Sequences & Series · JEE Main previous year questions

2012 5 questions

1. Q42012 · 26 May 2012 · Shift 1

   If the A.M. between $p^{\mathrm{th}}$ and $q^{\mathrm{th}}$ terms of an A.P. is equal to the A.M. between $r^{\mathrm{th}}$ and $s^{\mathrm{th}}$ terms of the same A.P., then $p+q$ is equal to

   1. A.$r+s-1$
   2. B.$r+s-2$
   3. C.$r+s+1$
   4. D.$r+s$
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   Answer: D

2. Q222012 · 26 May 2012 · Shift 1

   If the sum of the series $1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+\dots$ upto $n$ terms, when $n$ is even, is $\frac{n(n+1{)}^2}{2}$, then the sum of the series, when $n$ is odd, is

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

3. Q232012 · 12 May 2012 · Shift 1

   The sum of the series $\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\dots$ upto 15 terms is

   1. A.1
   2. B.2
   3. C.3
   4. D.4
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   Answer: C

4. Q42012 · 7 May 2012 · Shift 1

   The difference between the fourth term and the first term of a Geometrical Progression is 52. If the sum of its first three terms is 26 , then the sum of the first six terms of the progression is

   1. A.63
   2. B.189
   3. C.728
   4. D.364
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   Answer: C

5. Q222012 · 7 May 2012 · Shift 1

   The sum of the series $1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+\cdots +2(2m{)}^2$ is

   1. A.$m(2m+1{)}^2$
   2. B.$m^2(m+2)$
   3. C.$m^2(2m+1)$
   4. D.$m(m+2{)}^2$
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   Answer: A