1
JEE Main 2025 (Online) 2nd April Evening Shift
Numerical
+4
-1
Change Language
If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1+4 \cdot 1^4}+\frac{4 \cdot 2}{1+4 \cdot 2^4}+\frac{4 \cdot 3}{1+4 \cdot 3^4}+\ldots .$. is $\frac{\mathrm{m}}{\mathrm{n}}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to _______________
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2
JEE Main 2025 (Online) 29th January Evening Shift
Numerical
+4
-1
Change Language

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1+\left(a_5+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to _________.

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3
JEE Main 2025 (Online) 28th January Evening Shift
Numerical
+4
-1
Change Language

The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the polygon is 219°, then n is equal to _______.

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4
JEE Main 2025 (Online) 23rd January Evening Shift
Numerical
+4
-1
Change Language

The roots of the quadratic equation $3 x^2-p x+q=0$ are $10^{\text {th }}$ and $11^{\text {th }}$ terms of an arithmetic progression with common difference $\frac{3}{2}$. If the sum of the first 11 terms of this arithmetic progression is 88 , then $q-2 p$ is equal to ________ .

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