If $\mathrm{A} = \left(\begin{array}{cc}1& 5\\ 0& 2\end{array}\right)$, then

• A² - 2A + 2I = 0

• A² - 3A + 2I = 0

• A² - 5A + 2I = 0

• 2A² - A + I = 0

If $\left(\begin{array}{cc}2\mathrm{x} +\hspace{0.17em}\mathrm{y}& \mathrm{x} + \mathrm{y}\\ \mathrm{p} - \mathrm{q}& \mathrm{p} + \mathrm{q}\end{array}\right) = \left(\begin{array}{cc}1& 1\\ 0& 0\end{array}\right)$, then (x, y, p, q) equals

• 0, 1, 0, 0

• 0, - 1, 0, 0

• 1, 0, 0, 0

• 0, 1, 0, 1

The number of 3 x 3 matrices with entries - 1 or + 1 is

• 2^-4

• 2⁵

• 2⁶

• 2⁹

The value of a for which the matrix A = $\left[\begin{array}{cc}\mathrm{a}& 2\\ 2& 4\end{array}\right]$ is singular :

• $\mathrm{a} \ne 1$

• a = 1

• a = 0

• a = - 1

If A = $\left[\begin{array}{cc}2& - 1\\ - 1& 2\end{array}\right]$ and I is the unit matrix of order two, then A² is equal to :

• 4A - 3I

• 3A - 4I

• A - I

• A + I

If A and B are two square matrices of the same order, then (A - B)² :

• A² - AB - BA + B²

• A² - 2AB + B²

• A² - 2BA + B²

• A² - B²

If $\mathrm{P} = \left[\begin{array}{ccc}\mathrm{i}& 0& - \mathrm{i}\\ 0& - \mathrm{i}& \mathrm{i}\\ - \mathrm{i}& \mathrm{i}& 0\end{array}\right] \mathrm{and} \mathrm{Q} = \left[\begin{array}{cc}- \mathrm{i}& \mathrm{i}\\ 0& 0\\ \mathrm{i}& - \mathrm{i}\end{array}\right]$, then PQ is equal to

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

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

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

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

108.

For what value of $\mathrm{\lambda }$ the system of equations x + y + z = 6, x + 2y + 3z = 10, x + 2y + $\mathrm{\lambda }$z = 10 is consistent ?

• 1

• 2

• - 1

• 3

If a = 1 + 2 + 4 + ... to n terms, b = 1 + 3 + 9 + ... to n terms and c = 1 + 5 + 25 + ... to n terms, then

$\left|\begin{array}{ccc}\mathrm{a}& 2\mathrm{b}& 4\mathrm{c}\\ 2& 2& 2\\ 2^{\mathrm{n}}& 3^{\mathrm{n}}& 5^{\mathrm{n}}\end{array}\right|$ equals :

• (30)ⁿ

• (10)ⁿ

• 0

• 2ⁿ + 3ⁿ + 5ⁿ

The matrix $\left[\begin{array}{ccc}5& 10& 3\\ - 2& - 4& 6\\ - 1& - 2& \mathrm{b}\end{array}\right]$ is a singular matrix, if b is equal to :

• - 3

• 3

• 0

• for any value of b