IIT-JEE 2006 | Complex Numbers Question 46 | Mathematics

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

If $P$ is a point on $C_1$ and $Q$ in another point on $\mathrm{C}_2$, then $\frac{\mathrm{PA}^2+\mathrm{PB}^2+\mathrm{PC}^2+\mathrm{PD}^2}{\mathrm{QA}^2+\mathrm{QB}^2+\mathrm{QC}^2+\mathrm{QD}^2}$ is equal to :

0.75

1.25

0.5

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.5

$$a,\,b,\,c$$ are integers, not all simultaneously equal and $$\omega $$ is cube root of unity $$\left( {\omega \ne 1} \right),$$ then minimum value of $$\left| {a + b\omega + c{\omega ^2}} \right|$$ is

$${{\sqrt 3 } \over 2}$$

$${1 \over 2}$$

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

-1

If one of the vertices of the square circumscribing the circle $$|z-1|=\sqrt{2}$$ is $$(2+\sqrt{3 i})$$. Find the other vertices of square.

$$\left( {1 - 2\sqrt 3 } \right) + i,\left( {1 + \sqrt 3 } \right) - i, - \sqrt 3 i$$

$$\left( {1 - \sqrt 3 } \right) + i,\left( {2 + \sqrt 3 } \right) - i, - i$$

$$\left( {1 - \sqrt 3 } \right) + i,\left( {1 + 2\sqrt 3 } \right) - i, - \sqrt 5 i$$

$$\left( {1 - \sqrt 3 } \right) + i,\left( {1 + \sqrt 3 } \right) - i, - \sqrt 3 i$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If $$\omega $$ $$\left( { \ne 1} \right)$$ be a cube root of unity and $${\left( {1 + {\omega ^2}} \right)^n} = {\left( {1 + {\omega ^4}} \right)^n},$$ then the least positive value of n is

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