## 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 ${A}^{-1}=B\text{\hspace{0.17em}}and\text{\hspace{0.17em}}{B}^{-1}=A$
2.Using properties of determinant , show that $|\begin{array}{ccc}0& 99& -998\\ -99& 0& 997\\ 998& -997& 0\end{array}|=0$

Short Answer Type Questions ( 2 Mark)

3.Using properties of determinants show that $\Delta =|\begin{array}{ccc}1& {\mathrm{log}}_{x}y& {\mathrm{log}}_{x}z\\ {\mathrm{log}}_{y}x& 1& {\mathrm{log}}_{y}z\\ {\mathrm{log}}_{z}x& {\mathrm{log}}_{z}y& 1\end{array}|=0$
4.If A = $|\begin{array}{ccc}2& 3& 1\\ 1& 2& -1\\ 3& 4& 2\end{array}|$ 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 =$\left[\begin{array}{ccc}2& 3& 1\\ 1& 4& 5\end{array}\right]\text{\hspace{0.17em}}and\text{\hspace{0.17em}}matrix\text{\hspace{0.17em}}B=\left[\begin{array}{cc}3& 4\\ 1& 5\\ 2& 3\end{array}\right]$ then verify (AB)’ = B’A’
9.If A = $\left[\begin{array}{cc}3& -5\\ -4& 2\end{array}\right],\text{\hspace{0.17em}}show\text{\hspace{0.17em}}that\text{\hspace{0.17em}}{A}^{2}-5A-14I=0.\text{\hspace{0.17em}}Hence,\text{\hspace{0.17em}}find\text{\hspace{0.17em}}{A}^{-1}$
10.Using properties of determinants, show that $| sin 2 A cos 2 A sinAcosA sin 2 B cos 2 B sinBcosB sin 2 C cos 2 C sincCosC |=sin( A−B )sin(B−C)sin(C−A)$
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: $\left\{\begin{array}{c}5x-y+z=4\\ 3x+2y-5z=2\\ x+3y-2z=5\end{array}$

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