1
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $m, n, p, q$ be four positive integers. If

$$ \begin{aligned} & \int_0^{2 \pi} \sin ^m x \cos ^n x d x=4 \int_0^{\pi / 2} \sin ^m x \cos ^n x d x \int_0^{2 \pi} \sin ^p x \cos ^n x d x=0 \\ & \int_0^\pi \sin ^p x \cos ^q x d x=0, a=m+n+p \text { and } b=m+n+q, \text { then } \end{aligned} $$

A

$a$ is even number and $b$ is odd number

B

$a$ is odd number and $b$ is even number

C

Both $a$ and $b$ are even numbers

D

Both $a$ and $b$ are odd numbers

2
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^2 \sqrt{(x+3)(2-x)} d x= $$

A

$\frac{25}{8} \cos ^{-1}\left(\frac{1}{5}\right)-\frac{\sqrt{6}}{4}$

B

$\frac{25}{8} \sin ^{-1}\left(\frac{1}{5}\right)-\frac{\sqrt{6}}{4}$

C

$\frac{\pi}{2}$

D

$\pi$

3
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\pi / 4} x^2 \sin 2 x d x $$

A

$\frac{\pi^2-2}{8}$

B

$\frac{\pi(\pi-2)}{8}$

C

$\frac{\pi-2}{8}$

D

$\frac{\pi+2}{8}$

4
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_{-2 \pi}^{2 \pi} \sin ^4 x \cos ^6 x d x= $$

A

$\frac{3 \pi}{128}$

B

$\frac{9 \pi}{32}$

C

$\frac{9 \pi}{64}$

D

$\frac{3 \pi}{64}$

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