111.

The maximum value of 4 sin²(x) - 12sin(x) + 7 is

• 25

• 4

• does not exist

• None of the above

A line making angles 45° and 60° with the positive directions of the axes of x and y makes with the positive direction of z-axis, an angle of

• 60°

• 120°

• 60° or 120°

• None of these

If I = $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, J = $\left[\begin{array}{cc}0& 1\\ - 1& 0\end{array}\right]$ and $\mathrm{B} = \left[\begin{array}{cc}\cos \left(\mathrm{\theta }\right)& \sin \left(\mathrm{\theta }\right)\\ - \sin \left(\mathrm{\theta }\right)& \cos \left(\mathrm{\theta }\right)\end{array}\right]$, then B is equal to

• $\mathrm{I} \cos \left(\mathrm{\theta }\right) + \mathrm{Jsin}\left(\mathrm{\theta }\right)$

• $\mathrm{I} \sin \left(\mathrm{\theta }\right) + \mathrm{Jcos}\left(\mathrm{\theta }\right)$

• $\mathrm{I} \cos \left(\mathrm{\theta }\right) - \mathrm{Jsin}\left(\mathrm{\theta }\right)$

• $- \mathrm{I} \cos \left(\mathrm{\theta }\right) + \mathrm{Jsin}\left(\mathrm{\theta }\right)$

Find the value of $\sin \left(12°\right)\sin \left(48°\right)\sin \left(54°\right)$.

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{6}$

• $\frac{1}{8}$

If $3\sin \left(\mathrm{\theta }\right) + 5\cos \left(\mathrm{\theta }\right)$, then the value of $5\sin \left(\mathrm{\theta }\right) - 3\cos \left(\mathrm{\theta }\right)$ is equal to

• 5

• 3

• 4

• None of these

Domain of the function f(x) = log_x(cos(x)), is

• $\left(- \frac{\mathrm{\pi }}{2}, \frac{\mathrm{\pi }}{2}\right) - \left\{1\right\}$

• $\left[- \frac{\mathrm{\pi }}{2}, \frac{\mathrm{\pi }}{2}\right] - \left\{1\right\}$

• $\left(- \frac{\mathrm{\pi }}{2}, \frac{\mathrm{\pi }}{2}\right)$

• None of these

If x = $\sec \left(\mathrm{\theta }\right) - \cos \left(\mathrm{\theta }\right), \mathrm{y} = {\sec }^{\mathrm{n}}\left(\mathrm{\theta }\right) - {\cos }^{\mathrm{n}}\left(\mathrm{\theta }\right)$, then $\left({\mathrm{x}}^2 + 4\right){\left(\frac{d\mathrm{y}}{d\mathrm{x}}\right)}^2$ is equal to

• n²(y² - 4)

• n²(4 - y²)

• n²(y² + 4)

• None of these

The two curves y = 3 and y = 5 intersect at an angle

• ${\tan }^{-1}\left(\frac{\log \left(3\right) - \log \left(5\right)}{1 + \log \left(3\right)\log \left(5\right)}\right)$

• ${\tan }^{-1}\left(\frac{\log \left(3\right) + \log \left(5\right)}{1 - \log \left(3\right)\log \left(5\right)}\right)$

• ${\tan }^{-1}\left(\frac{\log \left(3\right) + \log \left(5\right)}{1 + \log \left(3\right)\log \left(5\right)}\right)$

• ${\tan }^{-1}\left(\frac{\log \left(3\right) - \log \left(5\right)}{1 - \log \left(3\right)\log \left(5\right)}\right)$

The period of ${\sin }^4\left(\mathrm{x}\right) + {\cos }^4\left(\mathrm{x}\right)$ is

• $\frac{{\mathrm{\pi }}^4}{2}$

• $\frac{{\mathrm{\pi }}^2}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

If 3 cos x $\ne$ 2 sin x, then the general solution of ${\sin }^2\left(\mathrm{x}\right) - \cos \left(2\mathrm{x}\right) = 2 - \sin \left(2\mathrm{x}\right)$ is

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\frac{\mathrm{n\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\left(4\mathrm{n} \pm 1\right)\frac{\mathrm{\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• (2n - 1)$\mathrm{\pi }, \mathrm{n} \in \mathrm{Z}$