1
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
$${{1 + x} \over {1 - x}} + {\log _e}(1 - x)$$
2
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If for x, y $$\in$$ R, x > 0, y = log10x + log10x1/3 + log10x1/9 + ...... upto $$\infty$$ terms

and $${{2 + 4 + 6 + .... + 2y} \over {3 + 6 + 9 + ..... + 3y}} = {4 \over {{{\log }_{10}}x}}$$, then the ordered pair (x, y) is equal to :
A
(106, 6)
B
(104, 6)
C
(102, 3)
D
(106, 9)
3
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The sum of the series

$${1 \over {x + 1}} + {2 \over {{x^2} + 1}} + {{{2^2}} \over {{x^4} + 1}} + ...... + {{{2^{100}}} \over {{x^{{2^{100}}}} + 1}}$$ when x = 2 is :
A
$$1 + {{{2^{101}}} \over {{4^{101}} - 1}}$$
B
$$1 + {{{2^{100}}} \over {{4^{101}} - 1}}$$
C
$$1 - {{{2^{100}}} \over {{4^{100}} - 1}}$$
D
$$1 - {{{2^{101}}} \over {{2^{400}} - 1}}$$
4
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
If the sum of an infinite GP a, ar, ar2, ar3, ....... is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, ....... is :
A
$${5 \over 2}$$
B
$${1 \over 2}$$
C
$${25 \over 2}$$
D
$${9 \over 2}$$
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