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Mathematics - Complex Number

Practise 12 KVPY previous year questions on Complex Number, compiled from papers spanning 2010 to 2020. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KVPY tests.

  1. 1Consider a regular 10 - gon with its vertices on the unit circle. With one vertex fixed, draw straight lines to the other 9 vertices. Call t2020 (SB/SX)
  2. 2The figure in the complex plane given by 10 z z - 3 z 2 + z 2 + 4 i z 2 - z 2 = 02020 (SB/SX)
  3. 3Let z = x + i y and w = u + i v be complex numbers on the unit circle such that z 2 + w 2 = 1 . Then the number of ordered pairs z , w is2019 (SB/SX)
  4. 4On any given arc of positive length on the unit circle | z | = 1 in the complex plane.2018 (SB/SX)
  5. 5Let a = cos 1 and b = sin 1 . We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,2018 (SB/SX)
  6. 6Suppose z is any root of 11 z 8 + 21 i z 7 + 10 i z - 22 = 0 where i = - 1 . Then, S = | z | 2 + | z | + 1 satisfies2018 (SB/SX)
  7. 7Let be the vertices of a regular heptagon that is inscribed in the unit circle with centre at the origin in the complex plane. Let , then is19 Nov, 2017 (SB/SX)
  8. 8In the complex plane, let and be two adjacent vertices of an n-sided regular polygon centered at origin. Then equals19 Nov, 2017 (SB/SX)
  9. 9Let a be a fixed non-zero complex number with and . Where is a complex number. Then2016 (SB/SX)
  10. 10If is a complex number satisfying , then the maximum possible value of is2015 (SB/SX)
  11. 11Let be a cube root of unity not equal to 1 . Then the maximum possible value of where , b, is2013 (SB/SX)
  12. 12Let and be the cube roots of unity. The least possible degree of a polynomial, with real coefficients, having and as roots is-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 12 questions compiled from KVPY papers spanning 2010 to 2020.

2.Are these questions only from KVPY, or from other exams too?

These are KVPY questions specifically for the Complex Number chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Complex Number an important chapter for KVPY Mathematics?

Complex Number has appeared in 8 of the 11 years of KVPY papers covered here, with 12 questions across 8 papers - about 2 per paper it appears in.