+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

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