PYQSidePowered byPrepblink ExamsMy practice

Complex Numbers and Quadratic Equations

JEE Main 2024 (Online) 29th January Evening ShiftMCQMedium📈 Topic in 7% papers+4−1
Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let r and respectively be the modulus and amplitude of the complex number z=2-i (2 5 8 ), then (r, ) is equal to

  1. (2 11 8, 11 8 )
  2. (2 3 8, 3 8 )
  3. (2 5 8, 3 8 )
  4. (2 3 8, 5 8 )

Answer

(2) (2 3 8, 3 8 )

Solution

5 8=- 3 8 z=2+i (2 3 8 )

=2 3 8 ( 3 8+i 3 8 )

3 8>0 and 3 8 (- , ]

r=2 3 8, = 3 8

Answer: (2)

Keep practising — Complex Numbers and Quadratic Equations

Ques. 2JEE Main 2024, 29 January (Evening Shift)

Let , be the roots of the equation x2- 6x+3=0 such that Im( )>Im( ). Let a, b be integers not divisible by 3 and n be a natural number such that 99 + 98=3n(a+ib), i= -1. Then n+a+b is equal to .

Ques. 3JEE Main 2024, 27 January (Morning Shift)

If S=\z :|z-i|=|z+i|=|z-1|\, then, n(S) is :

  1. 1
  2. 2
  3. 3
  4. 0
Ques. 4JEE Main 2024, 27 January (Morning Shift)

If satisfies the equation x2+x+1=0 and (1+ )7=A+B +C 2, A, B, C 0, then 5(3A-2B-C) is equal to .

Ques. 5JEE Main 2024, 27 January (Evening Shift)

If , are the roots of the equation, x2-x-1=0 and Sn=2023 n+2024 n, then :

  1. 2S12=S11+S10
  2. S12=S11+S10
  3. S11=S10+S12
  4. 2S11=S12+S10
Ques. 6JEE Main 2024, 27 January (Evening Shift)

Let the complex numbers and 1 lie on the circles |z-z0 |2=4 and |z-z0 |2=16 respectively, where z0=1+i. Then, the value of 100| |2 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)