Sequences & Series · NDA previous year questions

2015 4 questions

1. Q92015 · 27 Sept 2015

   If $p,q,r$ are in one geometric progression and $a,b,c$ are in another geometric progression, then $ap,bq,cr$ are in

   1. A.Arithmetic progression
   2. B.Geometric progression
   3. C.Harmonic progression
   4. D.None of the above
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   Answer: B

2. Q102015 · 27 Sept 2015

   What is the sum of $n$ terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\dots$?

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

3. Q122015 · 19 Apr 2015

   What is the sum of the series $0.5+0.55+0.555+\cdots$ to $n$ terms?

   1. A.$\frac{5}{9}\left[n-\frac{2}{9}\left(1-\frac{1}{10^n}\right)\right]$
   2. B.$\frac{1}{9}\left[5-\frac{2}{9}\left(1-\frac{1}{10^n}\right)\right]$
   3. C.$\frac{1}{9}\left[n-\frac{5}{9}\left(1-\frac{1}{10^n}\right)\right]$
   4. D.$\frac{5}{9}\left[n-\frac{1}{9}\left(1-\frac{1}{10^n}\right)\right]$
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   Answer: D

4. Q132015 · 19 Apr 2015

   If $${\log }_{10}2,{\log }_{10}(2^x-1)\text{ and }{\log }_{10}(2^x+3)$$ are three consecutive terms of an AP, then the value of $x$ is

   1. A.1
   2. B.${\log }_{5}2$
   3. C.${\log }_{2}5$
   4. D.${\log }_{10}5$
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   Answer: C