# HSC Maths Objective Questions

HSC State board/Matriculation objective type Maths questions from 34 to 40 are provided in this post. These questions are very important to score 100% in the public examination.

34) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 1 $cm^3$/min. The rate at which the diameter is diameter when the diameter is 10 cms is:

a) $-\frac{1}{50\pi} \; cm/min$

b) $\frac{1}{50\pi} \; cm/min$

c) $-\frac{11}{75\pi} \; cm/min$

d) $-\frac{2}{75\pi} \; cm/min$

35) The surface area of a sphere when the volume is increasing at the same rate as its radius, is:

a) 1

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

c) $4\pi$

d) $\frac{4\pi}{3}$

36) If $[\overrightarrow{a}+\overrightarrow{b}, \overrightarrow{b}+\overrightarrow{c}, \overrightarrow{c}+\overrightarrow{a}]$, then $[\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}]$ is:

a) 4

b) 16

c) 32

d) –4

37) The equation of the plane passing through the point (2, 1, –1) and the line of intersection of the planes $\overrightarrow{r}.(\overrightarrow{i}+3\overrightarrow{j}-\overrightarrow{k})=0$ and $\overrightarrow{r}.(\overrightarrow{j}+2\overrightarrow{k})=0$ is:

a) x + 4y – z = 0

b) x + 9y + 11z = 0

c) 2x + y – z + 5 = 0

d) 2x – y + z = 0

38) The two lines $\frac{x-1}{2}=\frac{y-1}{-1}=\frac{z}{1}$ and $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z-1}{2}$ are:

a) parallel

b) intersecting

c) skew

d) perpendicular

39) The angle between the two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ if $|\overrightarrow{a} \times \overrightarrow{b}|=\overrightarrow{a}.\overrightarrow{b}$, is:

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

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

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

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

40) Chord AB is a diameter of the sphere $|\overrightarrow{r}-(2\overrightarrow{i}+\overrightarrow{j}-6\overrightarrow{k})|=\sqrt18$ with coordinate of A as (3, 2, –2). The coordinate of B is:

a) (1, 0, 10)

b) (-1, 0, –10)

c) (-1, 0, 10)

d) (1, 0, –10)

Refer to the previous question range in Set 1 here for 1-6 , 7-12 , 13-19 , 20-26 , and 27-33 .