411.

In the group G = {1, 3, 7, 9} under multiplication modulo 10, the inverse of 3 is

• 1

• 3

• 7

• 9

If 2A + 3B = $\left[\begin{array}{ccc}2& - 1& 4\\ 3& 2& 5\end{array}\right] \mathrm{and} \mathrm{A} + 2\mathrm{B} = \left[\begin{array}{ccc}5& 0& 3\\ 1& 6& 2\end{array}\right]$, then B is

• $\left[\begin{array}{ccc}8& - 1& 2\\ - 1& 10& - 1\end{array}\right]$

• $\left[\begin{array}{ccc}8& 1& 2\\ - 1& 10& - 1\end{array}\right]$

• $\left[\begin{array}{ccc}8& 1& - 2\\ - 1& 10& - 1\end{array}\right]$

• $\left[\begin{array}{ccc}8& 1& 2\\ 1& 10& 1\end{array}\right]$

If O(A) = 2 x 3, O(B) = 3 x 2, and O(C) = 3 x 3, which one ofthe following is not defined?

• CB  + A'

• BAC

• C(A + B')'

• C(A + B')

If A = $\left[\begin{array}{cc}1& - 3\\ 2& \mathrm{k}\end{array}\right]$ and A² - 4A + 10I = A, then k is equal to :

• 0

• - 4

• 4 and not 1

• 1 or 4

The value of $\left|\begin{array}{ccc}\mathrm{x} + \mathrm{y}& \mathrm{y} + \mathrm{z}& \mathrm{z} +\hspace{0.17em}\mathrm{x}\\ \mathrm{x}& \mathrm{y}& \mathrm{z}\\ \mathrm{x} - \mathrm{y}& \mathrm{y} - \mathrm{z}& \mathrm{z} - \mathrm{x}\end{array}\right|$ is equal to :

• 2(x + y + z)²

• 2(x + y + z)³

• (x + y + z)³

• 0

If A = $\left[\begin{array}{ccc}0& \mathrm{x}& 16\\ \mathrm{x}& 5& 7\\ 0& 9& \mathrm{x}\end{array}\right]$is singular, then the possible values of x are

• 0, 12, - 12

• 0, 1, - 1

• 0, 4, - 4

• 0, 5, - 5

The value of $\left|\begin{array}{ccc}\mathrm{x}& \mathrm{p}& \mathrm{q}\\ \mathrm{p}& \mathrm{x}& \mathrm{q}\\ \mathrm{p}& \mathrm{q}& \mathrm{x}\end{array}\right|$ is

• x(x - p)(x - q)

• (x - p)(x - q)(x + p + q)

• (p - q)(x - q)(x - p)

• pq(x - p)(x - q)

The characteristic roots of the matrix $\left[\begin{array}{ccc}1& 0& 0\\ 2& 3& 0\\ 4& 5& 6\end{array}\right]$ are

• 1, 3, 6

• 1, 2, 4

• 4, 5, 6

• 2, 4, 6

If $\left|\begin{array}{ccc}1 + {\sin }^2\left(\mathrm{\theta }\right)& {\cos }^2\left(\mathrm{\theta }\right)& 4\sin \left(2\mathrm{\theta }\right)\\ {\sin }^2\left(\mathrm{\theta }\right)& 1 + {\cos }^2\left(\mathrm{\theta }\right)& 4\sin \left(2\mathrm{\theta }\right)\\ {\sin }^2\left(\mathrm{\theta }\right)& {\cos }^2\left(\mathrm{\theta }\right)& 4\sin \left(2\mathrm{\theta }\right) - 1\end{array}\right| = 0$ and $0 < \mathrm{\theta } < \frac{\mathrm{\pi }}{2}$, then $\cos \left(4\mathrm{\theta }\right)$ is equal to

• $\frac{\sqrt{3}}{2}$

• 0

• $\frac{- 1}{2}$

• $\frac{1}{2}$

If $\left|\begin{array}{ccc}\mathrm{x} +\hspace{0.17em}1& \mathrm{x} + 2& \mathrm{x} + \mathrm{a}\\ \mathrm{x} + 2& \mathrm{x} + 3& \mathrm{x} + \mathrm{b}\\ \mathrm{x} + 3& \mathrm{x} + 4& \mathrm{x} +\hspace{0.17em}\mathrm{c}\end{array}\right|$ = 0, then a, b, c are

• in GP

• in HP

• equal

• 9