PYQSidePowered byPrepblink ExamsMy practice

Complex Numbers and Quadratic Equations

JEE Main 2024 (Online) 5th April Morning ShiftMCQMedium📈 Topic in 21% papers+4−1
Ques. 1JEE Main 2024, 5 April (Morning Shift)

Consider the following two statements : Between the above two statements,

  1. both Statement I and Statement II are incorrect.
  2. Statement I is correct but Statement II is incorrect.
  3. Statement I is incorrect but Statement II is correct.
  4. both Statement I and Statement II are correct.

Answer

(2) Statement I is correct but Statement II is incorrect.

Solution

Statement I: z1|z1| and z2|z2| are unit complex numbers

| z1|z1| + z2|z2| | 1 + 1 = 2 (triangle inequality)

∵ |z1| + |z2| > 0, multiplying keeps the sign ⇒ Statement I is correct

Statement II: let each ratio = k ⇒ a2 = k2|y - z|2 = k2(y - z)( y - z)

a2y - z = k2( y - z); similarly for b, c

Sum = k2( y - z + z - x + x - y) = 0 1 ⇒ Statement II is incorrect

Answer: (2)

Keep practising — Complex Numbers and Quadratic Equations

Ques. 2JEE Main 2024, 5 April (Morning Shift)

The number of distinct real roots of the equation |x||x + 2| - 5|x + 1| - 1 = 0 is .

Ques. 3JEE Main 2024, 5 April (Evening Shift)

Let S1 = \z C : |z| 5\, S2 = \z C : Im ( z + 1 - 3 i1 - 3 i ) 0 \ and S3 = \z C : Re(z) 0\. Then the area of the region S1 S2 S3 is :

  1. 125 24
  2. 125 6
  3. 125 12
  4. 125 4
Ques. 4JEE Main 2024, 5 April (Evening Shift)

The number of real solutions of the equation x|x + 5| + 2|x + 7| - 2 = 0 is .

Ques. 5JEE Main 2024, 4 April (Morning Shift)

If 2 and 6 are the roots of the equation ax2+bx+1=0, then the quadratic equation, whose roots are 12a+b and 16a+b, is :

  1. x2+8x+12=0
  2. 2x2+11x+12=0
  3. 4x2+14x+12=0
  4. x2+10x+16=0
Ques. 6JEE Main 2024, 4 April (Morning Shift)

Let and be the sum and the product of all the non-zero solutions of the equation ( z)2+|z|=0, z . Then 4( 2+ 2) is equal to :

  1. 4
  2. 2
  3. 6
  4. 8
Ques. 7JEE Main 2024, 4 April (Evening Shift)

The area (in sq. units) of the region S = \z C : |z - 1| 2; (z + z) + i(z - z) 2, Im(z) 0\ is

  1. 7 4
  2. 3 2
  3. 7 3
  4. 17 8
Ques. 8JEE Main 2024, 4 April (Evening Shift)

Let S = \ 2 2 : ( 4 + 4 )x2 + ( 2 )x + ( 6 + 6 ) = 0 has real roots\. If and be the smallest and largest elements of the set S, respectively, then 3 (( - 2)2 + ( - 1)2 ) equals .

Ques. 9JEE Main 2024, 1 February (Morning Shift)

Let S= \z :|z-1|=1 and ( 2-1)(z+ z)-i(z- z)=2 2 \. Let z1, z2 be such that |z1|= z S|z| and |z2|= z S|z|. Then | 2z1-z2 |2 equals :

  1. 1
  2. 4
  3. 3
  4. 2
Ques. 10JEE Main 2024, 1 February (Morning Shift)

Let S= \x :( 3+ 2)x+( 3- 2)x=10 \. Then the number of elements in S is :

  1. 4
  2. 0
  3. 2
  4. 1
Ques. 11JEE Main 2024, 1 February (Morning Shift)

Let P=\z C: |z+2-3i| 1\ and Q=\z C: z(1+i)+ z(1-i) -8\. Let in P , |z-3+2i| be maximum and minimum at z1 and z2 respectively. If |z1|2+2|z2|2= + 2, where , are integers, then + equals .

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)