1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $m, l, r, s, n$ are integers such that $9 > m > l > s > n > r > 2$ and $\int_{-2 \pi}^{2 \pi} \sin ^{m} x \cos ^{n} x d x=4 \int_{0}^{\pi} \sin ^{m} x \cos ^{n} x d x, \int_{-\pi}^{\pi} \sin ^{r} x \cos ^{s} x d x$ $=4 \int_{0}^{\pi / 2} \sin ^{r} x \cos ^{s} x d x$ and $\int_{-\pi / 2}^{\pi / 2} \sin ^{l} x \cos ^{m} x d x=0$, then
A
$(s-2)(1-2)=m r$
B
$(s-2)(l+2)=r m+5$
C
$(s-2)(s+2)=\ln -3$
D
$(I-2)(I+2)=m s-5$
2
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_0^\pi\left(\sin ^3 x+\cos ^2 x\right)^2 d x=$
A
$\frac{15 \pi}{16}+\frac{8}{15}$
B
$\frac{11 \pi}{16}+\frac{8}{15}$
C
$\frac{15 \pi}{16}+\frac{4}{15}$
D
$\frac{11 \pi}{16}+\frac{4}{15}$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_{\frac{-\pi}{8}}^{\frac{\pi}{8}} \frac{\sin ^4(4 x)}{1+e^{4 x}} d x=$
A
$\frac{3 \pi}{128}$
B
$\frac{3 \pi}{256}$
C
$\frac{3 \pi}{64}$
D
$\frac{3 \pi}{32}$
4
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$ \int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x= $

A
$-\frac{\pi}{2} \log 2$
B
$-\frac{\pi}{8} \log 2$
C
$-\frac{\pi}{14} \log 2$
D
$-\frac{\pi}{28} \log 2$
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