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

If $$\int \frac{1}{1+\sin x} d x=\tan (f(x))+c$$, then $$f^{\prime}(0)$$ is equal to

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

If $$\int_0^{\pi / 2} \tan ^n(x) d x=k \int_0^{\pi / 2} \cot ^n(x) d x$$, then

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

$$\int_0^2 x e^x d x$$ is equal to

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

If $$x^2+y^2=1$$, then

A
$$y\left(y^{\prime \prime}\right)-4\left(y^{\prime}\right)^2+1=0$$
B
$$y\left(y^{\prime \prime}\right)+\left(y^{\prime}\right)^2+1=0$$
C
$$y\left(y^{\prime \prime}\right)-\left(y^{\prime}\right)^2-1=0$$
D
$$y\left(y^{\prime \prime}\right)+2\left(y^{\prime}\right)^2+1=0$$
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