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LIC AAO Quadratic Equations Questions with Answers & Explanations

20 Quadratic Equations questions from the Quantitative Aptitude section of LIC AAO, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 11x + 28 = 0 II. y² − 2y − 8 = 0

  1. Ax = y or relationship cannot be established
  2. Bx > y
  3. Cx < y
  4. Dx ≤ y
  5. Ex ≥ y
Show answer
Answer: (C) x < y Roots of I: -4, -7. Roots of II: 4, -2. Comparing every pair gives: x < y.
Question 2

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 8x + 15 = 0 II. y² + 13y + 42 = 0

  1. Ax ≥ y
  2. Bx ≤ y
  3. Cx > y
  4. Dx < y
  5. Ex = y or relationship cannot be established
Show answer
Answer: (C) x > y Roots of I: 5, 3. Roots of II: -7, -6. Comparing every pair gives: x > y.
Question 3

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 2x − 24 = 0 II. y² + 12y + 36 = 0

  1. Ax < y
  2. Bx = y or relationship cannot be established
  3. Cx > y
  4. Dx ≥ y
  5. Ex ≤ y
Show answer
Answer: (D) x ≥ y Roots of I: -6, 4. Roots of II: -6, -6. Comparing every pair gives: x ≥ y.
Question 4

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 11x + 28 = 0 II. y² − 4y − 21 = 0

  1. Ax < y
  2. Bx > y
  3. Cx = y or relationship cannot be established
  4. Dx ≥ y
  5. Ex ≤ y
Show answer
Answer: (A) x < y Roots of I: -7, -4. Roots of II: -3, 7. Comparing every pair gives: x < y.
Question 5

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 13x + 36 = 0 II. y² − 4 = 0

  1. Ax = y or relationship cannot be established
  2. Bx ≥ y
  3. Cx < y
  4. Dx > y
  5. Ex ≤ y
Show answer
Answer: (C) x < y Roots of I: -4, -9. Roots of II: 2, -2. Comparing every pair gives: x < y.
Question 6

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 7x + 12 = 0 II. y² − 9 = 0

  1. Ax ≤ y
  2. Bx = y or relationship cannot be established
  3. Cx < y
  4. Dx > y
  5. Ex ≥ y
Show answer
Answer: (E) x ≥ y Roots of I: 4, 3. Roots of II: 3, -3. Comparing every pair gives: x ≥ y.
Question 7

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 1x − 6 = 0 II. y² − 7y − 8 = 0

  1. Ax = y or relationship cannot be established
  2. Bx > y
  3. Cx < y
  4. Dx ≥ y
  5. Ex ≤ y
Show answer
Answer: (A) x = y or relationship cannot be established Roots of I: -2, 3. Roots of II: -1, 8. Comparing every pair gives: x = y or relationship cannot be established.
Question 8

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 3x + 2 = 0 II. y² + 1y − 2 = 0

  1. Ax < y
  2. Bx ≥ y
  3. Cx > y
  4. Dx ≤ y
  5. Ex = y or relationship cannot be established
Show answer
Answer: (B) x ≥ y Roots of I: 1, 2. Roots of II: -2, 1. Comparing every pair gives: x ≥ y.
Question 9

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 9x + 8 = 0 II. y² + 3y − 18 = 0

  1. Ax < y
  2. Bx > y
  3. Cx = y or relationship cannot be established
  4. Dx ≤ y
  5. Ex ≥ y
Show answer
Answer: (C) x = y or relationship cannot be established Roots of I: 1, 8. Roots of II: 3, -6. Comparing every pair gives: x = y or relationship cannot be established.
Question 10

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 15x + 54 = 0 II. y² + 13y + 40 = 0

  1. Ax ≥ y
  2. Bx > y
  3. Cx < y
  4. Dx ≤ y
  5. Ex = y or relationship cannot be established
Show answer
Answer: (B) x > y Roots of I: 9, 6. Roots of II: -8, -5. Comparing every pair gives: x > y.

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Question 11

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 11x + 24 = 0 II. y² + 2y − 3 = 0

  1. Ax > y
  2. Bx = y or relationship cannot be established
  3. Cx ≤ y
  4. Dx ≥ y
  5. Ex < y
Show answer
Answer: (A) x > y Roots of I: 3, 8. Roots of II: 1, -3. Comparing every pair gives: x > y.
Question 12

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 9x + 14 = 0 II. y² + 13y + 40 = 0

  1. Ax > y
  2. Bx ≥ y
  3. Cx < y
  4. Dx = y or relationship cannot be established
  5. Ex ≤ y
Show answer
Answer: (A) x > y Roots of I: 7, 2. Roots of II: -8, -5. Comparing every pair gives: x > y.
Question 13

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 15x + 56 = 0 II. y² + 3y − 54 = 0

  1. Ax < y
  2. Bx = y or relationship cannot be established
  3. Cx ≥ y
  4. Dx ≤ y
  5. Ex > y
Show answer
Answer: (B) x = y or relationship cannot be established Roots of I: -8, -7. Roots of II: 6, -9. Comparing every pair gives: x = y or relationship cannot be established.
Question 14

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 9x + 18 = 0 II. y² − 1y − 56 = 0

  1. Ax < y
  2. Bx ≤ y
  3. Cx ≥ y
  4. Dx = y or relationship cannot be established
  5. Ex > y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: 6, 3. Roots of II: 8, -7. Comparing every pair gives: x = y or relationship cannot be established.
Question 15

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 8x + 15 = 0 II. y² + 4y + 4 = 0

  1. Ax ≤ y
  2. Bx > y
  3. Cx < y
  4. Dx = y or relationship cannot be established
  5. Ex ≥ y
Show answer
Answer: (C) x < y Roots of I: -5, -3. Roots of II: -2, -2. Comparing every pair gives: x < y.
Question 16

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 3x − 28 = 0 II. y² − 17y + 72 = 0

  1. Ax ≤ y
  2. Bx ≥ y
  3. Cx < y
  4. Dx = y or relationship cannot be established
  5. Ex > y
Show answer
Answer: (C) x < y Roots of I: 4, -7. Roots of II: 8, 9. Comparing every pair gives: x < y.
Question 17

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² − 9x + 20 = 0 II. y² − 9y + 8 = 0

  1. Ax < y
  2. Bx ≥ y
  3. Cx > y
  4. Dx ≤ y
  5. Ex = y or relationship cannot be established
Show answer
Answer: (E) x = y or relationship cannot be established Roots of I: 4, 5. Roots of II: 1, 8. Comparing every pair gives: x = y or relationship cannot be established.
Question 18

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 7x + 10 = 0 II. y² − 14y + 49 = 0

  1. Ax = y or relationship cannot be established
  2. Bx ≥ y
  3. Cx > y
  4. Dx < y
  5. Ex ≤ y
Show answer
Answer: (D) x < y Roots of I: -5, -2. Roots of II: 7, 7. Comparing every pair gives: x < y.
Question 19

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 1x − 56 = 0 II. y² + 8y + 16 = 0

  1. Ax > y
  2. Bx ≤ y
  3. Cx < y
  4. Dx = y or relationship cannot be established
  5. Ex ≥ y
Show answer
Answer: (D) x = y or relationship cannot be established Roots of I: 7, -8. Roots of II: -4, -4. Comparing every pair gives: x = y or relationship cannot be established.
Question 20

In the following question, two equations I and II are given. Solve both and choose the correct relation. I. x² + 7x + 12 = 0 II. y² + 11y + 24 = 0

  1. Ax ≥ y
  2. Bx = y or relationship cannot be established
  3. Cx > y
  4. Dx < y
  5. Ex ≤ y
Show answer
Answer: (B) x = y or relationship cannot be established Roots of I: -3, -4. Roots of II: -3, -8. Comparing every pair gives: x = y or relationship cannot be established.

These are RankerClub practice questions written in the LIC AAO pattern. They are not official SSC/IBPS/RRB papers.

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