1.

If A = $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$, then ${\mathrm{A}}^{-1}$ is

• - A

• A

• 1

• None of these

If A = $\left[\begin{array}{ccc}6& 8& 5\\ 4& 2& 3\\ 9& 7& 1\end{array}\right]$ is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is :

• $\left[\begin{array}{ccc}6& 6& 7\\ 6& 2& 5\\ 7& 5& 1\end{array}\right]$

• $\left[\begin{array}{ccc}0& 2& - 2\\ - 2& 5& - 2\\ 2& 2& 0\end{array}\right]$

• $\left[\begin{array}{ccc}6& 6& 7\\ - 6& 2& - 5\\ - 7& 5& 1\end{array}\right]$

• $\left[\begin{array}{ccc}0& 6& - 2\\ 2& 0& - 2\\ - 2& - 2& 0\end{array}\right]$

If A = $\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$, then A¹⁰⁰ is equal to

• 2¹⁰⁰A

• 2⁹⁹A

• 100A

• 299A

If $\left[\begin{array}{ccc}1& 1& 1\\ 1& - 2& - 2\\ 1& 3& 1\end{array}\right]\left[\begin{array}{c}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right] = \left[\begin{array}{c}0\\ 3\\ 4\end{array}\right], \mathrm{then} \left[\begin{array}{c}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right]$ is equal to :

• $\left[\begin{array}{c}0\\ 1\\ 1\end{array}\right]$

• $\left[\begin{array}{c}1\\ 2\\ - 3\end{array}\right]$

• $\left[\begin{array}{c}5\\ - 2\\ 1\end{array}\right]$

• $\left[\begin{array}{c}1\\ - 2\\ 3\end{array}\right]$

$\frac{\mathrm{d}}{\mathrm{dx}}\left({\tan }^{-1}\left(\frac{\sqrt{1 + {\mathrm{x}}^2} - 1}{\mathrm{x}}\right)\right)$ is equal to :

• $\frac{1}{1 + {\mathrm{x}}^2}$

• $\frac{{\mathrm{x}}^2}{2\sqrt{1 + {\mathrm{x}}^2}\left(\sqrt{1 + {\mathrm{x}}^2} - 1\right)}$

• $\frac{2}{1 + {\mathrm{x}}^2}$

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

$\frac{\mathrm{d}}{\mathrm{dx}}\left({\tan }^{-1}\left(\sqrt{\frac{1 + \cos \left(\frac{\mathrm{x}}{2}\right)}{1 - \cos \left({\displaystyle \frac{\mathrm{x}}{2}}\right)}}\right)\right)$ is equal to :

• - 1/4

• 1/4

• - 1/2

• 1/2

The maximum value of x^1/x is :

• 1/e^e

• e

• e^1/e

• 1/e

The function f defined by f(x) = 4x⁴ - 2x + 1 is increasing for :

• x < 1

• x > 0

• x < 1/2

• x > 1/2

A particle moves in a straight line so that s = $\sqrt{\mathrm{t}}$, then its acceleration is proportional to :

• (velocity)³

• velocity

• (velocity)²

• (velocity)^3/2

If A and B are 2 x 2 matrices, then which of the following is true ?

• (A + B)² = A² + B² + 2AB

• (A - B)² = A² + B² - 2AB

• (A - B)(A + B) = A² + AB - BA - B²

• (A - B)(A + B) = A² - B²