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

When the coordinate axes are rotated through an angle 135$$\Upsilon$$, the coordinates of a point $$P$$ in the new system are known to be $$(4,-3)$$. Then find the coordinates of $$P$$ in the original system.

A
$$\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$$
B
$$\left(\frac{-1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)$$
C
$$\left(\frac{1}{\sqrt{2}}, \frac{-7}{\sqrt{2}}\right)$$
D
$$\left(\frac{-1}{\sqrt{2}}, \frac{-7}{\sqrt{2}}\right)$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

The maximum value of $$f(x)=\sin (x)$$ in the interval $$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$ is

A
0
B
$$-$$1
C
1
D
$$\sqrt2$$
3
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)$$ is equal to

A
$$\tan 3 \alpha$$
B
$$\tan ^2 2 \alpha-\tan ^2 60 \gamma$$
C
1
D
0
4
AP EAPCET 2021 - 19th August Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\sin \alpha - \cos \alpha = m$$ and $$\sin 2\alpha = n - {m^2}$$, where $$ - \sqrt 2 \le m \le \sqrt 2 $$, then n is equal to

A
0
B
1
C
2
D
$$-$$2
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