1
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
$${{143} \over {144}}$$
2
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r2, then r2 $$-$$ d is equal to :
A
7 $$-$$ 7$$\sqrt 3$$
B
7 + $$\sqrt 3$$
C
7 $$-$$ $$\sqrt 3$$
D
7 + 3$$\sqrt 3$$
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
If 0 < x < 1 and $$y = {1 \over 2}{x^2} + {2 \over 3}{x^3} + {3 \over 4}{x^4} + ....$$, then the value of e1 + y at $$x = {1 \over 2}$$ is :
A
$${1 \over 2}{e^2}$$
B
2e
C
$${1 \over 2}\sqrt e$$
D
2e2
4
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If 0 < x < 1, then $${3 \over 2}{x^2} + {5 \over 3}{x^3} + {7 \over 4}{x^4} + .....$$, is equal to :
A
$$x\left( {{{1 + x} \over {1 - x}}} \right) + {\log _e}(1 - x)$$
B
$$x\left( {{{1 - x} \over {1 + x}}} \right) + {\log _e}(1 - x)$$
C
$${{1 - x} \over {1 + x}} + {\log _e}(1 - x)$$
D
$${{1 + x} \over {1 - x}} + {\log _e}(1 - x)$$
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