Sequences & Series · NDA previous year questions

2014 6 questions

1. Q62014 · 28 Sept 2014

   For the next two (02) items that follow : Let $S_n$ denote the sum of first n terms of an AP and $3S_n=S_{2n}$. What is $S_{3n}:S_n$ equal to?

   1. A.$4:1$
   2. B.$6:1$
   3. C.$8:1$
   4. D.$10:1$
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   Answer: B

2. Q72014 · 28 Sept 2014

   For the next two (02) items that follow : Let $S_n$ denote the sum of first n terms of an AP and $3S_n=S_{2n}$. What is $S_{3n}:S_{2n}$ equal to?

   1. A.$2:1$
   2. B.$3:1$
   3. C.$4:1$
   4. D.$5:1$
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   Answer: A

3. Q662014 · 28 Sept 2014

   For the next three (03) items that follow: Let $f(x)=a{x}^2+bx+c$ such that $f(1)=f(-1)$ and a, b, c are in Arithmetic Progression. $f^{\prime }(a),f^{\prime }(b),f^{\prime }(c)$ are in

   1. A.A.P.
   2. B.G.P.
   3. C.H.P.
   4. D.Arithmetico-geometric progression
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   Answer: A

4. Q672014 · 28 Sept 2014

   For the next three (03) items that follow: Let $f(x)=a{x}^2+bx+c$ such that $f(1)=f(-1)$ and a, b, c are in Arithmetic Progression. $f^{\prime \prime }(a),f^{\prime \prime }(b),f^{\prime \prime }(c)$ are

   1. A.in A.P. only
   2. B.in G.P. only
   3. C.in both A.P. and G.P.
   4. D.neither in A.P. nor in G.P.
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   Answer: C

5. Q112014 · 20 Apr 2014

   The sum of an infinite GP is $x$ and the common ratio $r$ is such that $|r|<1$. If the first term of the GP is 2, then which one of the following is correct?

   1. A.$-1<x<1$
   2. B.$-\infty <x<1$
   3. C.$1<x<\infty$
   4. D.None of the above
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   Answer: C

6. Q122014 · 20 Apr 2014

   The sum of the series formed by the sequence $3,\sqrt{3},1\dots \dots$ upto infinity is:

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