The formula $\left(\frac{A}{B}\right)$ = $A\cap B^{c}$ represents the difference operation in terms of the operations of intersection and
complement. Then the formula for the union A U B in terms of the operations of intersection and complement is:
1). $A^{c}\cap B^{c}$
2). $A^{c}\cap B$
3). $(A\cap B)^{C}$
4). $(A^{C}\cap B^{C})^{C}$
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^{3}+px^{2}+q=0$ , where $q\neq0$, then the value of $\begin{bmatrix}\frac{1}{\alpha} & \frac{1}{\beta} & \frac{1}{\gamma} \\\frac{1}{\beta} & \frac{1}{\gamma} & \frac{1}{\alpha} \\\frac{1}{\gamma} & \frac{1}{\alpha} & \frac{1}{\beta} \end{bmatrix}$ is equal to :
1). $\frac{p}{q}$
2). 0
3). \frac{1}{p}
4). \frac{1}{q}
How many integer solutions are there for the equation x + y + z = 15.where
$x\geq0,y\geq0,z\geq0$ ?
1). 136
2). 6
3). 15
4). 1
Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be any three vectors such that $\mid\overrightarrow{a}\mid$ = 1, \mid\overrightarrow{b}\mid = 4, \mid\overrightarrow{c}\mid = 8, and $\overrightarrow{a}\cdot(\overrightarrow{b}+\overrightarrow{c})=\overrightarrow{b}\cdot(\overrightarrow{c}+\overrightarrow{a})=\overrightarrow{c}\cdot(\overrightarrow{a}+\overrightarrow{b})=0$, then $\mid \overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid$ is equal to :
1). 9
2). 12
3). 8
4). 7
If a system of equations x + y = 3,(1+ k )x+ (2 + k )y = 8 and x —(1+ k )y + (2 + k ) = 0 is consistent, then the
values of k are:
1). $1, \frac{-5}{3}$
2). $-1, \frac{1}{3}$
3). $\frac{2}{3}, -1$
4). 0, 1