1
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{n \rightarrow \infty} \frac{1^{17}+2^{77}+\ldots+n^{77}}{n^{78}}=$
A
$\frac{1}{77}$
B
1
C
76
D
$\frac{1}{78}$
2
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{6 x^2+1}{4 x^3+2 x+3} & , 0 < x < 1 \\ x^2+1 & , 1 \leq x < 2 \end{array} \text {, then } \int_0^2 f(x) d x=\right. $$

A
$\frac{1}{2} \log 3+\frac{10}{3}$
B
$\frac{1}{2} \log 3-\frac{10}{3}$
C
$\frac{1}{2} \log 3+\frac{13}{3}$
D
$\frac{1}{2} \log 3+\frac{20}{3}$
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int_1^n[x] d x=120$, then $n=$
A
15
B
16
C
14
D
12
4
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int\limits_{\frac{-1}{24}}^{\frac{1}{24}} \sec x \log \left(\frac{1-x}{1+x}\right) d x=$
A
$\frac{\pi}{2}$
B
$\pi$
C
1
D
0
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