Sequences & Series · NDA previous year questions

2011 13 questions

1. Q82011 · 21 Aug 2011

   What is the $10^{th}$ common term between the series $2+6+10+\dots \dots$ and $1+6+11+\dots \dots$?

   1. A.180
   2. B.186
   3. C.196
   4. D.206
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   Answer: B

2. Q92011 · 21 Aug 2011

   If the $10^{th}$ term of a GP is 9 and $4^{th}$ term is 4, then what is its $7^{th}$ term?

   1. A.6
   2. B.14
   3. C.27/14
   4. D.56/15
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   Answer: A

3. Q112011 · 21 Aug 2011

   If ${\log }_{10}2$, ${\log }_{10}(2^x-1)$, ${\log }_{10}(2^x+3)$ are three consecutive terms of an AP, then which one of the following is correct?

   1. A.$x=0$
   2. B.$x=1$
   3. C.$x={\log }_{2}5$
   4. D.$x={\log }_{5}2$
   Show answer

   Answer: C

4. Q372011 · 21 Aug 2011

   If $n!$, $3\times (n!)$ and $(n+1)!$ are in GP, then the value of $n$ will be

   1. A.3
   2. B.4
   3. C.8
   4. D.10
   Show answer

   Answer: C

5. Q522011 · 21 Aug 2011

   If a, b, c, d, e, f are in AP, then $(e-c)$ is equal to which one of the following ?

   1. A.$2(c-a)$
   2. B.$2(d-c)$
   3. C.$2(f-d)$
   4. D.$(d-c)$
   Show answer

   Answer: B

6. Q1202011 · 21 Aug 2011

   If the arithmetic and geometric means of two numbers are 10, 8 respectively, then one number exceeds the other number by

   1. A.8
   2. B.10
   3. C.12
   4. D.16
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   Answer: C

7. Q122011 · 17 Apr 2011

   Which one of the following statements is correct?

   1. A.${\sin }^{2}30^{\circ },{\sin }^{2}45^{\circ },{\sin }^{2}60^{\circ }$ are in GP
   2. B.${\cos }^{2}30^{\circ },{\cos }^{2}45^{\circ },{\cos }^{2}60^{\circ }$ are in GP
   3. C.${\cot }^{2}30^{\circ },{\cot }^{2}45^{\circ },{\cot }^{2}60^{\circ }$ are in AP
   4. D.${\tan }^{2}30^{\circ },{\tan }^{2}45^{\circ },{\tan }^{2}60^{\circ }$ are in GP
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   Answer: D

8. Q362011 · 17 Apr 2011

   In a GP of positive terms, any term is equal to one-third of the sum of next two terms. What is the common ratio of the GP?

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

   Answer: B

9. Q372011 · 17 Apr 2011

   If $(1+\tan \theta )(1+\tan \phi )=2$, then what is $(\theta +\phi )$ equal to?

   1. A.$30^{\circ }$
   2. B.$45^{\circ }$
   3. C.$60^{\circ }$
   4. D.$90^{\circ }$
   Show answer

   Answer: B

10. Q422011 · 17 Apr 2011

    Which term of the series $\frac{1}{4},-\frac{1}{2},1,\dots$ is $-128$?

    1. A.9th
    2. B.10th
    3. C.11th
    4. D.12th
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    Answer: B

11. Q432011 · 17 Apr 2011

    What is the number of ordered pairs of non-zero positive integers $(x,y)$ such that $x+y\le 4$?

    1. A.4
    2. B.5
    3. C.6
    4. D.8
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    Answer: C

12. Q452011 · 17 Apr 2011

    If $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c}$ then $a,b,c$ are in

    1. A.AP
    2. B.GP
    3. C.HP
    4. D.None of the above
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    Answer: C

13. Q512011 · 17 Apr 2011

    If $A,B,C$ are in AP and $b:c=\sqrt{3}:\sqrt{2}$, then what is the value of $\sin C$?

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