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