Atomos Test Generator Free PYQs ExamsMy practice Log in / Sign up free

Complex Numbers and Quadratic Equations

JEE Main 2026 (Online) 28th January Evening ShiftMCQMedium📈 Topic in 40% papers+4−1
Ques. 1JEE Main 2026, 28 January (Evening Shift)

Let A = \z C : |z - 2| 4\ and B = \z C : |z - 2| + |z + 2| = 5\. Then the \|z1 - z2| : z1 A and z2 B\ is :

  1. 172
  2. 8
  3. 9
  4. 152

Answer

(1) 172

Solution

A is the closed disc with centre S(2, 0) and radius 4.

B: |z - 2| + |z + 2| = 5 > 4, so B is an ellipse with foci ( 2, 0), 2a = 5 a = 52, ae = 2.

For a fixed z2 B, the farthest point of the disc A is at distance |z2 - 2| + 4, so |z1 - z2| = 4 + |z2 - 2|.

|z2 - 2| is the focal distance from S(2, 0), SP = a - ex, which is largest at x = -a:

|z2 - 2| = a + ae = 52 + 2 = 92 (at z2 = - 52)

Required maximum = 4 + 92 = 172

Answer: (1)

Keep practising — Complex Numbers and Quadratic Equations

Ques. 2JEE Main 2026, 24 January (Morning Shift)

The number of the real solutions of the equation: x|x + 3| + |x - 1| - 2 = 0 is

  1. 3
  2. 2
  3. 5
  4. 4
Ques. 3JEE Main 2026, 24 January (Morning Shift)

Let S = \z C : | z-6iz-2i | = 1 and | z-8+2iz+2i | = 35 \. Then z S |z|2 is equal to :

  1. 413
  2. 398
  3. 385
  4. 423
Ques. 4JEE Main 2026, 24 January (Evening Shift)

The smallest positive integral value of a, for which all the roots of x4 - ax2 + 9 = 0 are real and distinct, is equal to

  1. 7
  2. 3
  3. 4
  4. 9
Ques. 5JEE Main 2026, 24 January (Evening Shift)

Let z = (1 + i)(1 + 2i)(1 + 3i) (1 + ni), where i = -1. If |z|2 = 44200, then n is equal to .

Ques. 6JEE Main 2026, 23 January (Morning Shift)

If α and β (α < β) are the roots of the equation (-2 + 3 ) ( | x - 3 | ) + (x - 6 x ) + (9 - 2 3 ) = 0, x 0, then + is equal to :

  1. 8
  2. 10
  3. 9
  4. 11
Ques. 7JEE Main 2026, 23 January (Morning Shift)

Let S = \z : 3 |2z - 3(1 + i)| 7 \ be a set of complex numbers. Then Minz S | (z + 12(5 + 3i) ) | is equal to :

  1. 12
  2. 52
  3. 2
  4. 32
Ques. 8JEE Main 2026, 23 January (Morning Shift)

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :

  1. 36 days
  2. 24 days
  3. 30 days
  4. 42 days
Ques. 9JEE Main 2026, 23 January (Evening Shift)

If z = 32 + i2, i = -1, then (z201 - i )8 is equal to

  1. 1
  2. 0
  3. -1
  4. 256
Ques. 10JEE Main 2026, 22 January (Morning Shift)

The number of distinct real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 is

  1. 2
  2. 3
  3. 0
  4. 1
Ques. 11JEE Main 2026, 22 January (Morning Shift)

Let = -1 + i 32 and = -1 - i 32, i = -1. If (7 - 7 + 9 )20 + (9 + 7 - 7 )20 + (-7 + 9 + 7 )20 + (14 + 7 + 7 )20 = m10, then m is

All Complex Numbers and Quadratic Equations PYQs →

PDFDownload Complex Numbers and Quadratic Equations PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇
All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)