1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right]$$, then $$\operatorname{det}\left(A^6+B^6\right)=$$

A
$$-68$$
B
$$-106$$
C
$$665$$
D
$$720$$
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Let $$G(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$$. If $$x+y=0$$ then $$G(x) G(y)=$$

A
null Matrix
B
skew-symmetric Matrix
C
identity Matrix
D
symmetric Matrix
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

By simplifying $$i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}$$, we get

A
$$-1+3 i$$
B
$$1-3 i$$
C
$$1+3 i$$
D
$$-1-3 i$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The values of $$x$$ for which $$\sin x+i \cos 2 x$$ and $$\cos x-i \sin 2 x$$ are conjugate to each other are

A
$$x=n \pi \pm \frac{\pi}{6}$$
B
None
C
$$x=n \pi \pm \frac{\pi}{3}$$
D
$$x=\left(n+\frac{1}{2}\right) \pi$$
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