Complex Numbers & Quadratic Equations · JEE Main previous year questions

2015 3 questions

1. Q12015 · 4 Apr 2015 · Shift 1

   A complex number $z$ is said to be unimodular if $|z|=1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1-2z_2}{2-z_1{\bar{z}}_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a :

   1. A.circle of radius $2$.
   2. B.circle of radius $\sqrt{2}$.
   3. C.straight line parallel to x-axis
   4. D.straight line parallel to y-axis.
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   Answer: A

2. Q22015 · 4 Apr 2015 · Shift 1

   Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2=0$. If $a_n={\alpha }^n-{\beta }^n$, for $n\ge 1$, then the value of $\frac{a_{10}-2a_8}{2a_9}$ is equal to :

   1. A.$3$
   2. B.$-3$
   3. C.$6$
   4. D.$-6$
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   Answer: A

3. Q242015 · 4 Apr 2015 · Shift 1

   The normal to the curve, $x^2+2xy-3y^2=0$, at $(1,1)$

   1. A.meets the curve again in the third quadrant.
   2. B.meets the curve again in the fourth quadrant.
   3. C.does not meet the curve again.
   4. D.meets the curve again in the second quadrant.
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   Answer: B