Complex Numbers · NDA previous year questions

2019 4 questions

1. Q32019 · 21 Apr 2019

   If $A=\{x\in Z:x^3-1=0\}$ and $B=\{x\in Z:x^2+x+1=0\}$, where Z is set of complex numbers, then what is $A\cap B$ equal to?

   1. A.Null set
   2. B.$\left\{\frac{-1+\sqrt{3}i}{2},\frac{-1-\sqrt{3}i}{2}\right\}$
   3. C.$\left\{\frac{-1+\sqrt{3}i}{4},\frac{-1-\sqrt{3}i}{4}\right\}$
   4. D.$\left\{\frac{1+\sqrt{3}i}{2},\frac{1-\sqrt{3}i}{2}\right\}$
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   Answer: B

2. Q102019 · 21 Apr 2019

   Consider the following for the next 02 (two) items: A complex number is given by $z=\frac{1+2i}{1-(1-i{)}^2}$. What is the modulus of z?

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

3. Q112019 · 21 Apr 2019

   Consider the following for the next 02 (two) items: A complex number is given by $z=\frac{1+2i}{1-(1-i{)}^2}$. What is the principal argument of z?

   1. A.$0$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{2}$
   4. D.$\pi$
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   Answer: A

4. Q122019 · 21 Apr 2019

   What is the $n^{th}$ term of the sequence $25,-125,625,-3125,\dots$?

   1. A.$(-5{)}^{2n-1}$
   2. B.$(-1{)}^{2n}{5}^{n+1}$
   3. C.$(-1{)}^{2n-1}{5}^{n+1}$
   4. D.$(-1{)}^{n-1}{5}^{n+1}$
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   Answer: D