1.

The inverse matrix of $\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 3& 1& 1\end{array}\right]$, is

• $\left[\begin{array}{ccc}\frac{1}{2}& - \frac{1}{2}& \frac{1}{2}\\ - 4& 3& - 1\\ \frac{5}{2}& - \frac{3}{2}& \frac{1}{2}\end{array}\right]$

• $\left[\begin{array}{ccc}\frac{1}{2}& - 4& \frac{5}{2}\\ 1& - 6& 3\\ 1& 2& - 1\end{array}\right]$

• $\frac{1}{2}\left[\begin{array}{ccc}1& 2& 3\\ 3& 2& 1\\ 4& 2& 3\end{array}\right]$

• $\frac{1}{2}\left[\begin{array}{ccc}1& - 1& - 1\\ - 8& 6& - 2\\ 5& - 3& 1\end{array}\right]$

If $$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right) = \left\{\mathrm{xsin}\left(\frac{1}{\mathrm{x}}\right), \mathrm{x} \ne 0 \\ \mathrm{k}, \mathrm{x} = 0\right\} \end{gathered}$$ is continuous at x = 0, then the value of k is

• 1

• - 1

• 0

• 2

If x = $\frac{1 - {\mathrm{t}}^2}{1 + {\mathrm{t}}^2}$ and y = $\frac{2\mathrm{at}}{1 +\hspace{0.17em}{\mathrm{t}}^2}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is equal to

• $\frac{\mathrm{a}\left(1 - {\mathrm{t}}^2\right)}{2\mathrm{t}}$

• $\frac{\mathrm{a}\left({\mathrm{t}}^2 - 1\right)}{2\mathrm{t}}$

• $\frac{\mathrm{a}\left({\mathrm{t}}^2 + 1\right)}{2\mathrm{t}}$

• $\frac{\mathrm{a}\left({\mathrm{t}}^2 - 1\right)}{\mathrm{t}}$

The velocity of a particle at time t is given by the relation v = 6t - $\frac{{\mathrm{t}}^2}{6}$. The distance traveled in 3 s is, if s = 0 at t = 0

• $\frac{39}{2}$

• $\frac{57}{2}$

• $\frac{51}{2}$

• $\frac{33}{2}$

The maximum value of function x³ - 12x² + 36x + 17 in the interval [1, 10] is

• 17

• 177

• 77

• None of these

The value of $∆\log \left(\mathrm{f}\left(\mathrm{x}\right)\right) + {∆}^2\left(3^{\mathrm{x}}\right)$ is

• $\log \left[1 + \frac{∆\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\right] + 4 . 3^{\mathrm{x}}$

• $\log \left[1 + \frac{∆\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\right] + 3^{\mathrm{x}}$

• $\log \left[\frac{∆\mathrm{f}\left(\mathrm{x}\right)}{1 + \mathrm{f}\left(\mathrm{x}\right)}\right] + 4 . 3^{\mathrm{x}}$

• $\log \left[\frac{∆\mathrm{f}\left(\mathrm{x}\right)}{1 + \mathrm{f}\left(\mathrm{x}\right)}\right] + 3^{\mathrm{x}}$

The solution of the equation

$\left[\begin{array}{ccc}1& 0& 1\\ - 1& 1& 0\\ 0& - 1& 1\end{array}\right]\left[\begin{array}{c}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right] = \left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]$ is (x, y, z) = 

• (1, 1, 1)

• (0, - 1, 2)

• (- 1, 2, 2)

• (- 1, 0, 2)

The abscissae of the points, where the tangent is to curve y = x³ - 3x² - 9x + 5 is parallel to x-axis, are

• x = 0 and 0

• x = 1 and - 1

• x = 1 and - 3

• x = - 1 and 3

If $\overrightarrow{\mathrm{a}} . \hat{\mathrm{i}} = 4, \mathrm{then} \left(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{j}}\right) . \left(2\hat{\mathrm{j}} - 3\hat{\mathrm{k}}\right)$ is equal to

• 12

• 2

• 0

• - 12

The line joining the points $6\overrightarrow{\mathrm{a}} - 4\overrightarrow{\mathrm{b}} + 4\overrightarrow{\mathrm{c}}, - 4\overrightarrow{\mathrm{c}}$ and the line joining the points $- \overrightarrow{\mathrm{a}} - 2\overrightarrow{\mathrm{b}} - 3\overrightarrow{\mathrm{c}}, \overrightarrow{\mathrm{a}} + 2\overrightarrow{\mathrm{b}} - 5\overrightarrow{\mathrm{c}}$ intersect at

• $- 4\overrightarrow{\mathrm{a}}$

• $4\overrightarrow{\mathrm{a}} - \overrightarrow{\mathrm{b}} - \overrightarrow{\mathrm{c}}$

• $4\overrightarrow{\mathrm{c}}$

• None of the above