Sequences & Series · JEE Main previous year questions

2018 6 questions

1. Q72018 · 16 Apr 2018 · Shift 1

   Let $\frac{1}{x_1},\frac{1}{x_2},\dots ,\frac{1}{x_n}$ $(x_i\ne 0\text{ for }i=1,2,\dots ,n)$ be in A.P. such that $x_1=4$ and $x_{21}=20$. If n is the least positive integer for which $x_n>50$, then ${\sum }_{i=1}^n\left(\frac{1}{x_i}\right)$ is equal to :

   1. A.$\frac{1}{8}$
   2. B.3
   3. C.$\frac{13}{8}$
   4. D.$\frac{13}{4}$
   Show answer

   Answer: D

2. Q252018 · 16 Apr 2018 · Shift 1

   The sum of the first 20 terms of the series $1+\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+\dots$, is :

   1. A.$38+\frac{1}{2^{19}}$
   2. B.$38+\frac{1}{2^{20}}$
   3. C.$39+\frac{1}{2^{20}}$
   4. D.$39+\frac{1}{2^{19}}$
   Show answer

   Answer: A

3. Q72018 · 15 Apr 2018 · Shift 1

   If $x_1,x_2,\dots ,x_n$ and $\frac{1}{h_1},\frac{1}{h_2},\dots ,\frac{1}{h_n}$ are two A.P.s such that $x_3=h_2=8$ and $x_8=h_7=20$, then $x_5.h_{10}$ equals :

   1. A.2560
   2. B.2650
   3. C.3200
   4. D.1600
   Show answer

   Answer: A

4. Q82018 · 15 Apr 2018 · Shift 1

   If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

   1. A.$(-\infty ,-10]$
   2. B.$(-10,0)$
   3. C.$(0,10)$
   4. D.$[10,\infty )$
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   Answer: C

5. Q72018 · 8 Apr 2018 · Shift 1

   Let $a_1,a_2,a_3,\dots \dots \dots ,a_{49}$ be in A.P. such that ${\sum }_{k=0}^{12}{a}_{4k+1}=416$ and $a_9+a_{43}=66$. $a_1^2+a_2^2+\dots \dots \cdots +a_{17}^2=140m$, then m is equal to

   1. A.$33$
   2. B.$66$
   3. C.$68$
   4. D.$34$
   Show answer

   Answer: D

6. Q202018 · 8 Apr 2018 · Shift 1

   Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series $1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2\dots \dots \dots \dots$ If $\mathrm{B}-2A=100\lambda$, then $\lambda$ is equal to

   1. A.$496$
   2. B.$232$
   3. C.$248$
   4. D.$464$
   Show answer

   Answer: C