CLASS 12 MATHS UNIT TEST PAPER - MATRIX, DETERMINANT AND APPLICATIONS OF INTEGRALS

 UNIT TEST PAPER - MATRIX, DETERMINANT AND APPLICATIONS OF INTEGRALS 

Time – 1:30 Hr                                                                                                                        M.M. 50

Very short Answer Type Questions ( 1 Mark)

1.If matrix A = $\left[\begin{array}{cc}2& 3\\ 1& 2\end{array}\right]$ and matrix B = $\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]$ , Then show that $A^{-1}=Band{B}^{-1}=A$
2.Using properties of determinant , show that $\left|\begin{array}{ccc}0& 99& -998\\ -99& 0& 997\\ 998& -997& 0\end{array}\right|=0$

Short Answer Type Questions ( 2 Mark)

3.Using properties of determinants show that $\Delta =\left|\begin{array}{ccc}1& {\log }_{x}y& {\log }_{x}z\\ {\log }_{y}x& 1& {\log }_{y}z\\ {\log }_{z}x& {\log }_{z}y& 1\end{array}\right|=0$
4.If A = $\left|\begin{array}{ccc}2& 3& 1\\ 1& 2& -1\\ 3& 4& 2\end{array}\right|$ is a non singular matrix of order 3x3 Show that |adj A| = |A|²
5.Using elementary column operation find the inverse of the matrix $\left[\begin{array}{cc}2& 3\\ 3& 5\end{array}\right]$
6.If A = $\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]$ is such that $A^2=I$ then show that ${\alpha }^2+\beta \gamma =I$
7.Find the number of all possible matrices of order 3 x 2 with each entry 0, 1 and 2.

Long Answer Type Questions – I( 4 Marks)

8.If Matrix A =$\left[\begin{array}{ccc}2& 3& 1\\ 1& 4& 5\end{array}\right]andmatrixB=\left[\begin{array}{cc}3& 4\\ 1& 5\\ 2& 3\end{array}\right]$ then verify (AB)’ = B’A’
9.If A = $\left[\begin{array}{cc}3& -5\\ -4& 2\end{array}\right],showthat{A}^2-5A-14I=0.Hence,find{A}^{-1}$
10.Using properties of determinants, show that $$\left|\begin{array}{ccc}{\sin }^{2}A& {\cos }^{2}A& \sin A\cos A\\ {\sin }^{2}B& {\cos }^{2}B& \mathrm{sinB}\mathrm{cosB}\\ {\sin }^{2}C& {\cos }^{2}C& \mathrm{sincCosC}\end{array}\right|=\sin \left(A-B\right)\sin (B-C)\sin (C-A)$$
11.Using elementary row operation, find the inverse of matrix A = $\left[\begin{array}{ccc}2& 1& 3\\ 1& 0& 2\\ 1& 2& 1\end{array}\right]$
12.Vertices of a $\Delta ABC$are A(2, 3), B(4, 2), C(x, 0). Area of the $\Delta ABC$ is 5 sq. units. Find the value of x.

Long Answer Type Questions –I I( 6 Marks)

13.Using integration , find the area of the $\Delta ABC$ whose vertices are A(1, 0), B(2, 2) and C(3,1).
14.Using matrices, solve: $\{\begin{array}{c}5x-y+z=4\\ 3x+2y-5z=2\\ x+3y-2z=5\end{array}$

Also Read : Class 12 Maths Test Paper for Continuity,Differentiation and AOD
                   Important Questions for Matrix and Determinant