1
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1
Change Language

The coefficient of $$x^7$$ in $${(1 - x + 2{x^3})^{10}}$$ is ___________.

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2
JEE Main 2023 (Online) 8th April Morning Shift
Numerical
+4
-1
Change Language

Let $$[t]$$ denote the greatest integer $$\leq t$$. If the constant term in the expansion of $$\left(3 x^{2}-\frac{1}{2 x^{5}}\right)^{7}$$ is $$\alpha$$, then $$[\alpha]$$ is equal to ___________.

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3
JEE Main 2023 (Online) 8th April Morning Shift
Numerical
+4
-1
Change Language

The largest natural number $$n$$ such that $$3^{n}$$ divides $$66 !$$ is ___________.

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4
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

If $$(20)^{19}+2(21)(20)^{18}+3(21)^{2}(20)^{17}+\ldots+20(21)^{19}=k(20)^{19}$$, then $$k$$ is equal to ___________.

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