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

The value of $$\mathop {\lim }\limits_{n \to \infty } {{1 + 2 - 3 + 4 + 5 - 6\, + \,.....\, + \,(3n - 2) + (3n - 1) - 3n} \over {\sqrt {2{n^4} + 4n + 3} - \sqrt {{n^4} + 5n + 4} }}$$ is :

A
$${3 \over {2\sqrt 2 }}$$
B
$${3 \over 2}(\sqrt 2 + 1)$$
C
$$3(\sqrt 2 + 1)$$
D
$${{\sqrt 2 + 1} \over 2}$$
2
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $$S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}$$ and the event $$\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,of\,3\}}$$. Then P(A) is equal to :

A
$$\frac{1}{3}$$
B
$$\frac{1}{5}$$
C
$$\frac{7}{22}$$
D
$$\frac{15}{44}$$
3
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx} $$. If $$f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$$, then $$f(4)$$ is equal to

A
$${\log _e}19 - {\log _e}20$$
B
$${\log _e}17 - {\log _e}18$$
C
$${1 \over 2}({\log _e}19 - {\log _e}17)$$
D
$${1 \over 2}({\log _e}17 - {\log _e}19)$$
4
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The distance of the point P(4, 6, $$-$$2) from the line passing through the point ($$-$$3, 2, 3) and parallel to a line with direction ratios 3, 3, $$-$$1 is equal to :

A
3
B
$$\sqrt{14}$$
C
$$\sqrt6$$
D
$$2\sqrt3$$
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