HSC Maths Practice Question Paper - Part1 - AA1

It has been some time since we were posting practice questions on HSC Mathematics. Finally, got some time to post some interesting and challenging questions to train your minds in Mathematics. In this new bunch of questions, we have a full question paper in Maths for you to work out and solve. It would be great if you can post the answers to the questions on this set to see how far you have fared. We have a total of 80 questions with 45 questions on one mark questions and the rest all are of five mark question types. The questions are generic enough and even if you are from a state board / matriculation standard 10, 11 and 12 you can make an attempt on them. We have named the question paper as AA1 and to navigate to subsequent parts of this question paper you can search with AA1 - Part(x). Happy solving.
1) $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0, |\overrightarrow{a}|=3, |\overrightarrow{b}|=4, |\overrightarrow{c}|=5,$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is:

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

b) $5\frac{\pi}{3}$

c) $2\frac{\pi}{3}$

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

2) The point of intersection of the lines $\overrightarrow{r}=(-\overrightarrow{i}+2\overrightarrow{j}+3\overrightarrow{k}) + t(-2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k})$ and $\overrightarrow{r}=(2\overrightarrow{i}+3\overrightarrow{j}+5\overrightarrow{k}) + s(\overrightarrow{i}+2\overrightarrow{j}+3\overrightarrow{k})$ is:

a) (1, 1, 1)

b) (2, 1, 1)

c) (1, 1, 2)

d) (1, 2, 1)

3) The non-parametric vector equation of a plane passing through the points whose point vectors are $\overrightarrow{a}, \overrightarrow{b}$ and parallel to $\overrightarrow{v}$ is:

a) [$\overrightarrow{r}$ $\overrightarrow{b}$ - $\overrightarrow{a}$ $\overrightarrow{v}$]=0

b) [$\overrightarrow{r}$ - $\overrightarrow{a}$  $\overrightarrow{b}$ - $\overrightarrow{a}$ $\overrightarrow{v}$]=0

c) [$\overrightarrow{r}$  $\overrightarrow{a}$ $\overrightarrow{b}$]=0

d) [$\overrightarrow{a}$  $\overrightarrow{b}$ $\overrightarrow{v}$]=0

4) The distance from the origin to the plane $\overrightarrow{r}.(2\overrightarrow{i}-\overrightarrow{j}+5\overrightarrow{k}) =7$ is:

a) $\frac{7}{30}$

b) $\frac{\sqrt{30}}{7}$

c) $\frac{30}{7}$

d) $\frac{7}{\sqrt{30}}$

5) Chord AB is a diameter of the sphere $|\overrightarrow{r}-(2\overrightarrow{i}+\overrightarrow{j}-6\overrightarrow{k})|=\sqrt{18}$ with co-ordinate of A as (3, 2, –2). The co-ordinates of B is:

a) (1, 0, 10)

b) (-1, 0, –10)

c) (-1, 0, 10)

d) (1, 0, –10)

6) If A=(2     0     1), then the rank of $AA^{T}$ is:

a) 0

b) 2

c) 3

d) 4

7) If A is a square matrix of order n, then |adj A| is:

a) $|A|^2$

b) $|A|^n$

c) $|A|^{n-1}$

d) $|A|$

8) If A is a matrix of order 3, then det(KA)= ---------

a) $k^3 det (A)$

b) $k^2 det (A)$

c) $k det (A)$

d) $det (A)$

9) The inverse of $\begin{pmatrix}3\;\;\;\;\; 1\\5\;\;\;\;\; 2\\\end{pmatrix}$ is:

a) $\begin{pmatrix}2\;\;\;\;\; -1\\-5\;\;\;\;\; 3\\\end{pmatrix}$

b) $\begin{pmatrix}-2\;\;\;\;\; 5\\1\;\;\;\;\; -3\\\end{pmatrix}$

c) $\begin{pmatrix}3\;\;\;\;\; -1\\-5\;\;\;\;\; -3\\\end{pmatrix}$

d) $\begin{pmatrix}-3\;\;\;\;\; 5\\1\;\;\;\;\; -2\\\end{pmatrix}$

10) If A and B are any two matrices such that AB=0 and A is non-singular then,

a) B=0

b) B is singular

c) B is non-singular

d) B=A

11) If the matrix $\begin{pmatrix}-1\;\;\;\;\; 3\;\;\;\;\; 2\\1\;\;\;\;\; k\;\;\;\;\; -3\\1\;\;\;\;\; 4\;\;\;\;\; 5\end{pmatrix}$ has an inverse, then

a) k is any real number

b) k=-4

c) $k\neq –4$

d) $k\neq 4$

12) If $A= \begin{pmatrix}2\;\;\;\;\; 1\\3\;\;\;\;\; 4\\\end{pmatrix}$, then (adj A)A = --------

a) $\begin{pmatrix}\frac{1}{5}\;\;\;\;\; 0\\0\;\;\;\;\; \frac{1}{5}\\\end{pmatrix}$

b) $\begin{pmatrix}1\;\;\;\;\; 0\\0\;\;\;\;\; 1\\\end{pmatrix}$

c) $\begin{pmatrix}5\;\;\;\;\; 0\\0\;\;\;\;\; -5\\\end{pmatrix}$

d) $\begin{pmatrix}5\;\;\;\;\; 0\\0\;\;\;\;\; 5\\\end{pmatrix}$

13) In a system of 3 linear non-homogenous equations in three unknowns, if $\Delta=0$  and $\Delta x = 0$, $\Delta \neq 0$, $\Delta z = 0$, then the system has………..

a) A unique solution

b) Two solutions

c) Infinitely manly solutions

d) No solutions

14) If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0, \;|\overrightarrow{a}|=3, \;|\overrightarrow{b}|=4, \;|\overrightarrow{c}|=5$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is ……………

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

b) $\frac{2\pi}{3}$

c) $\frac{5\pi}{3}$

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

15) The area of the parallelogram having a diagonal $3\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k}$ and a side $\overrightarrow{i}-3\overrightarrow{j}+4\overrightarrow{k}$ is :

a) $10\sqrt{3}$

b) $6\sqrt{30}$

c) $\frac{3}{2}\sqrt{30}$

d) $3\sqrt{30}$