1
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
If sum of the first 21 terms of the series $${\log _{{9^{1/2}}}}x + {\log _{{9^{1/3}}}}x + {\log _{{9^{1/4}}}}x + .......$$, where x > 0 is 504, then x is equal to
A
243
B
9
C
7
D
81
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 $$-$$ S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
A
7000
B
1000
C
3000
D
5000
3
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
If $$\alpha$$, $$\beta$$ are natural numbers such that
100$$\alpha$$ $$-$$ 199$$\beta$$ = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through ($$\alpha$$, $$\beta$$) and origin is :
A
540
B
550
C
530
D
510
4
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
$${1 \over {{3^2} - 1}} + {1 \over {{5^2} - 1}} + {1 \over {{7^2} - 1}} + .... + {1 \over {{{(201)}^2} - 1}}$$ is equal to
A
$${{101} \over {404}}$$
B
$${{25} \over {101}}$$
C
$${{101} \over {408}}$$
D
$${{99} \over {400}}$$
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