If * is the operation defined by a b = ab for a, b $\in$ N, then (2 * 3) * 2 is equal to

• 81

• 512

• 216

• 64

The domain of the function f(x) $$\begin{gathered} \left\{\left({\mathrm{x}}^2 - 9\right)/\left(\mathrm{x} - 3\right), \mathrm{if} \mathrm{x} \ne 3 \\ 6, \mathrm{if} \mathrm{x} = 3\right\} \end{gathered}$$ is

• (0, 3)

• $\left(- \infty , 3\right)$

• $\left(- \infty , \infty \right)$

• $\left(3, \infty \right)$

13.

Let f(x) = x³ and g(x) = 3^*. The values of A such that g[f (A)] = f[g(A)] are

• 0, 2

• 1, 3

• 0, $\pm$ 3

• 0, $\pm \sqrt{3}$

If $\mathrm{f}\left(\frac{\mathrm{x} + 1}{2\mathrm{x} - 1}\right) = 2\mathrm{x}, \mathrm{x} \in \mathrm{N}$, then the value of f(2) is equal to

• 1

• 4

• 3

• 2

If the square of the matrix $\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{a}& - \mathrm{a}\end{array}\right]$ is the unit matrix, then b is equal to

• $\frac{\mathrm{a}}{1 + {\mathrm{a}}^2}$

• $\frac{1 - {\mathrm{a}}^2}{\mathrm{a}}$

• $\frac{1 + {\mathrm{a}}^2}{\mathrm{a}}$

• $\frac{\mathrm{a}}{1 - {\mathrm{a}}^2}$

If [1 x 1]$\left[\begin{array}{ccc}1& 3& 2\\ 0& 5& 1\\ 0& 2& 0\end{array}\right]\left[\begin{array}{c}1\\ 1\\ \mathrm{x}\end{array}\right] = 0$, then the values of x are

• 1, 5

• - 1, - 5

• 1, 6

• - 1, - 6

If A = $\left|\begin{array}{ccc}8& 27& 125\\ 2& 3& 5\\ 1& 1& 1\end{array}\right|$, then the value of A² is equal to

• 0

• 36

• 64

• 3600

If A = $\left[\begin{array}{ccc}\mathrm{x}& 1& - \mathrm{x}\\ 0& 1& - 1\\ \mathrm{x}& 0& 7\end{array}\right]$ and det(A) = $\left|\begin{array}{ccc}3& 0& 1\\ 2& - 1& 0\\ 0& 6& 7\end{array}\right|$, then value of x is

• - 3

• 3

• 2

• - 8

The coefficient of x² in the expansion of the determinnat $\left|\begin{array}{ccc}{\mathrm{x}}^2& {\mathrm{x}}^3 + 1& {\mathrm{x}}^5 + 2\\ {\mathrm{x}}^3 + 3& {\mathrm{x}}^2 + \mathrm{x}& {\mathrm{x}}^3 + {\mathrm{x}}^4\\ \mathrm{x} + 4& {\mathrm{x}}^3 + {\mathrm{x}}^4& 2^3\end{array}\right|$ is

• - 10

• - 8

• - 2

• - 6

Let A = $\left[\begin{array}{cc}1& \frac{- 1 - \mathrm{i}\sqrt{3}}{2}\\ \frac{- 1 + \mathrm{i}\sqrt{3}}{2}& 1\end{array}\right]$. Then A¹⁰⁰ is equal to

• 2¹⁰⁰A

• 2⁹⁹A

• 2⁹⁸A

• A