1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1
Out of Syllabus

Let $$\{ {a_n}\} _{n = 0}^\infty$$ be a sequence such that $${a_0} = {a_1} = 0$$ and $${a_{n + 2}} = 2{a_{n + 1}} - {a_n} + 1$$ for all n $$\ge$$ 0. Then, $$\sum\limits_{n = 2}^\infty {{{{a_n}} \over {{7^n}}}}$$ is equal to:

A
$${6 \over {343}}$$
B
$${7 \over {216}}$$
C
$${8 \over {343}}$$
D
$${{49} \over {216}}$$
2
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is :

A
21
B
22
C
23
D
24
3
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = $${1 \over {1296}}$$ and A2 + A4 = $${7 \over {36}}$$, then the value of A6 + A8 + A10 is equal to

A
33
B
37
C
43
D
47
4
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1
Out of Syllabus

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
$${{{7^2}} \over {{3^3}}}$$
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