1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of the integral } \int_\limits{\frac{1}{3}}^1 \frac{\left(x-x^3\right)^{\frac{1}{3}}}{x^4} d x \text { is } $$

A
4
B
0
C
3
D
6
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$a$$ is a real number such that $$\int_\limits0^a x d x \leq a+4$$ then

A
$$ -2 \leq a \leq 0 $$
B
$$ 0 \leq a \leq 4 $$
C
$$ -2 \leq a \leq 4 $$
D
$$ a \leq-2 \text { or } a \geq 4 $$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n x d x \text {, for } n \geq 2 \text {, then } I_n+I_{n-2}= $$

A
$$\frac{1}{n-1}$$
B
$$\frac{1}{n+1}$$
C
$$\frac{1}{n}+\frac{1}{n-2}$$
D
$$\frac{1}{n}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is } $$

A
$$ \frac{\pi}{4} $$
B
$$ -\frac{\pi}{2} $$
C
$$ -\frac{\pi}{4} $$
D
$$ \frac{\pi}{2} $$
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