+2 Maths - Important One Mark Questions

+2 HSC Maths - Important Sums / One mark questions. New bunch of 15 sample questions for practice.

1) If two rows or columns of a determinants are identical, then the value of the determinants is:

a) 1

b) 2

c) 0

d) 3

2) If the number of rows and columns are equal, then this matrix is called:

a) rectangular matrix

b) square matrix

c) null matrix

d) diagonal matrix

3) If A and B are matrices conformable to multiplication, then $(AB)^T =$

a) $A^TB$

b) $AB^T$

c) $A^TB^T$

d) AB

4) Solve 2x+3y=7; 4x+6y=10 by determinant method.

a) (1,1)

b) (1,0)

c) (0,1)

d) no solution

5) If $A=\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$, then the rank of $AA^{T}$ is

a) 3

b) 0

c) 1

d) 2

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

a) $|A|^2$

b) $|A|_{n}$

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

d) $|A|$

7) In a system of 3 linear non-homogenous equations with three unknowns, if $\Delta=0$ and $\Delta x=0$, $\Delta y\neq 0$ and $\Delta z=0$, then the system has

a) unique solution

b) two solutions

c) infinitely many solutions

d) no solution

8) Given $\rho (A, B) = \rho(A) <$number of unknowns then the system has

a) unique solution

b) no solution

c) two solutions

d) infinitely many solutions

9) The rank of the matrix $\begin{bmatrix} 1\; \; \; 2\; \; \; 3 \\ 2 \; \; \; 4\; \;\; 6 \\ 3\;\;\; 6\;\;\; 9 \\ \end{bmatrix}$ is

a) 1

b) 2

c) 3

d) none of these

10) The condition for a unique solution of a system of equation is

a) $\Delta \neq 0$

b) $\Delta > 0$

c) $\Delta = 0$

d) $\Delta < 0$

11) Which of the following is a singular matrix?

a) $\begin{bmatrix} 1\; \; \; 0\\ 0 \; \; \; 1 \\ \end{bmatrix}$

b) $\begin{bmatrix} 3\; \; \; 4\\ 6 \; \; \; 8 \\ \end{bmatrix}$

c) $\begin{bmatrix} 2\; \; \; 0\\ 0 \; \; \; 5 \\ \end{bmatrix}$

d) $\begin{bmatrix} 7\; \; \; 8\\ 1 \; \; \; 2 \\ \end{bmatrix}$

12) The rank of a zero matrix of order 3 x 4 is:

a) 0

b) 1

c) 2

d) 3