1
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $A$ is a square matrix of order $3 \times 3, \operatorname{det} A=3$, then the value of $\operatorname{det}\left(3 A^{-1}\right)$ is
A
$\frac{1}{3}$
B
3
C
27
D
9
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $B=\left[\begin{array}{ll}1 & 3 \\ 1 & \alpha\end{array}\right]$ be the adjoint of a matrix $A$ and $|A|=2$, then the value of $\alpha$ is
A
4
B
5
C
2
D
3
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0

The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has

A
No solution
B
Infinitely many solutions
C
A unique solution
D
Only two solutions
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

A
1
B
$\pm 1$
C
-1
D
0
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