Complex Numbers & Quadratic Equations · JEE Main previous year questions

2010 3 questions

1. Q22010 · 25 Apr 2010 · Shift 1

   The number of complex numbers $z$ such that $|z-1|=|z+1|=|z-i|$ equals :

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

2. Q32010 · 25 Apr 2010 · Shift 1

   If $\alpha$ and $\beta$ are the roots of the equation $x^2-x+1=0$, then ${\alpha }^{2009}+{\beta }^{2009}=$

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

3. Q132010 · 25 Apr 2010 · Shift 1

   Consider the system of linear equations; $$\begin{array}{rl}{x}_1+2x_2+x_3& =3\\ 2x_1+3x_2+x_3& =3\\ 3x_1+5x_2+2x_3& =1\end{array}$$ The system has :

   1. A.exactly 3 solutions
   2. B.a unique solution
   3. C.no solution
   4. D.infinite number of solutions
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   Answer: C