A square matrix [a₀] in which a₀ = 0 for $\mathrm{i} \ne \mathrm{j}$ and a₀ = k (constant) for i = j is callled a

• unit matrix

• scalar matrix

• null matrix

• diagonal matrix

If A = $\left[\begin{array}{cc}0& 2\\ 3& - 4\end{array}\right], \mathrm{hA} = \left[\begin{array}{cc}0& 3\mathrm{a}\\ 2\mathrm{b}& 24\end{array}\right]$, then the values of h, a, b are respectively

• - 6, - 12, - 18

• - 6, 4, 9

• - 6, - 4, - 9

• - 6, + 12, 18

73.

If $\left|\begin{array}{cc}1 - \mathrm{i}& \mathrm{i}\\ 1 + 2\mathrm{i}& - \mathrm{i}\end{array}\right| = \mathrm{x} +\hspace{0.17em}\mathrm{iy}$, then x is equal to

• - 2

• - 1

• 1

• 2

${\sec }^2\left({\tan }^{ - 1}\left(2\right)\right) + {\mathrm{cosec}}^2 \left({\cot }^{ - 1}\left(3\right)\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• 3

• 10

• 15

• 20

${\sinh }^{ - 1}\left(\frac{\mathrm{x}}{\sqrt{1 - {\mathrm{x}}^2}}\right) \mathrm{is} \mathrm{equal} \mathrm{to}$

• ${\coth }^{ - 1}\left(\mathrm{x}\right)$

• ${\sinh }^{ - 1}\left(\mathrm{x}\right)$

• $- {\tanh }^{ - 1}\left(\mathrm{x}\right)$

• ${\tanh }^{ - 1}\left(\mathrm{x}\right)$

If $\mathrm{a} = \hat{\mathrm{i}} + 4\hat{\mathrm{j}}, \mathrm{b} = 2\hat{\mathrm{i}} - 2\hat{\mathrm{j}}, \mathrm{c} = 5\hat{\mathrm{i}} + 9\hat{\mathrm{j}}$, then c is equal to

• 2a + b

• a + 2b

• 3a + b

• a + 3b

ABCD is a parallelogram, with AC, BD as diagonals, then AC - BD is equal to

• 4AB

• AB

• 3AB

• 2AB

If $\mathrm{a} = \hat{\mathrm{i}} + \hat{\mathrm{j}} + \mathrm{t}\hat{\mathrm{k}}, \mathrm{b} = \hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ then the values of 't' for which (a + b) and (a - b) are perpendicular, are

• $\pm 2$

• $\pm 2\sqrt{3}$

• $\pm 3\sqrt{2}$

• $\pm 3$

If $\mathrm{\theta }$ is the angle between a and b and $\left|\mathrm{a} \times \mathrm{b}\right| = \left|\mathrm{a} . \mathrm{b}\right|$, then $\mathrm{\theta }$ is equal to

• 0

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

$\left[\hat{\mathrm{i}} - \hat{\mathrm{j}}, \hat{\mathrm{j}} - \hat{\mathrm{k}}, \hat{\mathrm{k}} - \hat{\mathrm{i}}\right]$ is equal to

• 0

• 1

• 2

• 3