1
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\begin{aligned} & \lim _{n \rightarrow \infty}\left[\frac{n}{(n+1) \sqrt{2 n+1}}+\frac{n}{(n+2) \sqrt{2(2 n+2)}}\right. \\ & \left.+\frac{n}{(n+3) \sqrt{3(2 n+3)}}+\ldots n \text { terms }\right]=\int_\limits0^1 f(x) d x \end{aligned}$$

then $$f(x)=$$

A
$$\frac{1}{(1+x) \sqrt{x^2+2 x}}$$
B
$$\frac{1}{(1+x) \sqrt{x+2}}$$
C
$$\frac{1}{(1+x) \sqrt{x^2+x+1}}$$
D
$$\frac{1}{(1+x) \sqrt{x^2-2 x}}$$
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $$\frac{d y}{d x}=\cos ^2(3 x+y)$$ is $$\tan ^{-1}\left(\frac{\sqrt{3}}{2} \tan (3 x+y)\right)=f(x)$$. Then, $$f(x)=$$

A
$$2 \sqrt{3}(x+C)$$
B
$$x+C$$
C
$$\frac{x+C}{2 \sqrt{3}}$$
D
$$\frac{\sqrt{3}}{2}(x+C)$$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x}$$ satisfies $$y\left(\frac{\pi}{4}\right)=1$$, then $$C=$$

A
e
B
1
C
$$-$$1
D
$$\frac{1}{e}$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Assertion (A) Order of the differential equations of a family of circles with constant radius is two.

Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.

A
A and R are true, R is the correct explanation to A
B
A is true, R is false
C
A and R are true, R is not the correct explanation to A
D
A is false, R is true
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