1
JEE Main 2024 (Online) 27th January Evening Shift
Numerical
+4
-1
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The coefficient of $$x^{2012}$$ in the expansion of $$(1-x)^{2008}\left(1+x+x^2\right)^{2007}$$ is equal to _________.

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2
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1
Change Language

The remainder, when $$7^{103}$$ is divided by 17, is __________

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3
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
Change Language

Let $$\alpha$$ be the constant term in the binomial expansion of $$\left(\sqrt{x}-\frac{6}{x^{\frac{3}{2}}}\right)^{n}, n \leq 15$$. If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of $$x^{-n}$$ is $$\lambda \alpha$$, then $$\lambda$$ is equal to _____________.

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4
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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