1
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect at right angles, then $$a^2$$ is equal to

A
$$\frac{2}{3}$$
B
$$\frac{2}{\sqrt{3}}$$
C
$$\frac{4}{3}$$
D
$$\frac{3}{4}$$
2
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $$x$$ and $$y$$ be the sides of two squares such that, $$y=x-x^2$$. The rate of change of area of the second square with respect to area of the first square is

A
$$1-3 x+2 x^2$$
B
$$1+3 x-2 x^2$$
C
$$2 x$$
D
$$x+2 x^3-3 x^2$$
3
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$f^{\prime \prime}(x)$$ is a positive function for all $$x \in R, f^{\prime}(3)=0$$ and $$g(x)=f\left(\tan ^2(x)-2 \tan (x)+4\right)$$ for $$0 < x <\frac{\pi}{2}$$, then the interval in which $$g(x)$$ is increasing is

A
$$\left(\frac{\pi}{6}, \frac{\pi}{3}\right)$$
B
$$\left(0, \frac{\pi}{4}\right)$$
C
$$\left(0, \frac{\pi}{3}\right)$$
D
$$\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$$
4
AP EAPCET 2021 - 19th August Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$$ is equal to

A
$$\frac{1}{2}(\sqrt{1+x})+c$$
B
$$\sqrt{1+x}+c$$
C
$$2(1+x)^{3 / 2}+c$$
D
$$\frac{2}{3}(1+x)^{3 / 2}+c$$
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