1
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x=a+\log b$, then $(a-b)=$
A
4
B
$-\frac{4}{5}$
C
$\frac{4}{5}$
D
-4
2
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
$\frac{1}{78}$
3
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
$\frac{1}{2} \log 3+\frac{20}{3}$
4
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
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