1
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
Out of Syllabus
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
2
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
Out of Syllabus
$${1 \over {{3^2} - 1}} + {1 \over {{5^2} - 1}} + {1 \over {{7^2} - 1}} + .... + {1 \over {{{(201)}^2} - 1}}$$ is equal to
A
$${{101} \over {404}}$$
B
$${{25} \over {101}}$$
C
$${{101} \over {408}}$$
D
$${{99} \over {400}}$$
3
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Out of Syllabus
The sum of the series

$$\sum\limits_{n = 1}^\infty {{{{n^2} + 6n + 10} \over {(2n + 1)!}}}$$ is equal to :
A
$${{41} \over 8}e + {{19} \over 8}{e^{ - 1}} - 10$$
B
$${{41} \over 8}e - {{19} \over 8}{e^{ - 1}} - 10$$
C
$${{41} \over 8}e + {{19} \over 8}{e^{ - 1}} + 10$$
D
$$- {{41} \over 8}e + {{19} \over 8}{e^{ - 1}} - 10$$
4
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Out of Syllabus
The sum of the infinite series
$$1 + {2 \over 3} + {7 \over {{3^2}}} + {{12} \over {{3^3}}} + {{17} \over {{3^4}}} + {{22} \over {{3^5}}} + ......$$ is equal to :
A
$${9 \over 4}$$
B
$${13 \over 4}$$
C
$${15 \over 4}$$
D
$${11 \over 4}$$
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