Complex Numbers · NDA previous year questions

2010 6 questions

1. Q102010 · 22 Aug 2010

   If $\omega$ is a complex cube root of unity, then what is ${\omega }^{10}+{\omega }^{-10}$ equal to?

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

2. Q1192010 · 22 Aug 2010
   
   1. A.$0$
   2. B.$1$
   3. C.$2$
   4. D.$3$
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   Answer: A

3. Q722010 · 18 Apr 2010

   If $\omega$ is a complex cube root of unity and $x={\omega }^2-\omega -2$, then what is the value of $x^2+4x+7$?

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

4. Q732010 · 18 Apr 2010

   If $\cos x\ne -1$, then what is $\frac{\sin x}{1+\cos x}$ equal to?

   1. A.$-\cot \frac{x}{2}$
   2. B.$\cot \frac{x}{2}$
   3. C.$\tan \frac{x}{2}$
   4. D.$-\tan \frac{x}{2}$
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   Answer: C

5. Q812010 · 18 Apr 2010

   What is the modulus of $\frac{1+2i}{1-(1-i{)}^2}$?

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

6. Q822010 · 18 Apr 2010

   If the line through the points A (k, 1, -1) and B (2k, 0, 2) is perpendicular to the line through the points B and C (2 + 2k, k, 1), then what is the value of k?

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