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 .