PYQSide ExamsMy practice

Complex Numbers and Quadratic Equations · Question 56

JEE Main 2025 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 35% papers+4−1
1

The number of solutions of the equation ( 9x - 9 x + 2 ) ( 2x - 7 x + 3 ) = 0 is :

  1. 3
  2. 2
  3. 1
  4. 4

Answer

(4) 4

Solution

Let t = 1 x, t > 0 (x > 0 for the equation to be defined).

First factor: 9t2 - 9t + 2 = 0 (3t - 1)(3t - 2) = 0

t = 13, 23 x = 9, 94

Second factor: 2t2 - 7t + 3 = 0 (2t - 1)(t - 3) = 0

t = 12, 3 x = 4, 19

All four values are positive and distinct.

Number of solutions = 4

Answer: (4)

JEE Main 2025 (Online) 29th January Morning Shift

Keep practising — Complex Numbers and Quadratic Equations

2

Let |z1 - 8 - 2i| 1 and |z2 - 2 + 6i| 2, z1, z2 C. Then the minimum value of |z1 - z2| is :

  1. 3
  2. 10
  3. 7
  4. 13
JEE Main 2025 (Online) 29th January Morning Shift
3

The sum, of the squares of all the roots of the equation x2 + |2x - 3| - 4 = 0, is

  1. 6(2 - 2)
  2. 3(3 - 2)
  3. 3(2 - 2)
  4. 6(3 - 2)
JEE Main 2025 (Online) 28th January Morning Shift
4

Let O be the origin, the point A be z1 = 3 + 2 2i, the point B(z2) be such that 3|z2| = |z1| and (z2) = (z1) + 6. Then

  1. area of triangle ABO is 114
  2. area of triangle ABO is 11 3
  3. ABO is a scalene triangle
  4. ABO is an obtuse angled isosceles triangle
JEE Main 2025 (Online) 28th January Morning Shift
5

If + i and + i are the roots of x2 - (3 - 2i)x - (2i - 2) = 0, i = -1, then + is equal to:

  1. 2
  2. -6
  3. 6
  4. -2
JEE Main 2025 (Online) 28th January Evening Shift

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)