1
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

$$x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} } }$$, where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc $$\ne$$ 0, then :

A
x, y, z are in A.P.
B
x, y, z are in G.P.
C
$${1 \over x}$$, $${1 \over y}$$, $${1 \over z}$$ are in A.P.
D
$${1 \over x}$$ + $${1 \over y}$$ + $${1 \over z}$$ = 1 $$-$$ (a + b + c)
2
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
$$-$$$${{11} \over 3}$$
3
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
$${{9\,.\,{3^{10}} + 1} \over 2}$$
4
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
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