1
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\left|\begin{array}{ccc}1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3\end{array}\right|=A \lambda^3+B \lambda^2+C \lambda+D$, then $D+A=$

A

1

B

-4

C

-5

D

3

2
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and $2 A-B=\left[\begin{array}{ccc}2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2\end{array}\right]$, then $\operatorname{tr}(A)-\operatorname{tr}(B)=$

A

1

B

2

C

3

D

4

3
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$A, C$ are $3 \times 3$ matrices $B, D$ are $3 \times 1$ matrices. If $A X=B$ has unique solution and $C X=D$ has infinite number of solutions, then

A

rank of $[A: D]=\operatorname{rank}$ of $[C: B]$

B

rank of $A=$ rank of $C$

C

rank of $[A: B]<\operatorname{rank}$ of $[B: D]$

D

rank of $[A: D] \geq$ rank of $[C: B]$

4
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$A$ and $B$ are two non-square matrices. If $P=A+B, Q=A^T B, R=A B^T$, then the matrices whose order is equal to the order of $A$ are

A

$P Q$ and $Q R$

B

$R Q$ and $Q P$

C

$P Q$ and $R P$

D

$P Q R$ and $R P Q$

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