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1
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are

A
$\pm \frac{\pi}{4}, \pm \frac{3 \pi}{4}$
B
$\pm \frac{\pi}{6}, \frac{\pi}{3}$
C
$\pm \frac{\pi}{8}$
D
$\frac{\pi}{3}$
2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of the equation $\tan x+\tan 2 x-\tan 3 x=0$ is
A
$\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{3}\right.\right.$ or $\left.\frac{n \pi}{2}, n \in Z\right\}$
B
$\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{3}\right.\right.$ or $\left.n \pi, n \in Z\right\}$
C
$\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{3}\right.\right.$ or $\frac{n \pi}{2}$ or $\left.n \pi, n \in Z\right\}$
D
$\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{6}\right.\right.$ or $\left.\frac{n \pi}{2}, n \in Z\right\}$
3
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ is
A
2
B
3
C
4
D
5
4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
For $a \in R-\{0\}$, if $a \cos x+a \sin x+a=2 k+1$ has a solution, then $k$ lies in the interval
A
$\left[\frac{a-1-\sqrt{2} a}{2}, \frac{a-1+\sqrt{2} a}{2}\right]$
B
$\left[\frac{a+1-\sqrt{2}}{2}, \frac{a+1+\sqrt{2}}{2}\right]$
C
$\left[\frac{a-1-\sqrt{2}}{2}, \frac{a-1+\sqrt{2}}{2}\right]$
D
$\left[-\frac{\left(\sqrt{2 a^2+2 a+1}+1\right)}{2}, \frac{\left(\sqrt{2 a^2+2 a+1}-1\right)}{2}\right]$
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