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

If $$a_r$$ is the coefficient of $$x^{10-r}$$ in the Binomial expansion of $$(1 + x)^{10}$$, then $$\sum\limits_{r = 1}^{10} {{r^3}{{\left( {{{{a_r}} \over {{a_{r - 1}}}}} \right)}^2}} $$ is equal to

A
3025
B
4895
C
5445
D
1210
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
Out of Syllabus
Change Language

Let $$x,y,z > 1$$ and $$A = \left[ {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 2 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 3 \cr } } \right]$$. Then $$\mathrm{|adj~(adj~A^2)|}$$ is equal to

A
$$6^4$$
B
$$2^8$$
C
$$4^8$$
D
$$2^4$$
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