jee-advanced 2016 Q38

jee-advanced · India · paper2 Arithmetic Sequences and Series Arithmetic-Geometric Hybrid Problem

Let $b _ { i } > 1$ for $i = 1,2 , \ldots , 101$. Suppose $\log _ { e } b _ { 1 } , \log _ { e } b _ { 2 } , \ldots , \log _ { e } b _ { 101 }$ are in Arithmetic Progression (A.P.) with the common difference $\log _ { e } 2$. Suppose $a _ { 1 } , a _ { 2 } , \ldots , a _ { 101 }$ are in A.P. such that $a _ { 1 } = b _ { 1 }$ and $a _ { 51 } = b _ { 51 }$. If $t = b _ { 1 } + b _ { 2 } + \cdots + b _ { 51 }$ and $s = a _ { 1 } + a _ { 2 } + \cdots + a _ { 51 }$, then
(A) $s > t$ and $a _ { 101 } > b _ { 101 }$
(B) $s > t$ and $a _ { 101 } < b _ { 101 }$
(C) $s < t$ and $a _ { 101 } > b _ { 101 }$
(D) $s < t$ and $a _ { 101 } < b _ { 101 }$

Let $b _ { i } > 1$ for $i = 1,2 , \ldots , 101$. Suppose $\log _ { e } b _ { 1 } , \log _ { e } b _ { 2 } , \ldots , \log _ { e } b _ { 101 }$ are in Arithmetic Progression (A.P.) with the common difference $\log _ { e } 2$. Suppose $a _ { 1 } , a _ { 2 } , \ldots , a _ { 101 }$ are in A.P. such that $a _ { 1 } = b _ { 1 }$ and $a _ { 51 } = b _ { 51 }$. If $t = b _ { 1 } + b _ { 2 } + \cdots + b _ { 51 }$ and $s = a _ { 1 } + a _ { 2 } + \cdots + a _ { 51 }$, then\\
(A) $s > t$ and $a _ { 101 } > b _ { 101 }$\\
(B) $s > t$ and $a _ { 101 } < b _ { 101 }$\\
(C) $s < t$ and $a _ { 101 } > b _ { 101 }$\\
(D) $s < t$ and $a _ { 101 } < b _ { 101 }$

Paper Questions

Q37 Q38 Q39 Q40 Q41 Q42 Q43 Q44 Q45 Q46 Q47 Q48 Q49 Q50 Q51 Q52 Q53 Q54