1
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Let Sn = 1 . (n $$-$$ 1) + 2 . (n $$-$$ 2) + 3 . (n $$-$$ 3) + ..... + (n $$-$$ 1) . 1, n $$\ge$$ 4.

The sum $$\sum\limits_{n = 4}^\infty {\left( {{{2{S_n}} \over {n!}} - {1 \over {(n - 2)!}}} \right)}$$ is equal to :
A
$${{e - 1} \over 3}$$
B
$${{e - 2} \over 6}$$
C
$${e \over 3}$$
D
$${e \over 6}$$
2
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Let a1, a2, ..........., a21 be an AP such that $$\sum\limits_{n = 1}^{20} {{1 \over {{a_n}{a_{n + 1}}}} = {4 \over 9}}$$. If the sum of this AP is 189, then a6a16 is equal to :
A
57
B
72
C
48
D
36
3
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Let a1, a2, a3, ..... be an A.P. If $${{{a_1} + {a_2} + .... + {a_{10}}} \over {{a_1} + {a_2} + .... + {a_p}}} = {{100} \over {{p^2}}}$$, p $$\ne$$ 10, then $${{{a_{11}}} \over {{a_{10}}}}$$ is equal to :
A
$${{19} \over {21}}$$
B
$${{100} \over {121}}$$
C
$${{21} \over {19}}$$
D
$${{121} \over {100}}$$
4
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
The sum of 10 terms of the series

$${3 \over {{1^2} \times {2^2}}} + {5 \over {{2^2} \times {3^2}}} + {7 \over {{3^2} \times {4^2}}} + ....$$ is :
A
1
B
$${{120} \over {121}}$$
C
$${{99} \over {100}}$$
D
$${{143} \over {144}}$$
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