# +2 HSC Maths - Practice Questions

Question series from 20 to 26 are provided below. For more questions, refer to 'Related Post' section.

20) The are 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) $3\sqrt{30}$

21) In the set of integers under the operation * defined by $a*b=a+b-1$, the identity element is

a) 0

b) 1

c) a

d) b

22) $\mu_{2}=20$, $\mu_{2}=276$ for a discrete random variable X. Then, the mean of the random variable X is:

a) 16

b) 5

c) 3

d) 1

23) The random variable X follows normal distribution, $f(x)=ce^{-\frac{1}{2}\frac{(x-100)^2}{25}}$. Then the value of ‘c’ is:

a) $\sqrt{2\pi}$

b) $\frac{1}{\sqrt{2\pi}}$

c) $5\sqrt{2\pi}$

d) $\frac{1}{5\sqrt{2\pi}}$

24) A discrete random variable X has probability mass function p(x), then

a) $0\leq p(x)\leq1$

b) $p(x)\geq 0$

c) $p(x)\leq1$

d) 0< p(x)<1

25) In 16 throws of a die, getting an even number is considered a success. Then the variance of the success is:

a) 4

b) 6

c) 2

d) 256

26) The area of the region bounded by the graph of $y = sin x$ and $y = cos \;x$ between $x = 0$ and $x = \frac{\pi}{4}$ is :

a) $\sqrt2\;+\;1$

b) $\sqrt2\;-\;1$

c) $2\sqrt2\;-\;2$

d) $2\sqrt2\;+\;2$

Refer to questions 1-6 , 7-12 and 13-19 here.