+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
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
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