COMEDK 2025 Evening Shift | Matrices and Determinants Question 1 | Mathematics

Kiran purchased 3 pencils, 2 notebooks and one pen for ₹41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for ₹ 29 , while Shreya purchased 3 pencils, 2 notebooks and 2 pens for ₹ 44. The above situation can be represented in matrix form as $A X=B$. Then $|\operatorname{adj} A|$ is equal to

$-$9

$-$1

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

If $X=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $Y=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$ and $B=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$ then $B$ equals :

$-X \cos \theta+Y \sin \theta$

$X \sin \theta+y \cos \theta$

$X \cos \theta-Y \sin \theta$

$X \cos \theta+Y \sin \theta$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

If $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ and $(A I)^2=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]$ where I is the identity matrix then

$\alpha=a^2+b^2, \beta=2 a b$

$\alpha=2 a b, \beta=a^2+b^2$

$\alpha=a^2+b^2, \beta=a b$

$\alpha=a^2+b^2, \beta=a^2-b^2$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

Value of the determinant of a matrix $A$ of order $3 \times 3$ is 7 . Then the value of the determinant formed by the cofactors of matrix A is

343

COMEDK Subjects