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

Complex Numbers and Quadratic Equations

JEE Main 2025 (Online) 2nd April Morning ShiftMCQEasy📈 Topic in 21% papers+4−1
Ques. 1JEE Main 2025, 2 April (Morning Shift)

Let z be a complex number such that |z| = 1. If 2 + k2 zk + z = kz, k R, then the maximum distance of k + ik2 from the circle |z - (1 + 2i)| = 1 is :

  1. 5 + 1
  2. 3
  3. 3 + 1
  4. 2

Answer

(1) 5 + 1

Solution

|z| = 1, we have z = 1z, so the given relation becomes

2 + k2zk + 1z = kz z(2 + k2z)kz + 1 = kz

2z + k2z2 = k2z2 + kz

2z = kz, and since z 0, k = 2.

Hence k + ik2 = 2 + 4i, i.e. the point (2, 4).

The circle has centre (1, 2) and radius 1, and the distance of (2, 4) from the centre is 12 + 22 = 5 > 1, so the point lies outside the circle.

Maximum distance from the circle = 5 + 1

Answer: (1)

Keep practising — Complex Numbers and Quadratic Equations

Ques. 2JEE Main 2025, 2 April (Morning Shift)

Let Pn = n + n, n N. If P10 = 123, P9 = 76, P8 = 47 and P1 = 1, then the quadratic equation having roots 1 and 1 is :

  1. x2 + x - 1 = 0
  2. x2 - x + 1 = 0
  3. x2 + x + 1 = 0
  4. x2 - x - 1 = 0
Ques. 3JEE Main 2025, 2 April (Evening Shift)

If the set of all a R - \1\, for which the roots of the equation (1 - a)x2 + 2(a - 3)x + 9 = 0 are positive is (- , - ] [ , ), then 2 + + is equal to .

Ques. 4JEE Main 2025, 29 January (Morning Shift)

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
Ques. 5JEE Main 2025, 29 January (Morning Shift)

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
Ques. 6JEE Main 2025, 29 January (Evening Shift)

If the set of all a R, for which the equation 2x2 + (a - 5)x + 15 = 3a has no real root, is the interval ( , ), and X = \x Z; < x < \, then x X x2 is equal to:

  1. 2139
  2. 2119
  3. 2109
  4. 2129
Ques. 7JEE Main 2025, 29 January (Evening Shift)

Let integers a, b [-3,3] be such that a+b 0. Then the number of all possible ordered pairs (a, b), for which | z-az+b |=1 and vmatrixz+1& & 2\ &z+ 2&1\ 2&1&z+ vmatrix=1, z C, where and 2 are the roots of x2+x+1=0, is equal to .

Ques. 8JEE Main 2025, 28 January (Morning Shift)

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)
Ques. 9JEE Main 2025, 28 January (Morning Shift)

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
Ques. 10JEE Main 2025, 28 January (Evening Shift)

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
Ques. 11JEE Main 2025, 24 January (Morning Shift)

The product of all the rational roots of the equation (x2-9x+11)2-(x-4)(x-5)=3, is equal to

  1. 7
  2. 21
  3. 28
  4. 14

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)