Sequences & Series · NDA previous year questions

2010 9 questions

1. Q282010 · 22 Aug 2010

   The sum of an infinite geometric progression is 6. If the sum of the first two terms is $9/2$, then what is the first term?

   1. A.1
   2. B.$5/2$
   3. C.3 or $3/2$
   4. D.9 or 3
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   Answer: D

2. Q212010 · 18 Apr 2010

   If p times the $p^{\text{th}}$ term of an AP is q times the $q^{\text{th}}$ term, then what is the $(p+q{)}^{\text{th}}$ term equal to?

   1. A.$p+q$
   2. B.$pq$
   3. C.1
   4. D.0
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   Answer: D

3. Q372010 · 18 Apr 2010

   The $59^{\text{th}}$ term of an AP is 449 and the $449^{\text{th}}$ term is 59. Which term is equal to 0 (zero)?

   1. A.$501^{\text{st}}$ term
   2. B.$502^{\text{nd}}$ term
   3. C.$508^{\text{th}}$ term
   4. D.$509^{\text{th}}$ term
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   Answer: C

4. Q1082010 · 18 Apr 2010

   If angles A, B, C are in AP, then what is $\sin A+2\sin B+\sin C$ equal to?

   1. A.$4\sin B{\cos }^2\left(\frac{A-C}{2}\right)$
   2. B.$4\sin B{\cos }^2\left(\frac{A-C}{4}\right)$
   3. C.$4\sin (2B){\cos }^2\left(\frac{A-C}{2}\right)$
   4. D.$4\sin (2B){\cos }^2\left(\frac{A-C}{4}\right)$
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   Answer: B

5. Q1092010 · 18 Apr 2010

   Statement I: If $-1\le x<0$, then $\cos ({\sin }^{-1}x)=-\sqrt{1-x^2}$. Statement II: If $-1\le x<0$, then $\sin ({\cos }^{-1}x)=\sqrt{1-x^2}$. Which one of the following is correct in respect of the above statements?

   1. A.Both statements I and II are independently correct and statement II is the correct explanation of statement I
   2. B.Both statements I and II are independently correct but statement II is not the correct explanation of statement I
   3. C.Statement I is correct but statement II is false
   4. D.Statement I is false but statement II is correct
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   Answer: D

6. Q1122010 · 18 Apr 2010

   Let a, b, c be in AP. Consider the following statements: 1. $\frac{1}{ab},\frac{1}{ca},\frac{1}{bc}$ are in AP. 2. $\frac{1}{\sqrt{b}+\sqrt{c}},\frac{1}{\sqrt{c}+\sqrt{a}},\frac{1}{\sqrt{a}+\sqrt{b}}$ are in AP. Which of the statements given above is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: C

7. Q1132010 · 18 Apr 2010

   What is the differentiation of ${\log }_{x}x$ with respect to $\ln x$?

   1. A.0
   2. B.1
   3. C.1/x
   4. D.x
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   Answer: A

8. Q1142010 · 18 Apr 2010

   What is $\tan \left(7{\frac{1}{2}}^{\circ }\right)$ equal to?

   1. A.$\sqrt{6}+\sqrt{3}-\sqrt{2}+2$
   2. B.$\sqrt{6}+\sqrt{3}+\sqrt{2}+2$
   3. C.$\sqrt{6}-\sqrt{3}+\sqrt{2}-2$
   4. D.$\sqrt{6}+\sqrt{3}+\sqrt{2}-2$
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   Answer: C

9. Q1152010 · 18 Apr 2010

   What is the value of $\frac{\cos 15^{\circ }+\cos 45^{\circ }}{{\cos }^{3}15^{\circ }+{\cos }^{3}45^{\circ }}$?

   1. A.$\frac{1}{4}$
   2. B.$\frac{1}{2}$
   3. C.$\frac{1}{3}$
   4. D.None of the above
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   Answer: D