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

If $$a, b$$ and $$c$$ are three distinct real numbers and $$\lim _\limits{x \rightarrow \infty} \frac{(b-c) x^2+(c-a) x+(a-b)}{(a-b) x^2+(b-c) x+(c-a)}=\frac{1}{2}$$, then $$a+2 c=$$

A
b
B
2b
C
3b
D
4b
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\lim _\limits{x \rightarrow-\infty} \frac{3|x|-x}{|x|-2 x}-\lim _\limits{x \rightarrow 0} \frac{\log \left(1+x^3\right)}{\sin ^3 x}=$$

A
$$\frac{1}{3}$$
B
$$-\frac{1}{4}$$
C
2
D
$$-\frac{5}{3}$$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$3 f(\cos x)+2 f(\sin x)=5 x$$, then $$f^{\prime}(\cos x)+f^{\prime}(\sin x)=$$

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

Assertion (A) $$\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)=\frac{x^2 \sin x}{\log x}\left(\cot x+\frac{2}{x}-\frac{1}{x \log x}\right)$$

Reason (R) $$\frac{d}{d x}\left(\frac{u v}{w}\right)=\frac{u v}{w}\left[\frac{u^{\prime}}{u}+\frac{v^{\prime}}{v}+\frac{w^{\prime}}{w}\right]$$

A
A is true, R is true and R is correct explanation of A
B
A is true, R is true and R is not correct explanation of A
C
A is true, R is not correct
D
A is not correct, R is correct
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