1
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Out of Syllabus
Let  Sk = $${{1 + 2 + 3 + .... + k} \over k}.$$ If   $$S_1^2 + S_2^2 + .....\, + S_{10}^2 = {5 \over {12}}$$A,  then A is equal to :
A
283
B
156
C
301
D
303
2
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :
A
36
B
28
C
32
D
24
3
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :
A
2 : 1
B
4 : 1
C
1 : 3
D
3 : 1
4
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
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