jee-main 2023 Q61

jee-main · India · session2_10apr_shift2 Complex Numbers Argand & Loci Algebraic Conditions for Geometric Properties (Real, Imaginary, Collinear)

Let $S = \left\{ z = x + iy : \frac { 2z - 3i } { 4z + 2i } \text{ is a real number} \right\}$. Then which of the following is NOT correct?
(1) $y + x ^ { 2 } + y ^ { 2 } \neq - \frac { 1 } { 4 }$
(2) $( x , y ) = \left( 0 , - \frac { 1 } { 2 } \right)$
(3) $x = 0$
(4) $y \in \left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , \infty \right)$

Let $S = \left\{ z = x + iy : \frac { 2z - 3i } { 4z + 2i } \text{ is a real number} \right\}$. Then which of the following is NOT correct?\\
(1) $y + x ^ { 2 } + y ^ { 2 } \neq - \frac { 1 } { 4 }$\\
(2) $( x , y ) = \left( 0 , - \frac { 1 } { 2 } \right)$\\
(3) $x = 0$\\
(4) $y \in \left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , \infty \right)$

Paper Questions

Q1 Q2 Q5 Q6 Q8 Q9 Q15 Q17 Q21 Q22 Q23 Q24 Q28 Q29 Q30 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75