1
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression $${{{x^m}{y^n}} \over {\left( {1 + {x^{2m}}} \right)\left( {1 + {y^{2n}}} \right)}}$$ is :
A
$${1 \over 2}$$
B
$${1 \over 4}$$
C
$${{m + n} \over {6mn}}$$
D
1
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is $${{27} \over {19}}$$.Then the common ratio of this series is :
A
$${4 \over 9}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${2 \over 9}$$
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Let a1, a2, . . . . . ., a10 be a G.P.    If $${{{a_3}} \over {{a_1}}} = 25,$$ then $${{{a_9}} \over {{a_5}}}$$ equals
A
53
B
2(52)
C
4(52)
D
54
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let a1, a2, a3, ..... a10 be in G.P. with ai > 0 for i = 1, 2, ….., 10 and S be the set of pairs (r, k), r, k $$\in$$ N (the set of natural numbers) for which

$$\left| {\matrix{ {{{\log }_e}\,{a_1}^r{a_2}^k} & {{{\log }_e}\,{a_2}^r{a_3}^k} & {{{\log }_e}\,{a_3}^r{a_4}^k} \cr {{{\log }_e}\,{a_4}^r{a_5}^k} & {{{\log }_e}\,{a_5}^r{a_6}^k} & {{{\log }_e}\,{a_6}^r{a_7}^k} \cr {{{\log }_e}\,{a_7}^r{a_8}^k} & {{{\log }_e}\,{a_8}^r{a_9}^k} & {{{\log }_e}\,{a_9}^r{a_{10}}^k} \cr } } \right|$$ $$=$$ 0.

Then the number of elements in S, is -
A
10
B
4
C
2
D
infinitely many
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