1
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1

Consider two G.Ps. 2, 22, 23, ..... and 4, 42, 43, .... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is $${(2)^{{{225} \over 8}}}$$, then $$\sum\limits_{k = 1}^n {k(n - k)}$$ is equal to :

A
560
B
1540
C
1330
D
2600
2
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

The sum $$\sum\limits_{n = 1}^{21} {{3 \over {(4n - 1)(4n + 3)}}}$$ is equal to

A
$$\frac{7}{87}$$
B
$$\frac{7}{29}$$
C
$$\frac{14}{87}$$
D
$$\frac{21}{29}$$
3
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

The value of $$1 + {1 \over {1 + 2}} + {1 \over {1 + 2 + 3}} + \,\,....\,\, + \,\,{1 \over {1 + 2 + 3 + \,\,.....\,\, + \,\,11}}$$ is equal to:

A
$${{20} \over {11}}$$
B
$${{11} \over {6}}$$
C
$${{241} \over {132}}$$
D
$${{21} \over {11}}$$
4
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+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
$${{280} \over {125}}$$
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