1
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1
Change Language

The mean of the coefficients of $$x, x^{2}, \ldots, x^{7}$$ in the binomial expansion of $$(2+x)^{9}$$ is ___________.

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2
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1
Change Language

The number of integral terms in the expansion of $$\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$$ is equal to ___________.

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3
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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4
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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