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

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 _____________.

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

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

3
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1

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

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

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

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