1
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

The value of $$\left|\begin{array}{ccc}b+c & a & a \\ b & c+a & b \\ c & c & a+b\end{array}\right|$$ is

A
$$a b c$$
B
$$(a+b)(b+c)(c+a)$$
C
$$4 a b c$$
D
$$(a-b)(b-c)(c-a)$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $$A, B, C, D$$ be square real matrices such that $$C^T=D A B, D^{\mathrm{T}}=A B C$$ and $$S=A B C D$$, then $$S^2$$ is equal to

A
$$S$$
B
$$B C D$$
C
$$S^T$$
D
$$\left(S^T\right)^2=\left(S^2\right)^T$$
3
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$$ and $$B=\left[\begin{array}{ccc}2 a & 3 & 5 \\ 2 & 2 b & 8 \\ 1 & 4 & 2 c-3\end{array}\right]$$ are two matrices such that the sum of the principal diagonal elements of both $$A$$ and $$B$$ are equal, then the product of the principal diagonal elements of $$B$$ is

A
4
B
0
C
$$-$$4
D
$$-$$12
4
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $$a, b$$ and $$c$$ be such that $$b+c \neq 0$$ and $$\begin{aligned} & \left|\begin{array}{ccc} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \end{array}\right| \\ & +\left|\begin{array}{ccc} a+1 & b+1 & c-1 \\ a-1 & b-1 & c+1 \\ (-1)^{n+2} a & (-1)^{n-1} b & (-1)^n c \end{array}\right|=0 \text {, } \\ & \end{aligned}$$

then the value of $$n$$ is

A
zero
B
any even integer
C
any odd integer
D
any integer
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