1
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

The condition that $$f(x)=a x^3+b x^2+c x+d$$ has no extreme value is

A
$$b^2-4 a c$$
B
$$b^2=3 a c$$
C
$$b^2<3 a c$$
D
$$b^2>3 a c$$
2
AP EAPCET 2022 - 4th July Morning Shift
+1
-0

At any point $$(x, y)$$ on a curve if the length of the subnormal is $$(x-1)$$ and the curve passes through $$(1,2)$$, then the curve is a conic. A vertex of the curve is

A
$$(1,0)$$
B
$$(0,1)$$
C
$$(\sqrt{5}, 0)$$
D
$$(0, \sqrt{5})$$
3
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

If $$y=4 x-6$$ is a tangent to the curve $$y^2=a x^4+b$$ at $$(3,6)$$, then the values of $$a$$ and $$b$$ are

A
$$a=\frac{4}{9}$$ and $$b=\frac{-4}{9}$$
B
$$a=0$$ and $$b=\frac{4}{9}$$
C
$$a=\frac{-4}{9}$$ and $$b=\frac{-4}{9}$$
D
$$a=\frac{4}{9}$$ and $$b=0$$
4
AP EAPCET 2021 - 20th August Morning Shift
+1
-0

Find the positive value of $$a$$ for which the equality $$2 \alpha+\beta=8$$ holds, where $$\alpha$$ and $$\beta$$ are the points of maximum and minimum, respectively, of the function $$f(x)=2 x^3-9 a x^2+12 a^2 x+1$$.

A
0
B
2
C
1
D
$$\frac{1}{4}$$
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