1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The set of all real values of a such that the real valued function $f(x)=x^3+2 a x^2+3(a+1) x+5$ is strictly increasing in its entire domain is
A
$\left(-\infty-\frac{3}{4}\right) \cup(3, \infty)$
B
$\left(-\frac{3}{4}, 3\right)$
C
( 13
D
$(-\infty, 1) \cup(3-=)$
2
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
$$\frac{5}{\sin x}+\frac{5}{\cos x}$$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the normal drawn at a point $$P$$ on the curve $$3 y=6 x-5 x^3$$ passes through $$(0,0)$$, then the positive integral value of the abscissa of the point $$P$$ is

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

The line joining the points $$(0,3)$$ and $$(5,-2)$$ is a tangent to the curve $$y=\frac{c}{x+1}$$, then $$c=$$

A
1
B
$$-$$2
C
4
D
5
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