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

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

On the set Q of all rational numbers the operation * which is both associative and commutative is given by a * b, is :

• a + b + ab

• a² + b²

• ab + 1

• 2a + 3b

If ${\cos }^{-1}\left(\mathrm{x}\right) = \mathrm{\alpha }, \left(0 < \mathrm{x} < 1\right)$ and ${\sin }^{-1}\left(2\mathrm{x}\sqrt{1 - {\mathrm{x}}^2}\right)$ + ${\sec }^{-1}\left(\frac{1}{2{\mathrm{x}}^2 - 1}\right) = \frac{2\mathrm{\pi }}{3}$, then ${\tan }^{-1}\left(2\mathrm{x}\right)$ equals :

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

If a > b > 0, then the value of ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right) + {\tan }^{-1}\left(\frac{\mathrm{a} + \mathrm{b}}{\mathrm{a} - \mathrm{b}}\right)$ depends on :

• both a and b

• b and not a

• a and not b

• neither a nor b

The function f : X $\to$ Y defined by f(x) = sin(x) is one-one but not onto, if X and Y are respectively equal to :

• R and R

• $\left[0, \mathrm{\pi }\right] \mathrm{and} \left[0, 1\right]$

• $\left[0, \frac{\mathrm{\pi }}{2}\right] \mathrm{and} \left[- 1, 1\right]$

• $\left[\frac{- \mathrm{\pi }}{2}, \frac{\mathrm{\pi }}{2}\right] \mathrm{and} \left[- 1, 1\right]$

In the group G = {1, 5, 7, 11} under multiplication modulo 12, the solution of $7^{- 1} {\otimes }_{12} \left(\mathrm{x} {\otimes }_{12} 11\right) = 5$ is equals :

• 5

• 1

• 7

• 11

If the curve y = 2x³ + ax² + bx + c passes through the origin and the tangents drawn to it at x = - 1 and x = 2 are parallel to the x-axis, then the values of a, b and c are respectively :

• 12, - 3 and 0

• - 3, - 12 and 0

• - 3, 12 and 0

• 3, - 12 and 0