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Mathematics - Quadratic Equation

Practise 52 KVPY previous year questions on Quadratic Equation, 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. 1Let p 1 x = x 3 - 2020 x 2 + b 1 x + c 1 and p 2 x = x 3 - 2021 x 2 + b 2 x + c 2 be polynomials having two common roots and . Suppose there2020 (SA)
  2. 2Let a , b , c be non-zero real roots of the equation x 3 + a x 2 + b x + c = 0 . Then2020 (SB/SX)
  3. 3Let b be an non-zero real number. Suppose the quadratic equation 2 x 2 + b x + 1 b = 0 has two distinct real roots. Then2019 (SA)
  4. 4Let p x = x 2 + a x + b have two distinct real roots, where a , b are real number. Define g x = p x 3 for all real number x Then, which of t2019 (SA)
  5. 5The number of cubic polynomials P ( x ) satisfying P ( 1 ) = 2 , P ( 2 ) = 4 , P ( 3 ) = 6 , P ( 4 ) = 8 is2019 (SA)
  6. 6Let S = { 1 , 2 , 3 , , 100 } . Suppose b and c are chosen at random from the set S . The probability that 4 x 2 + b x + c has equal roots i2019 (SA)
  7. 7Let a , b , c , d be distinct real numbers such that a , b are roots of x 2 - 5 c x - 6 d = 0 , and c , d are roots of x 2 - 5 a x - 6 b = 02019 (SA)
  8. 8Let P be a non-zero polynomial such that P 1 + x = P 1 - x for all real x and P 1 = 0 . Let m be the largest integer such that x - 1 m divid2019 (SB/SX)
  9. 9Let f x = x 6 - 2 x 5 + x 3 + x 2 - x - 1 and g x = x 4 - x 3 - x 2 - 1 be two polynomials. Let a , b , c and d be the roots of g x = 0 . Th2019 (SB/SX)
  10. 10The number of real roots of the polynomial equation x 4 - x 2 + 2 x - 1 = 0 is2018 (SA)
  11. 11The number of polynomials p ( x ) with integer coefficients such that curve y = p ( x ) passes through ( 2 , 2 ) and ( 4 , 5 ) is2018 (SA)
  12. 12What is the sum of all natural numbers n such that the product of the digits of n (in base 10 ) is equal to n 2 - 10 n - 36 ?2018 (SA)
  13. 13Let be real numbers between and 5 such that , Then the product abcd is19 Nov, 2017 (SA)
  14. 14If are real numbers such that and , then is equal to19 Nov, 2017 (SA)
  15. 15Let where is the set of real numbers. Then equals [2017]19 Nov, 2017 (SB/SX)
  16. 16The sum of all non-integer roots of the equation is05 Nov, 2017 (SA)
  17. 17Let be the remainder when the polynomial is divided by Then05 Nov, 2017 (SA)
  18. 18The quotient when is divided by is05 Nov, 2017 (SB/SX)
  19. 19Consider the equation , where are real numbers. Then2016 (SA)
  20. 20Consider the quadratic equation , where is a positive integer. Which of the following statements are necessarily correct? I. For any , the r2016 (SA)
  21. 21Suppose the quadratic polynomial has positive coefficients in arithmetic progression in that order. If has integer roots and , then equals2016 (SA)
  22. 22Suppose a is a positive real number such that Then2016 (SA)
  23. 23The polynomial equation has -2016 (SB/SX)
  24. 24Number of integers for which the equation has at least two distinct integer roots is -2016 (SB/SX)
  25. 25The remainder when the polynomial is divided by is -2016 (SB/SX)
  26. 26Two distinct polynomial and are defined as follows: If the equation and have a common root then the sum of the roots of the equation is2015 (SA)
  27. 27Let be a polynomial such that , where is a positive integer. Then equals.2015 (SB/SX)
  28. 28The number of ordered pairs of real numbers that satisfy the simultaneous equations. is2015 (SB/SX)
  29. 29Let2015 (SB/SX)
  30. 30If is a cubic polynomial with and , then is2015 (SB/SX)
  31. 31Let be non-zero real numbers such that ; let and Then2014 (SA)
  32. 32Let be a root of the equation . The value of is equal to .2014 (SA)
  33. 33Let and , where and are positive integers. Suppose and . If the coefficient of the highest degree term of is 1, the sum of the roots of is.2014 (SA)
  34. 34If is a positive integer and is a cube root of unity, the number of possible values of is2014 (SB/SX)
  35. 35The under of integers for which has three real roots is2014 (SB/SX)
  36. 36Let be non-zero real numbers. Which of the following statements about the quadratic equation is neccesarily true? It has at least one negati2013 (SA)
  37. 37In a triangle with , points are on the interior of segments , respectively. Which of the following triangles be similar to ?2013 (SA)
  38. 38The sum of non-real roots of the polynomial equation .2013 (SB/SX)
  39. 39Let be a non-constant polynomial with real coefficients such that and for all real . Which of the following statements is NOT necessarily tr2013 (SB/SX)
  40. 40Two workers A and B are engaged to do a piece of work. Working alone, A takes 8 hours more to complete the work than if both worked together2012 (SA)
  41. 41Let be a quadratic polynomial with and . Then the coefficient of in is-2012 (SA)
  42. 42In the real number system, the equation has2012 (SB/SX)
  43. 43Suppose are real numbers, and each of the equations and has two distinct real roots. Then the equation has-2012 (SB/SX)
  44. 44The maximum value of , as varies over reals, satisfies -2012 (SB/SX)
  45. 45Let be numbers in the set such that the curves and have no point in common. The maximum possible value of is2012 (SB/SX)
  46. 46Let a, b, be real numbers such that and . Then the set of all possible values of ay is -2011 (SA)
  47. 47Let , where are integers. Suppose , and for some integer . Then the value of is2011 (SA)
  48. 48Below are four equations in . Assume that . Which of the following has the largest solution for ?2011 (SA)
  49. 49Consider the cubic equation , where are real numbers. Which of the following statements is correct?2011 (SB/SX)
  50. 50Let . Which of the following is true?2011 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Quadratic Equation?

This chapter includes 52 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 Quadratic Equation chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Quadratic Equation an important chapter for KVPY Mathematics?

Quadratic Equation has appeared in 11 of the 11 years of KVPY papers covered here, with 52 questions across 22 papers - about 2 per paper it appears in.