12th Maths - HSC - Important Questions

In our new series of one mark questions covering plus 2 mathematics, we will provide a new bunch of sample questions collected from different sources. We have a total of 40 questions split into five parts with eight questions in each part. Post your answers to this questions, which will help other students as well. Some of these questions are tough enough to test you from an examination point of view. These questions are applicable to all boards (State Board / Matriculation / CBSE), give it a go and provide your feedback to us.

Take me directly to Questions 9-16, 17-24, 25-32, 33-40

1) If $ \rho (A)=\rho (A,B) $, then the system is:

a) consistent and has infinitely many solutions

b) consistent

c) consistent and has a unique solution

d) inconsistent



2) If the rank of the matrix

$ \begin{bmatrix} \lambda \; \; \; \; -1 \; \; \; \; \; 0 \\ 0 \; \; \; \; \;\; \; \lambda \; \; \; \; \; -1 \\ -1 \; \; \; \; \; 0 \; \; \; \; \; \lambda \\ \end{bmatrix} $ is 2, then $ \lambda $ is:

a) 1

b) 2

c) 3

d) any real number



3) If A is a scalar matrix with scalar $ k\neq 0 $ of order 3, then $ A^{-1} $ is:

a) $ \frac{1}{K^2}I $

b) $ \frac{1}{K^3}I $

c) $ \frac{1}{K}I $

d) $ KI $



4) The system of equations $ ax+y+z=0, x+by+z=0, x+y+cz=0 $ has a non-trivial solution, then $ \frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}= $

a) 1

b) 2

c) –1

d) 0



5) The point of intersection of the lines $ \frac{x-6}{-6}=\frac{y+4}{4}=\frac{z-4}{-8} $ and $ \frac{x+1}{2}=\frac{y+2}{4}=\frac{z+3}{-2} $ is:

a) (0, 0, –4)

b) (1, 0, 0)

c) (0, 2, 0)

d) (1, 2, 0)



6) The projection of $ \overrightarrow{OP} $ on a unit vector $ \overrightarrow{OQ} $ equals three times of the area of the parallelogram OPRQ, then $ \angle POQ $ is:

a) $ sin^{-1}(\frac{3}{\sqrt{10}}) $

b) $ cos^{-1}(\frac{3}{\sqrt{10}}) $

c) $ tan^{-1}(\frac{1}{3}) $

d) $ sin^{-1}(\frac{1}{3}) $



7) 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) 2[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]

d) 3[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]



8) If $ \overrightarrow{a} $ and $ \overrightarrow{b} $ are two unit vectors and $ \Theta $ is the angle between them, then $ (\overrightarrow{a}+\overrightarrow{b}) $ is a unit vector if

a) $ \Theta =\frac{\pi}{3} $

b) $ \Theta =\frac{\pi}{4} $

c) $ \Theta =\frac{\pi}{2} $

d) $ \Theta =\frac{2\pi}{3} $