1
JEE Main 2021 (Online) 25th February Morning Shift
Numerical
+4
-1
Let A1, A2, A3, ....... be squares such that for each n $$\ge$$ 1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one, is __________.
2
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
The sum of first four terms of a geometric progression (G. P.) is $${{65} \over {12}}$$ and the sum of their respective reciprocals is $${{65} \over {18}}$$. If the product of first three terms of the G.P. is 1, and the third term is $$\alpha$$, then 2$$\alpha$$ is _________.
3
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to _________ .
4
JEE Main 2020 (Online) 3rd September Morning Slot
Numerical
+4
-0
The value of $${\left( {0.16} \right)^{{{\log }_{2.5}}\left( {{1 \over 3} + {1 \over {{3^2}}} + ....to\,\infty } \right)}}$$ is equal to ______.