HSC Maths - Important Questions - Collection

Back again, this time with a dozen new one mark questions (12th / all boards) compiled from a random pool of sample questions for Mathematics. Questions are generic enough to be applied across all boards and will give a good practice to prospective students. If you know the answers to any of these questions, have a go and let us see if you are right..or not..

1) If the points $ (\lambda,0,3),(1,3,-1) $ and $ (-5,-3,7) $ are collinear, then the value of $ \lambda $ is:

a) 1

b) 2

c) –2

d) 0



2) If the planes $ \overrightarrow{r}.(2\overrightarrow{i}+\lambda\overrightarrow{j}-3\overrightarrow{k})=10 $ and $ \overrightarrow{r}.(\lambda\overrightarrow{i}+3overrightarrow{j}+\overrightarrow{k})=5 $ are perpendicular, then the value of $ \lambda $ is:

a) 3/5

b) 5/3

c) 3

d) 5



3) If $ \overrightarrow{p}, \overrightarrow{q} $ and $ \overrightarrow{p} + \overrightarrow{q} $ are vectors of magnitude $ \lambda $, then the magnitude of $ |\overrightarrow{p} - \overrightarrow{q}| $ is:

a) $ 2 \lambda $

b) $ \sqrt{3}\; \lambda $

c) $ \sqrt{2}\; \lambda $

d) 1



4) If a line makes 45 degree, 60 degree with positive direction of X and Y axes then the angle it makes with the Z-axis is:

a) 30 degree

b) 90 degree

c) 45 degree

d) 60 degree



5) If the magnitude of moment about the point $ \overrightarrow{j} + \overrightarrow{k} $ of a force $ \overrightarrow{i}+a\overrightarrow{j} - \overrightarrow{k} $ acting through the point $ \overrightarrow{i}+\overrightarrow{j} $ is $ \sqrt{8} $, then the value of ‘a’ is:

a) 1

b) 2

c) 3

d) 4



6) The workdone by the force $ \overrightarrow{F}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k} $ acting on a particle, if the particle is displaced from A(3, 3, 3) to the point B(4, 4, 4) is:

a) 2 units

b) 3 units

c) 4 units

d) 7 units



7) If the straight line $ \overrightarrow{r}=\overrightarrow{a} + t\overrightarrow{b} $ and $ \overrightarrow{r}=\overrightarrow{c} + s\overrightarrow{d} $ are perpendicular, then:

a) $ \overrightarrow{a} \times \overrightarrow{b}=0 $

b) $ \overrightarrow{a} . \overrightarrow{c}=0 $

c) $ \overrightarrow{b}. \overrightarrow{d}=0 $

d) $ \overrightarrow{b} \times \overrightarrow{d}=0 $



8) If $ e_{1} $ and $ e_{2} $ are two unit vectors at right angles, then $ |\overrightarrow{e_{1}}+\overrightarrow{e_{2}}|= $:

a) 2

b) >2

c) $ \geq 2 $

d) $ \sqrt{2} $



9) The condition of the line $ \overrightarrow{r}=\overrightarrow{a} + t\overrightarrow{b} $ and the plane $ \overrightarrow{r}-\overrightarrow{n}=q $ to be parallel is:

a) $ \overrightarrow{a}.\overrightarrow{n}=0 $

b) $ \overrightarrow{b}.\overrightarrow{n}=0 $

c) $ \overrightarrow{a}.\overrightarrow{b}=0 $

d) $ \overrightarrow{b}.\overrightarrow{n}=1 $



10) The angle between the planes 2x – y + 2Z = 1 and x – y = 2 is:

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

b) $ \frac{\pi}{3} $

c) $ \frac{\pi}{6} $

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



11) The angle between the vector $ \overrightarrow{i} -2\overrightarrow{j}+2\overrightarrow{k} $ and the X-axis is:

a) $ cos^{-1}\frac{1}{3} $

b) $ cos^{-1}\frac{1}{9} $

c) $ sin^{-1}\frac{1}{3} $

d) $ cos^{-1}\frac{}{3} $



12) The value of $ [\overrightarrow{a}, \overrightarrow{a}+\overrightarrow{b}, \overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}] $is:

a) $ [\overrightarrow{a}\;\overrightarrow{b}\; \overrightarrow{c}] $

b) $ [\overrightarrow{a}\;\overrightarrow{b}\; \overrightarrow{c}]^2 $

c) $ 3[\overrightarrow{a}\;\overrightarrow{b}\; \overrightarrow{c}] $

s) $ 2[\overrightarrow{a}\;\overrightarrow{b}\; \overrightarrow{c}] $