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 Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f:\mathbb{R}\to\mathbb{R}$$ be a function defined by $$f(x) = {\log _{\sqrt m }}\{ \sqrt 2 (\sin x - \cos x) + m - 2\} $$, for some $$m$$, such that the range of $$f$$ is [0, 2]. Then the value of $$m$$ is _________

A
4
B
3
C
5
D
2
3
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :

A
120
B
6
C
72
D
12
4
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$y=y(t)$$ be a solution of the differential equation $${{dy} \over {dt}} + \alpha y = \gamma {e^{ - \beta t}}$$ where, $$\alpha > 0,\beta > 0$$ and $$\gamma > 0$$. Then $$\mathop {\lim }\limits_{t \to \infty } y(t)$$

A
is 0
B
is 1
C
is $$-1$$
D
does not exist
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