1.

Define a relation R on A = {1, 2, 3, 4} as xRy if x divides y. R is

• reflexive and transitive

• reflexive and symmetric

• symmetric and transitive

• equivalence

If lines represented by x + 3y - 6 = 0, 2x + y - 4 = 0 and kx - 3y + 1 = 0 are concurrent, then the value of k is

• $\frac{6}{19}$

• $\frac{19}{6}$

• $- \frac{19}{6}$

• $- \frac{6}{19}$

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

• 0

• - 1

• 1

• e

If A = $\left[\begin{array}{cc}\cos \left(\mathrm{\theta }\right)& \sin \left(\mathrm{\theta }\right)\\ - \sin \left(\mathrm{\theta }\right)& \cos \left(\mathrm{\theta }\right)\end{array}\right]$, then A . A' is

• I

• A

• - A

• A²

If $\left[\begin{array}{ccc}1& 2& - 1\\ 1& \mathrm{x} - 2& 1\\ \mathrm{x}& 1& 1\end{array}\right]$ is singular, then the value of x is

• 2

• 3

• 1

• 0

If A and B are symmetric matrices of the same order, then which one of the following is not true ?

• A + B is symmetric

• A - B is symmetric

• AB + BA is symmetric

• AB - BA is symmetric

If w is an imaginary cube root of unity, then the value $\left[\begin{array}{ccc}1& {\mathrm{w}}^2& 1 - {\mathrm{w}}^4\\ \mathrm{w}& 1& 1 + {\mathrm{w}}^5\\ 1& \mathrm{w}& {\mathrm{w}}^2\end{array}\right]$ is

• - 4

• w² - 4

• w²

• 4

On the set of all non-zero reals, an operation * is defined as a * b = $\frac{3\mathrm{ab}}{2}$. In this group, a solution of (2 * x) * 3^-1 = 4^-1 is

• 6

• 1

• 1/6

• 3/2

G = $\left\{\left[\begin{array}{cc}\mathrm{x}& \mathrm{x}\\ \mathrm{x}& \mathrm{x}\end{array}\right], \mathrm{x} \mathrm{is} \mathrm{a} \mathrm{non}-\mathrm{zero} \mathrm{real} \mathrm{number}\right\}$ is a roup with respect to matrix multiplication. In this group, the inverse of $\left[\begin{array}{cc}\frac{1}{3}& \frac{1}{3}\\ \frac{1}{3}& \frac{1}{3}\end{array}\right]$ is

• $\left[\begin{array}{cc}\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.& \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\\ \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.& \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\end{array}\right]$

• $\left[\begin{array}{cc}\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.& \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\\ \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.& \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\end{array}\right]$

• $\left[\begin{array}{cc}3& 3\\ 3& 3\end{array}\right]$

• $\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$

The domain of f(x) = ${\sin }^{-1}\left[{\log }_2\left(\frac{\mathrm{x}}{2}\right)\right]$ is

• $0 \le \mathrm{x} \le 1$

• $0 \le \mathrm{x} \le 4$

• $1 \le \mathrm{x} \le 4$

• $4 \le \mathrm{x} \le 6$