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

The sum of the infinite series $$1 + {5 \over 6} + {{12} \over {{6^2}}} + {{22} \over {{6^3}}} + {{35} \over {{6^4}}} + {{51} \over {{6^5}}} + {{70} \over {{6^6}}} + \,\,.....$$ is equal to :

A
$${{425} \over {216}}$$
B
$${{429} \over {216}}$$
C
$${{288} \over {125}}$$
D
$${{280} \over {125}}$$
2
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
$${{49} \over {216}}$$
3
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
4
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
EXAM MAP
Medical
NEET