1
MHT CET 2020 16th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1+2 e^{-x}}{1-2 e^{-x}} d x=$$

A
$$x+\log \left(1-2 e^{-x}\right)+c$$
B
$$x+2 \log \left(1-2 e^{-x}\right)+c$$
C
$$\log \left(1-2 e^{-x}\right)+c$$
D
$$x-\log \left(1-2 e^{-x}\right)+c$$
2
MHT CET 2020 16th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the volume of the parallelopiped whose conterminus edges are along the vectors $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ is 12, then the volume of the tetrahedron whose conterminus edges are $$\mathbf{a}+\mathbf{b}, \mathbf{b}+\mathbf{c}$$ and $$c+a$$ is

A
12 (units)$${ }^3$$
B
24 (units)$${ }^3$$
C
4 (units)$$^3$$
D
6 (units)$${ }^3$$
3
MHT CET 2020 16th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

The function $$f(x)=\frac{x+1}{9 x+x^3}$$ is

A
discontinuous at exactly two points
B
discontinuous at exactly one point
C
continuous for all real values of $$x$$
D
discontinuous at exactly three points
4
MHT CET 2020 16th October Evening Shift
MCQ (Single Correct Answer)
+2
-0

For any non-zero vectors $$\mathbf{a}$$ and $$\mathbf{b}$$,

A
$$a \times b$$
B
$$|a \times b|^2$$
C
0
D
$$|\mathbf{a} \times \mathbf{b}|$$
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