The value of $$\theta $$lying between 0 and $$\pi /2$$and satisfying the equation $$\left| \,\begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 4\theta \ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 4\theta \ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 1+4\sin 4\theta \ \end{matrix}\, \right|=0$$ [IIT 1988; MNR 1992; Kurukshetra CEE 1998; DCE 1996]

Question

The value of $$\theta $$lying between 0 and $$\pi /2$$and satisfying the equation  $$\left| \,\begin{matrix}    1+{{\sin }^{2}}\theta  & {{\cos }^{2}}\theta  & 4\sin 4\theta   \    {{\sin }^{2}}\theta  & 1+{{\cos }^{2}}\theta  & 4\sin 4\theta   \    {{\sin }^{2}}\theta  & {{\cos }^{2}}\theta  & 1+4\sin 4\theta   \ \end{matrix}\, \right|=0$$ [IIT 1988; MNR 1992; Kurukshetra CEE 1998; DCE 1996]

TuteeHUB · Accepted Answer

$$\frac{5\pi }{24}$$

TuteeHUB · Answer

$$\frac{7\pi }{24}$$ or $$\frac{11\pi }{24}$$

TuteeHUB · Answer

$$\frac{\pi }{24}$$

TuteeHUB · Answer

None of these

1.	The value of \[\theta \]lying between 0 and \[\pi /2\]and satisfying the equation \[\left\| \,\begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 4\theta \\ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 4\theta \\ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 1+4\sin 4\theta \\ \end{matrix}\, \right\|=0\] [IIT 1988; MNR 1992; Kurukshetra CEE 1998; DCE 1996]
A.	\[\frac{7\pi }{24}\] or \[\frac{11\pi }{24}\]
B.	\[\frac{5\pi }{24}\]
C.	\[\frac{\pi }{24}\]
D.	None of these
Answer» B. \[\frac{5\pi }{24}\]

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