Complex Numbers · NDA previous year questions

2018 9 questions

1. Q52018 · 22 Apr 2018

   What is the principal argument of $(-1-i)$, where $i=\sqrt{-1}$ ?

   1. A.$\pi /4$
   2. B.$-\pi /4$
   3. C.$-3\pi /4$
   4. D.$3\pi /4$
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   Answer: C

2. Q72018 · 22 Apr 2018

   If $\alpha$ and $\beta$ are different complex numbers with $|\alpha |=1$, then what is $\left|\frac{\alpha -\beta }{1-\alpha \bar{\beta }}\right|$ equal to ?

   1. A.$|\beta |$
   2. B.2
   3. C.1
   4. D.0
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   Answer: C

3. Q82018 · 22 Apr 2018

   What is $i^{1000}+i^{1001}+i^{1002}+i^{1003}$ equal to (where $i=\sqrt{-1}$) ?

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

4. Q92018 · 22 Apr 2018

   The modulus-amplitude form of $\sqrt{3}+i$, where $i=\sqrt{-1}$ is

   1. A.$2\left(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}\right)$
   2. B.$2\left(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}\right)$
   3. C.$4\left(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}\right)$
   4. D.$4\left(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}\right)$
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   Answer: B

5. Q102018 · 22 Apr 2018

   What is the value of the sum ${\sum }_{n=2}^{11}(i^n+i^{n+1})$, where $i=\sqrt{-1}$ ?

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

6. Q112018 · 22 Apr 2018

   If the ratio of AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to

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

7. Q122018 · 22 Apr 2018

   If $x=1-y+y^2-y^3+\dots$ up to infinite terms, where $|y|<1$, then which one of the following is correct ?

   1. A.$x=\frac{1}{1+y}$
   2. B.$x=\frac{1}{1-y}$
   3. C.$x=\frac{y}{1+y}$
   4. D.$x=\frac{y}{1-y}$
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   Answer: A

8. Q132018 · 22 Apr 2018

   What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder ?

   1. A.1565
   2. B.1585
   3. C.1635
   4. D.1655
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   Answer: C

9. Q162018 · 22 Apr 2018

   Let $\alpha$ and $\beta$ be real numbers and z be a complex number. If $z^2+\alpha z+\beta =0$ has two distinct non-real roots with $\text{Re}(z)=1$, then it is necessary that

   1. A.$\beta \in (-1,0)$
   2. B.$|\beta |=1$
   3. C.$\beta \in (1,\infty )$
   4. D.$\beta \in (0,1)$
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   Answer: C