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

Let $$S = 2 + {6 \over 7} + {{12} \over {{7^2}}} + {{20} \over {{7^3}}} + {{30} \over {{7^4}}} + \,.....$$. Then 4S is equal to

A
$${\left( {{7 \over 3}} \right)^2}$$
B
$${{{7^3}} \over {{3^2}}}$$
C
$${\left( {{7 \over 3}} \right)^3}$$
D
$${{{7^2}} \over {{3^3}}}$$
2
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

If a1, a2, a3 ...... and b1, b2, b3 ....... are A.P., and a1 = 2, a10 = 3, a1b1 = 1 = a10b10, then a4 b4 is equal to -

A
$${{35} \over {27}}$$
B
1
C
$${{27} \over {28}}$$
D
$${{28} \over {27}}$$
3
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)
4
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
$$-$$$${{11} \over 3}$$
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