1
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

The sum $$\sum\limits_{n = 1}^\infty {{{2{n^2} + 3n + 4} \over {(2n)!}}}$$ is equal to :

A
$${{11e} \over 2} + {7 \over {2e}}$$
B
$${{13e} \over 4} + {5 \over {4e}} - 4$$
C
$${{11e} \over 2} + {7 \over {2e}} - 4$$
D
$${{13e} \over 4} + {5 \over {4e}}$$
2
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

The sum of 10 terms of the series

$${1 \over {1 + {1^2} + {1^4}}} + {2 \over {1 + {2^2} + {2^4}}} + {3 \over {1 + {3^2} + {3^4}}}\, + \,....$$ is

A
$${{58} \over {111}}$$
B
$${{56} \over {111}}$$
C
$${{55} \over {111}}$$
D
$${{59} \over {111}}$$
3
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Let $a_1, a_2, a_3, \ldots$ be an A.P. If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :
A
24
B
$\frac{381}{4}$
C
9
D
$\frac{33}{4}$
4
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

A
7
B
14
C
3
D
$$\frac{9}{2}$$
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