# HSC +2 Maths Important Questions AA4 - Part 1

In this new series, we present a collection of 40 one mark questions in +2 mathematics subject, divided into five parts of eight questions each. Students are advised to take these questions as practice questions only and solve them carefully as aligned to their subjects. Once solved, post your answers to these questions in the comments section of this blog post. This will help other students to understand how you have solved the questions and help them to learn as well. Let us get started with the questions now. Post your solutions and don't forget to share this post..
Questions from 1-8 of 40 - AA4 Series
1) If $A=\begin{bmatrix} 1\\ 2\\ 3\\ \end{bmatrix}$, then the rank of $AA^{T}$ is:

a) 3                 b) 0                 c) 1                 d) 2

2) If I is the unit matrix of order n, where $k \neq 0$ is a constant,

a) $k^{n}(adj\: I)$              b) $k(adj\: I)$

c) $k^{2}(adj\: (I))$              d) $k^{n-1}(adj\: I)$

3) In a system of 3 linear non-homogenous equation with three unknowns,

if $\Delta=0$ and $\Delta_{x}=0$, $\Delta_{y} \neq 0$

and $\Delta_{z}=0$, then the system has:

a) unique solution         b) two solutions         c) infinitely many solutions         d) no solutions

4) If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors

and $\Theta$ is the angle between them, then  $(\overrightarrow{a}+\overrightarrow{b})$

is a unit vector if:

a) $\Theta=\frac{\pi}{3}$      b) $\Theta=\frac{\pi}{4}$

c) $\Theta=\frac{\pi}{2}$      d) $\Theta=\frac{2\pi}{3}$

5) If $|\overrightarrow{a}+\overrightarrow{b}| = |\overrightarrow{a}-\overrightarrow{b}|$, then:

a) $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$

b) $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$

c) $|\overrightarrow{a}|=|\overrightarrow{b}|$

d) $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors

6) If $\overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c})+\overrightarrow{b} \times (\overrightarrow{c} \times \overrightarrow{a}) +\overrightarrow{c} \times (\overrightarrow{a} \times \overrightarrow{b}) = \overrightarrow{x} \times \overrightarrow{y}$, then:

a) $\overrightarrow{x}= \overrightarrow{0}$

b) $\overrightarrow{y}= \overrightarrow{0}$

c) $\overrightarrow{x}$ and $\overrightarrow{y}$ are parallel

d) x=0 or y=0 or $\overrightarrow{x}$ and $\overrightarrow{y}$ are parallel

7) If $\overrightarrow{PR}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$,

$\overrightarrow{QS}=-\overrightarrow{i}+3\overrightarrow{j}+2\overrightarrow{k}$,

then the area of the quadrilateral PQRS is:

a) $5\sqrt3$                     b) $10\sqrt3$

c) $5\frac{\sqrt3}{2}$      d) $\frac{3}{2}$

8) The shortest distance between the parallel lines $\frac{x-3}{4}=\frac{y-1}{2}=\frac{z-5}{-3}$

and $\frac{x-1}{4}=\frac{y-2}{2}=\frac{z-3}{-3}$ is:

a) 3        b) 2        c) 1        d) 0