Sequences & Series · JEE Main previous year questions

2004 3 questions

1. Q142004 · 24 Apr 2004 · Shift 1

   Let $T_r$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, $m\ne n$, $T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then a - d equals

   1. A.$\frac{1}{m}+\frac{1}{n}$
   2. B.1
   3. C.$\frac{1}{mn}$
   4. D.0
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   Answer: D

2. Q532004 · 24 Apr 2004 · Shift 1

   The sum of the first n terms of the series $1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+\dots$ is $\frac{n(n+1{)}^2}{2}$ when n is even. When n is odd the sum is

   1. A.${\left[\frac{n(n+1)}{2}\right]}^2$
   2. B.$\frac{n^2(n+1)}{2}$
   3. C.$\frac{n(n+1{)}^2}{4}$
   4. D.$\frac{3n(n+1)}{2}$
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   Answer: B

3. Q542004 · 24 Apr 2004 · Shift 1

   The sum of series $\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+\dots \dots$ is

   1. A.$\frac{(e^2-2)}{e}$
   2. B.$\frac{(e-1{)}^2}{2e}$
   3. C.$\frac{(e^2-1)}{2e}$
   4. D.$\frac{(e^2-1)}{2}$
   Show answer

   Answer: B