1
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1
Out of Syllabus

If $$\operatorname{gcd}~(\mathrm{m}, \mathrm{n})=1$$ and $$1^{2}-2^{2}+3^{2}-4^{2}+\ldots . .+(2021)^{2}-(2022)^{2}+(2023)^{2}=1012 ~m^{2} n$$ then $$m^{2}-n^{2}$$ is equal to :

A
220
B
200
C
240
D
180
2
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1
Out of Syllabus

The sum of the first $$20$$ terms of the series $$5+11+19+29+41+\ldots$$ is :

A
3420
B
3450
C
3250
D
3520
3
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1
Out of Syllabus

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
$${{13e} \over 4} + {5 \over {4e}}$$
4
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1
Out of Syllabus

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
$${{59} \over {111}}$$
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