1
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

The constant term in the expansion of $${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$$ is ___________.

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2
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1
Change Language

Let the sum of the coefficients of the first three terms in the expansion of $${\left( {x - {3 \over {{x^2}}}} \right)^n},x \ne 0.~n \in \mathbb{N}$$, be 376. Then the coefficient of $$x^4$$ is __________.

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3
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Suppose $$\sum\limits_{r = 0}^{2023} {{r^2}{}~^{2023}{C_r} = 2023 \times \alpha \times {2^{2022}}} $$. Then the value of $$\alpha$$ is ___________

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4
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

$$ \text { If } \sum\limits_{k=1}^{10} K^{2}\left(10_{C_{K}}\right)^{2}=22000 L \text {, then } L \text { is equal to }$$ ________.

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