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