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JEE Advanced 2010Paper 2
Exam
JEE Advanced
Year
2010
Paper
Paper 2
Subject
Mathematics
Chapter
Complex Number

JEE Advanced 2010 · Paper 2 · Mathematics · Complex Number

Match the statements of Column I with these in Column II. [Note :...

Match the statements of Column I with these in Column II. [Note : Here zz takes values in the complex plane and Im⁡(z)\operatorname{Im}(z) and Re⁡(z)\operatorname{Re}(z) denote respectively, the imaginary part and the real part of zz ] Match the statements of Column I with these in Column II. [Note : Here z takes values in the complex plane and Im(z)

Options

  1. A(A) q, (B) p, (C) p,s, (D) q,r,s
  2. B(A) q,r, (B) p, (C) p,s,t, (D) q,r,s,t
  3. C(A) q, (B) q, (C) p,s,t, (D) q,r,s,t
  4. D(A) q,r, (B) q, (C) p,s, (D) q,r,s

Correct answer

B. (A) q,r, (B) p, (C) p,s,t, (D) q,r,s,t

Step-by-step solution

(A) zz is equidistant from the points i∣z∣i|z| and −i∣z∣-i|z|, whose perpendicular bisector is Im⁡(z)=0\operatorname{Im}(z)=0. (B) Sum of distance of zz from (4,0)(4,0) and (−4,0)(-4,0) is a constant 10 , hence locus of zz is ellipse with semi-major axis 5 and focus at (±4,0),ae=4(\pm 4,0), a e=4. \therefore \quad e=45(\frac{4}{5} (C) ∣z∣≤∣w∣+∣1w∣=52<3|z| \leq|w|+\left|\frac{1}{w}\right|=\frac{5}{2} \lt 3 (D) ∣z∣≤∣w∣+∣1w∣=2|z| \leq|w|+\left|\frac{1}{w}\right|=2 \therefore \quad \operatorname{Re}(z) \leq|z| \leq 2
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