{\theta x^{2}-2\left(\theta^{2}-3\right) x-12 \theta}, g(x)=\ln \left(x^{2}-49\right), \\
h(\theta)=\ln \left[\int_{0}^{\theta} 4 \cos ^{2} t d t-\theta^{2}\right], \text { where } \theta \text { is in radians. }
\end{array}
\]
Complete set of values of \( \theta \) which are intelligent is
(a) \( \left[\frac{6}{7}, \frac{7}{2}\right] \)
(b) \( \left(0, \frac{\pi}{3}\right] \)
(c) \( \left[\frac{1}{4}, \frac{6}{7}\right] \)
(d) \( \left[\frac{1}{2}, \frac{\pi}{2}\right] \)
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