1
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If $$A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}$$ and $$B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}$$, then $${A \over B}$$ is equal to :

A
$${{11} \over 9}$$
B
1
C
$$-$$$${{11} \over 9}$$
D
$$-$$$${{11} \over 3}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

The sum 1 + 2 . 3 + 3 . 32 + ......... + 10 . 39 is equal to :

A
$${{2\,.\,{3^{12}} + 10} \over 4}$$
B
$${{19\,.\,{3^{10}} + 1} \over 4}$$
C
$$5\,.\,{3^{10}} - 2$$
D
$${{9\,.\,{3^{10}} + 1} \over 2}$$
3
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

If $${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N}$$, then

A
$${b_3} - {b_2},\,{b_4} - {b_3},\,{b_5} - {b_4}$$ are in A.P. with common difference $$-$$2
B
$${1 \over {{b_3} - {b_2}}},{1 \over {{b_4} - {b_3}}},{1 \over {{b_5} - {b_4}}}$$ are in an A.P. with common difference 2
C
$${b_3} - {b_2},\,{b_4} - {b_3},\,{b_5} - {b_4}$$ are in a G.P.
D
$${1 \over {{b_3} - {b_2}}},{1 \over {{b_4} - {b_3}}},{1 \over {{b_5} - {b_4}}}$$ are in an A.P. with common difference $$-$$2
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is

A
30
B
32
C
36
D
40
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