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1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $2 \sin ^2 x+3 \sin x-2>0$ and $x^2-x-2<0$. ( $x$ is measured in radians). The $x$ lies in the interval

A
$\left(\frac{\pi}{6}, \frac{5 \pi}{6}\right)$
B
$\left(-1, \frac{5 \pi}{6}\right)$
C
$(-1,2)$
D
$\left(\frac{\pi}{6}, 2\right)$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\theta$ and $\alpha$ are not odd multiples of $\frac{\pi}{2}$ then $\tan \theta=\tan \alpha$ implies principal solution is

A
$\theta=\alpha+\frac{\mathrm{n} \pi}{2}, \mathrm{n} \in \mathbb{Z}$
B
$\quad \theta=\alpha+\frac{3 \mathrm{n} \pi}{2}, \mathrm{n} \in \mathbb{Z}$
C
$\theta=\mathrm{n} \pi+\alpha, \mathrm{n} \in \mathbb{Z}$
D
$\quad \theta=\frac{\mathrm{n} \pi}{4}+\alpha, \mathrm{n} \in \mathbb{Z}$
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of $2 \sqrt{3} \cos ^2 \theta=\sin \theta$ is

A
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$
B
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{\pi}{6}, \mathrm{n} \in \mathbb{Z}$
C
$\mathrm{n} \pi \pm(-1)^{\mathrm{n}} \frac{\pi}{4}, \mathrm{n} \in \mathbb{Z}$
D
$\mathrm{n} \pi+(-1)^{\mathrm{n}} \frac{2 \pi}{3}, \mathrm{n} \in \mathbb{Z}$
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The principal solutions, of the equation $\sqrt{3} \sec x+2=0$, are

A
$\frac{2 \pi}{3}, \frac{4 \pi}{3}$
B
$\frac{4 \pi}{3}, \frac{5 \pi}{3}$
C
$\frac{5 \pi}{6}, \frac{7 \pi}{6}$
D
$\frac{7 \pi}{6}, \frac{11 \pi}{6}$
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