1
MHT CET 2021 21th September Morning Shift
+2
-0

If $$f(x)=|x-1|+|x-2|+|x-3|, \forall x \in[1,4]$$, then $$\int_\limits1^4 f(x) d x=$$

A
$$\frac{1}{2}$$
B
7
C
$$\frac{9}{2}$$
D
$$\frac{19}{2}$$
2
MHT CET 2021 20th September Evening Shift
+2
-0

If $$2 f(x)-3 f\left(\frac{1}{x}\right)=x$$, then $$\int_\limits1^e f(x) d x=$$

A
$$-\left(\frac{2+\mathrm{e}^2}{5}\right)$$
B
$$\frac{2+e}{5}$$
C
$$\frac{2+e^2}{5}$$
D
$$\frac{2-e^2}{5}$$
3
MHT CET 2021 20th September Evening Shift
+2
-0

If $$\int_\limits2^e\left[\frac{1}{\log x}-\frac{1}{(\log x)^2}\right] d x=a+\frac{b}{\log 2}$$, then

A
$$a=-e, b=2$$
B
$$a=e, b=-2$$
C
$$a=e, b=2$$
D
$$a=-e, b=-2$$
4
MHT CET 2021 20th September Morning Shift
+2
-0

$$\int_\limits0^{\pi / 4} \log (1+\tan x) d x=$$

A
$$\frac{\pi}{16} \log 2$$
B
$$\frac{\pi}{4} \log 2$$
C
$$\frac{\pi}{8} \log 2$$
D
$$\pi \log 2$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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