# HSC Maths Practice Question Paper - Part2 - AA1

This post is Part 2 of the AA1 question paper series on HSC Mathematics. You may wish to refer to Part 1 - HSC Maths before attempting this section. We presented 15 practice questions in Part 1. The Next set of 15 questions will be provided in this section.
16) 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) $\overrightarrow{x} =\overrightarrow{0}$ (or) $\overrightarrow{y} =\overrightarrow{0}$ (or) $\overrightarrow{x}$ and $\overrightarrow{y}$ are parallel

17) If $[\overrightarrow{a} \times \overrightarrow{b}, \overrightarrow{b} \times \overrightarrow{c}, \overrightarrow{c} \times \overrightarrow{a}]=64$, then $[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}]$ is ………

a) 32

b) 8

c) 128

d) 0

18) If a line makes $45^{\circ}, 60^{\circ}$ with positive direction of axes x and y, then the angle it makes with the z-axis is …….

a) $30^{\circ}$

b) $90^{\circ}$

c) $45^{\circ}$

d) $60^{\circ}$

19) The shortest distance of the point (2, 10, 1) from the plane $\overrightarrow{r}.(3\overrightarrow{i}-\overrightarrow{j}+4\overrightarrow{k}) =2\sqrt{26}$ is ……..

a) $2\sqrt{26}$

b) $\sqrt{26}$

c) $2$

d) $\frac{1}{\sqrt{26}}$

20) $\overrightarrow{r}=s\overrightarrow{i}+t\overrightarrow{j}$ is the equation of ……..

a) A straight line joining the points $\overrightarrow{i}$ and $\overrightarrow{j}$

b) xoy plane

c) yoz plane

d) zox plane

21) The point of intersection of the line $\overrightarrow{r}=(\overrightarrow{i}-\overrightarrow{j})+t(3\overrightarrow{i}+2\overrightarrow{j}+7\overrightarrow{k})$ and the plane $\overrightarrow{r}.(\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k})=8$ is …………

a) (8, 6, 22)

b) (-8, –6, –22)

c) (4, 3, 11)

d) (-4, –3, –11)

22) The point of intersection of the line $\frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8}$ and $\frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2}$ is ………….

a) (0, 0 –4)

b) (1, 0, 0)

c) (0, 2, 0)

d) (1, 2, 0)

23) The centre and radius of the sphere given by the equation: $x^2+y^2+z^2-6x+8y-10z+1=0$ are ……..

a) (-3, 4, –5), 49

b) (-6, 8, –10), 1

c) (3, –4, 5), 7

d) (6, –8, 10), 7

24) The modulus and amplitude of the complex number $[e^{3-\frac{i\pi}{4}}]^3$ are respectively ………

a) $e^9, \frac{\pi}{2}$

b) $e^9, \frac{-\pi}{2}$

c) $e^6, \frac{-3\pi}{4}$

d) $e^9, \frac{-3\pi}{4}$

25) The modulus of the complex number $2+i\sqrt{3}$ is ……….

a) $\sqrt{3}$

b) $\sqrt{13}$

c) $\sqrt{7}$

d) $7$

26) If Z represents a complex number, then $arg(z)+arg(\overline{z})$ is …………

a) $\frac{\pi}{4}$

b) $\frac{\pi}{2}$

c) 0

d) $\frac{3\pi}{4}$

27) The polar form of the complex number $(i^{25})^3$ is …………….

a) $cos \frac{\pi}{2}+i\;sin\frac{\pi}{2}$

b) $cos \frac{\pi}{2}-i\;sin\frac{\pi}{2}$

c) $cos \pi+i\;sin\pi$

d) $cos \pi-i\;sin\pi$

28) $\frac{1+e^{-i\Theta}}{1+e^{i\Theta}}$ = …………….

a) $cos\;\Theta+i\;sin\;\Theta$

b) $cos\;\Theta-i\;sin\;\Theta$

c) $sin\;\Theta-i\;cos\;\Theta$

d) $sin\;\Theta+i\;cos\;\Theta$

29) If $x= cos\;\Theta+i\;sin\;\Theta$, the value of $x^n+\frac{1}{x^n}$ is …………

a) $2 \; cos \;n\Theta$

b) $2i \; sin \;n\Theta$

c) $2 \; sin \;n\Theta$

d) $2i \; cos \;n\Theta$

30) The value of $i+i^22+i^23+i^24+i^25$ is ……..

a) i

b) –i

c) 1

d) –1