Complex Numbers & Quadratic Equations · JEE Main previous year questions

2014 2 questions

1. Q22014 · 6 Apr 2014 · Shift 1

   If $z$ is a complex number such that $|z|\ge 2$, then the minimum value of $\left|z+\frac{1}{2}\right|$ :

   1. A.is strictly greater that $\frac{5}{2}$
   2. B.is strictly greater that $\frac{3}{2}$ but less than $\frac{5}{2}$
   3. C.is equal to $\frac{5}{2}$
   4. D.lie in the interval $(1,2)$
   Show answer

   Answer: D

2. Q42014 · 6 Apr 2014 · Shift 1

   Let $\alpha$ and $\beta$ be the roots of equation $p{x}^2+qx+r=0,p\ne 0$. If $p,q,r$ in A.P. and $\frac{1}{\alpha }+\frac{1}{\beta }=4$, then the value of $|\alpha -\beta |$ is :

   1. A.$\frac{\sqrt{34}}{9}$
   2. B.$\frac{2\sqrt{13}}{9}$
   3. C.$\frac{\sqrt{61}}{9}$
   4. D.$\frac{2\sqrt{17}}{9}$
   Show answer

   Answer: B