1
JEE Advanced 2023 Paper 1 Online
Numerical
+4
-0
Let $\overbrace{75 \cdots 57}^r$ denote the $(r+2)$ digit number where the first and the last digits are 7 and the remaining $r$ digits are 5 . Consider the sum $S=77+757+7557+\cdots+ \overbrace{75 \cdots 57}^{98}$. If $S=\frac{\overbrace{75 \cdots 57}^{99}+m}{n}$, where $m$ and $n$ are natural numbers less than 3000 , then the value of $m+n$ is
2
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0 Let $$l_{1}, l_{2}, \ldots, l_{100}$$ be consecutive terms of an arithmetic progression with common difference $$d_{1}$$, and let $$w_{1}, w_{2}, \ldots, w_{100}$$ be consecutive terms of another arithmetic progression with common difference $$d_{2}$$, where $$d_{1} d_{2}=10$$. For each $$i=1,2, \ldots, 100$$, let $R_{i}$ be a rectangle with length $$l_{i}$$, width $$w_{i}$$ and area $A_{i}$. If $$A_{51}-A_{50}=1000$$, then the value of $$A_{100}-A_{90}$$ is __________.
3
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0 Let m be the minimum possible value of $${\log _3}({3^{{y_1}}} + {3^{{y_2}}} + {3^{{y_3}}})$$, where $${y_1},{y_2},{y_3}$$ are real numbers for which $${{y_1} + {y_2} + {y_3}}$$ = 9. Let M be the maximum possible value of $$({\log _3}{x_1} + {\log _3}{x_2} + {\log _3}{x_3})$$, where $${x_1},{x_2},{x_3}$$ are positive real numbers for which $${{x_1} + {x_2} + {x_3}}$$ = 9. Then the value of $${\log _2}({m^3}) + {\log _3}({M^2})$$ is ...........
4
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0 Let a1, a2, a3, .... be a sequence of positive integers in arithmetic progression with common difference 2. Also, let b1, b2, b3, .... be a sequence of positive integers in geometric progression with common ratio 2. If a1 = b1 = c, then the number of all possible values of c, for which the equality 2(a1 + a2 + ... + an) = b1 + b2 + ... + bn holds for some positive integer n, is ...........
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