1
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The integral $$16\int\limits_1^2 {{{dx} \over {{x^3}{{\left( {{x^2} + 2} \right)}^2}}}} $$ is equal to

A
$${{11} \over {12}} + {\log _e}4$$
B
$${{11} \over 6} + {\log _e}4$$
C
$${{11} \over {12}} - {\log _e}4$$
D
$${{11} \over 6} - {\log _e}4$$
2
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The minimum value of the function $$f(x) = \int\limits_0^2 {{e^{|x - t|}}dt} $$ is :

A
2
B
$$2(e-1)$$
C
$$e(e-1)$$
D
$$2e-1$$
3
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\int_{{{3\sqrt 2 } \over 4}}^{{{3\sqrt 3 } \over 4}} {{{48} \over {\sqrt {9 - 4{x^2}} }}dx} $$ is equal to

A
$${\pi \over 2}$$
B
$${\pi \over 3}$$
C
$${\pi \over 6}$$
D
$$2\pi $$
4
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area enclosed by the curves $${y^2} + 4x = 4$$ and $$y - 2x = 2$$ is :

A
$${{22} \over 3}$$
B
9
C
$${{23} \over 3}$$
D
$${{25} \over 3}$$
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