1
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
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -
A
1356
B
1256
C
1365
D
1465
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
The sum of the following series

$$1 + 6 + {{9\left( {{1^2} + {2^2} + {3^2}} \right)} \over 7} + {{12\left( {{1^2} + {2^2} + {3^2} + {4^2}} \right)} \over 9}$$

$$+ {{15\left( {{1^2} + {2^2} + ... + {5^2}} \right)} \over {11}} + .....$$ up to 15 terms, is :
A
7520
B
7510
C
7830
D
7820
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then $${a \over c}$$ equal to :
A
2
B
$${1 \over 2}$$
C
$${7 \over 13}$$
D
4
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