jee-main 2023 Q66

jee-main · India · session2_08apr_shift1 Arithmetic Sequences and Series Summation of Derived Sequence from AP

Let $S _ { K } = \frac { 1 + 2 + \ldots + K } { K }$ and $\sum _ { j = 1 } ^ { n } S ^ { 2 } { } _ { j } = \frac { n } { A } \left( B n ^ { 2 } + C n + D \right)$ where $A , B , C , D \in N$ and $A$ has least value then
(1) $A + C + D$ is not divisible by $D$
(2) $A + B = 5 ( D - C )$
(3) $A + B + C + D$ is divisible by 5
(4) $A + B$ is divisible by $D$

Let $S _ { K } = \frac { 1 + 2 + \ldots + K } { K }$ and $\sum _ { j = 1 } ^ { n } S ^ { 2 } { } _ { j } = \frac { n } { A } \left( B n ^ { 2 } + C n + D \right)$ where $A , B , C , D \in N$ and $A$ has least value then\\
(1) $A + C + D$ is not divisible by $D$\\
(2) $A + B = 5 ( D - C )$\\
(3) $A + B + C + D$ is divisible by 5\\
(4) $A + B$ is divisible by $D$

Paper Questions

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