1
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int_{-\pi / 15}^{\pi / 5} \frac{\cos 5 x}{1+e^{5 x}} d x=$
A
$\frac{1}{5}$
B
$\frac{\sqrt{3}}{10}$
C
$\frac{1}{15}$
D
$\frac{1}{10}$
2
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\frac{3}{25} \int_{0}^{25 \pi} \sqrt{\left|\cos x-\cos ^{3} x\right|} d x=$
A
8
B
4
C
1
D
0
3
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
$(I-2)(I+2)=m s-5$
4
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
$\frac{11 \pi}{16}+\frac{4}{15}$
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