PYQSide ExamsMy practice

Complex Numbers and Quadratic Equations · Question 27

JEE Main 2026 (Online) 23rd January Morning ShiftMCQEasy📈 Topic in 35% papers+4−1
1

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

Answer

(1) 36 days

Solution

Let A alone take t days B alone takes (t + 24) days.

Work per day together: 1t + 1t + 24 = 122.5 = 245

45(2t + 24) = 2t(t + 24)

t2 - 21t - 540 = 0

(t - 36)(t + 15) = 0

t = 36 days (t > 0)

Answer: (1)

JEE Main 2026 (Online) 23rd January Morning Shift

Keep practising — Complex Numbers and Quadratic Equations

2

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

  1. 1
  2. 0
  3. -1
  4. 256
JEE Main 2026 (Online) 23rd January Evening Shift
3

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
JEE Main 2026 (Online) 22nd January Morning Shift
4

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

JEE Main 2026 (Online) 22nd January Morning Shift
5

Let , be the roots of the quadratic equation 12x2 - 20x + 3 = 0, Z. If 12 | - | 32, then the sum of all possible values of is :

  1. 3
  2. 6
  3. 1
  4. 4
JEE Main 2026 (Online) 22nd January Evening Shift
6

Let S = \z C : 4z2 + z = 0\. Then z S |z|2 is equal to:

  1. 564
  2. 116
  3. 764
  4. 316
JEE Main 2026 (Online) 22nd January Evening Shift
7

If x2 + x + 1 = 0, then the value of (x + 1x )4 + (x2 + 1x2 )4 + (x3 + 1x3 )4 + + (x25 + 1x25 )4 is:

  1. 162
  2. 145
  3. 128
  4. 175
JEE Main 2026 (Online) 21st January Morning Shift
8

The sum of all the roots of the equation (x - 1)2 - 5|x - 1| + 6 = 0, is :

  1. 3
  2. 1
  3. 4
  4. 5
JEE Main 2026 (Online) 21st January Morning Shift
9

Let and be the roots of the equation x2 + 2ax + (3a + 10) = 0 such that < 1 < . Then the set of all possible values of a is :

  1. (- , -115 ) (5, )
  2. (- , -115 )
  3. (- , -3)
  4. (- , -2) (5, )
JEE Main 2026 (Online) 21st January Evening Shift
10

Let z be the complex number satisfying |z - 5| 3 and having maximum positive principal argument. Then 34 | 5z - 125iz + 16 |2 is equal to:

  1. 20
  2. 26
  3. 12
  4. 16
JEE Main 2026 (Online) 21st January Evening Shift
11

Let be a solution of x2 + x + 1 = 0, and for some a and b in R, bmatrix 4 & a & b bmatrix bmatrix 1 & 16 & 13 \ -1 & -1 & 2 \ -2 & -14 & -8 bmatrix = bmatrix 0 & 0 & 0 bmatrix. If 4 4 + m a + n b = 3, then m + n is equal to

  1. 11
  2. 3
  3. 8
  4. 7
JEE Main 2025 (Online) 8th April 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)