11.

If $\left|\begin{array}{ccc}0& 3& 2\mathrm{b}\\ 2& 0& 1\\ 4& - 1& 6\end{array}\right|$ is singular, then the value of  b is

• - 3

• 3

• - 6

• 6

If A = $\left[\begin{array}{cc}\mathrm{x}& \mathrm{x} - 1\\ 2\mathrm{x}& 1\end{array}\right]$ and if det A = - 9, then the avlue of x are

• $\frac{3}{2}, - 3$

• $\frac{- 2}{3}, 3$

• $\frac{2}{3}, 3$

• $- \frac{3}{2}, 3$

The value of the determinant $\left|\begin{array}{ccc}{\sin }^2\left(36°\right)& {\cos }^2\left(36°\right)& \cot \left(135°\right)\\ {\sin }^2\left(53°\right)& \cot \left(135°\right)& {\cos }^2\left(53°\right)\\ \cot \left(135°\right)& {\cos }^2\left(25°\right)& {\cos }^2\left(65°\right)\end{array}\right|$ is

• - 2

• - 1

• 0

• 1

If A and B are square matrices of the same order and if A = A^T, B = B^T, then (ABA)^T is equal to

• BAB

• ABA

• ABAB

• AB^T

$2{\tan }^{-1}\left(\frac{1}{3}\right) + {\tan }^{-1}\left(\frac{1}{4}\right)$ is equal to

• ${\tan }^{-1}\left(\frac{16}{13}\right)$

• ${\tan }^{-1}\left(\frac{17}{23}\right)$

• $\frac{\mathrm{\pi }}{4}$

• 0

If ${\cos }^{-1}\left(\mathrm{x}\right) + {\cos }^{-1}\left(\mathrm{y}\right) = \frac{2\mathrm{\pi }}{7}$, then the value of ${\sin }^{-1}\left(\mathrm{x}\right) + {\sin }^{-1}\left(\mathrm{y}\right)$ is

• $\frac{4\mathrm{\pi }}{7}$

• $\frac{3\mathrm{\pi }}{7}$

• $\frac{2\mathrm{\pi }}{7}$

• $\frac{5\mathrm{\pi }}{7}$

If ${\cos }^{-1}\left(\mathrm{x}\right) > {\sin }^{-1}\left(\mathrm{x}\right)$, then x lies in the interval

• $(\frac{1}{2}, 1]$

• (0, 1]

• $[- 1, \frac{1}{\sqrt{2}})$

• [- 1, 1]

A function f satisfies the relation f(n) = f(n²) + 6 for $\mathrm{n} \ge 2$  and f(2) = 8. Then, the value of f(256) is

• 24

• 26

• 22

• 28

The number of points at which the function $\mathrm{f}\left(\mathrm{x}\right) = \frac{1}{{\log }_{\mathrm{e}}\left|\mathrm{x}\right|}$ is discontinuous, is

• 1

• 2

• 3

• infinitely many

The functions f, g and h satisfy the relations f'(x) = g (x + 1) and g'(x) = h(x - 1). Then, f"(2x) is equal to

• h(2x)

• 4h(2x)

• h(2x - 1)

• h(2x + 1)