1
JEE Main 2025 (Online) 22nd January Morning Shift
Numerical
+4
-1
Change Language

If $\sum_\limits{r=0}^5 \frac{{ }^{11} C_{2 r+1}}{2 r+2}=\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}-\mathrm{n}$ is equal to __________.

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2
JEE Main 2024 (Online) 9th April Morning Shift
Numerical
+4
-1
Change Language

The remainder when $$428^{2024}$$ is divided by 21 is __________.

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3
JEE Main 2024 (Online) 6th April Morning Shift
Numerical
+4
-1
Change Language

If the second, third and fourth terms in the expansion of $$(x+y)^n$$ are 135, 30 and $$\frac{10}{3}$$, respectively, then $$6\left(n^3+x^2+y\right)$$ is equal to __________.

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4
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

If the constant term in the expansion of $$\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9$$ is $$\mathrm{p}$$, then $$108 \mathrm{p}$$ is equal to ________.

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