Complex Numbers · NDA previous year questions

2023 10 questions

1. Q332023 · 3 Sept 2023

   Consider the following for the next items that follow: Consider equation-I : $z^3+2z^2+2z+1=0$ and equation-II : $z^{1985}+z^{100}+1=0$. What are the roots of equation-I ?

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

2. Q342023 · 3 Sept 2023

   Consider the following for the next items that follow: Consider equation-I : $z^3+2z^2+2z+1=0$ and equation-II : $z^{1985}+z^{100}+1=0$. Which one of the following is a root of equation-II?

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

3. Q352023 · 3 Sept 2023

   What is the number of common roots of equation-I and equation-II?

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

4. Q362023 · 3 Sept 2023

   Consider the following for the next items that follow: A quadratic equation is given by $(a+b)x^2-(a+b+c)x+k=0$, where a, b, c are real. If $k=\frac{c}{2}$, $(c\ne 0)$, then the roots of the equation are :

   1. A.Real and equal
   2. B.Real and unequal
   3. C.Real iff a > c
   4. D.Complex but not real
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   Answer: B

5. Q12023 · 16 Apr 2023

   If $\omega$ is a non-real cube root of 1, then what is the value of $\left|\frac{1-\omega }{\omega +{\omega }^2}\right|$ ?

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

6. Q22023 · 16 Apr 2023

   What is the number of 6-digit numbers that can be formed only by using 0, 1, 2, 3, 4 and 5 (each once); and divisible by 6 ?

   1. A.96
   2. B.120
   3. C.192
   4. D.312
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   Answer: D

7. Q122023 · 16 Apr 2023
   
   1. A.$\frac{\pi }{3}$
   2. B.$\frac{2\pi }{3}$
   3. C.$\frac{4\pi }{3}$
   4. D.$\frac{5\pi }{6}$
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   Answer: B

8. Q202023 · 16 Apr 2023

   If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?

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

9. Q212023 · 16 Apr 2023

   How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?

   1. A.Only one
   2. B.Only two
   3. C.Only three
   4. D.Infinitely many
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   Answer: B

10. Q222023 · 16 Apr 2023

    A mapping $f:A\to B$ defined as $f(x)=\frac{2x+3}{3x+5},x\in A$. If f is to be onto, then what are A and B equal to ?

    1. A.$A=R\setminus \{-\frac{5}{3}\}$ and $B=R\setminus \{-\frac{2}{3}\}$
    2. B.$A=R$ and $B=R\setminus \{-\frac{5}{3}\}$
    3. C.$A=R\setminus \{-\frac{3}{2}\}$ and $B=R\setminus \{0\}$
    4. D.$A=R\setminus \{-\frac{5}{3}\}$ and $B=R\setminus \{\frac{2}{3}\}$
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    Answer: D