Complex Numbers · NDA previous year questions

2011 7 questions

1. Q432011 · 21 Aug 2011

   If $\alpha$ and $\beta$ are the complex cube roots of unity, then what is the value of $(1+\alpha )(1+\beta )(1+{\alpha }^2)(1+{\beta }^2)$ ?

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

2. Q772011 · 21 Aug 2011

   If p, q, r are positive integers and $\omega$ is the cube root of unity and $f(x)=x^{3p}+x^{3q+1}+x^{3r+2}$, then what is $f(\omega )$ equal to?

   1. A.$\omega$
   2. B.$-{\omega }^2$
   3. C.$-\omega$
   4. D.0
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   Answer: D

3. Q882011 · 21 Aug 2011

   What is the argument of $(1-\sin \theta )+i\cos \theta$? $(i=\sqrt{-1})$

   1. A.$\frac{\pi }{2}-\frac{\theta }{2}$
   2. B.$\frac{\pi }{2}+\frac{\theta }{2}$
   3. C.$\frac{\pi }{4}-\frac{\theta }{2}$
   4. D.$\frac{\pi }{4}+\frac{\theta }{2}$
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   Answer: D

4. Q152011 · 17 Apr 2011

   If $\omega$ is the imaginary cube root of unity, then what is $(2-\omega +2{\omega }^2{)}^{27}$ equal to?

   1. A.$3^{27}\omega$
   2. B.$-3^{27}{\omega }^2$
   3. C.$3^{27}$
   4. D.$-3^{27}$
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   Answer: D

5. Q162011 · 17 Apr 2011

   What is the modulus of $\frac{1}{1+3i}-\frac{1}{1-3i}$?

   1. A.$\frac{3}{5}$
   2. B.$\frac{9}{25}$
   3. C.$\frac{3}{25}$
   4. D.$\frac{5}{3}$
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   Answer: A

6. Q682011 · 17 Apr 2011

   If $p,q,r$ are rational numbers, then the roots of the equation $x^2-2px+p^2-q^2+2qr-r^2=0$ are

   1. A.complex
   2. B.pure imaginary
   3. C.irrational
   4. D.rational
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   Answer: D

7. Q692011 · 17 Apr 2011

   If $A=\{1,2,5,6\}$ and $B=\{1,2,3\}$, then what is $(A\times B)\cap (B\times A)$ equal to?

   1. A.$\{(1,1),(2,1),(6,1),(3,2)\}$
   2. B.$\{(1,1),(1,2),(2,1),(2,2)\}$
   3. C.$\{(1,1),(2,2)\}$
   4. D.$\{(1,1),(1,2),(2,5),(2,6)\}$
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   Answer: B