Quantitative Aptitude: Quadratic Equations Set 20

Quadratic Equations Practice Sets IBPS PO NICL, NIACL, LIC, Dena Bank PO PGDBF, BOI, Bank of Baroda and other competitive exams

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-

1. I. 4x² – 9x – 9 = 0,
   II. 4y² + 11y + 6 = 0
   A) If x > y
   B) If x < y
   C) If x ≥ y
   D) If x ≤ y
   E) If x = y or relation cannot be established
   
   View Answer

    Option C
   Solution: 
   4x² – 9x – 9 = 0
   4x² – 12x + 3x – 9 = 0
   Gives x = -3/4, 3
   4y² + 11y + 6 = 0
   4y² + 8y + 3y + 6 = 0
   Gives y = -2, -3/4
   Put all values on number line and analyze the relationship
   -2…. -3/4….3
2. I. 3x² – 2x – 21 = 0,
   II. 6y² + 17y + 7 = 0
   A) If x > y
   B) If x < y
   C) If x ≥ y
   D) If x ≤ y
   E) If x = y or relation cannot be established
   
   View Answer

    Option E
   Solution: 
   3x² – 2x – 21 = 0
   3x² – 9x + 7x – 21 = 0
   Gives x = -7/3, 3
   6y² + 17y + 7 = 0
   6y² + 3y + 14y + 7 = 0
   Gives y = -7/3, -1/2
   
3. I. 3x² – 13x + 14 = 0,
   II. 3y² – 20y + 32 = 0
   A) If x > y
   B) If x < y
   C) If x ≥ y
   D) If x ≤ y
   E) If x = y or relation cannot be established
   
   View Answer

    Option B
   Solution: 
   3x² – 13x + 14 = 0
   3x² – 6x – 7x + 14 = 0
   Gives x = 2, 7/3
   3y² – 20y + 32 = 0
   3y² – 12y – 8y + 32 = 0
   Gives y = 8/3, 4
   
4. I. 3x² – 2x – 16 = 0,
   II. 3y² – 20y + 32 = 0
   A) If x > y
   B) If x < y
   C) If x ≥ y
   D) If x ≤ y
   E) If x = y or relation cannot be established
   
   View Answer

    Option D
   Solution: 
   3x² – 2x – 16 = 0
   3x² – + 6x – 8x – 16 = 0
   Gives x = -2, 8/3
   3y² – 20y + 32 = 0
   3y² – 12y – 8y + 32 = 0
   Gives y = 8/3, 4
   
5. I. 5x² – 16x – 16 = 0,
   II. 3y² – 14y + 8 = 0
   A) If x > y
   B) If x < y
   C) If x ≥ y
   D) If x ≤ y
   E) If x = y or relation cannot be established
   
   View Answer

    Option E
   Solution: 
   5x² – 16x – 16 = 0
   5x² – 20x + 4x – 16 = 0
   Gives x = -4/5, 4
   3y² – 14y + 8 = 0
   3y² – 12y – 2y + 8 = 0
   Gives y= 2/3, 4
6. I. 4x² – 17x + 18 = 0,
   II. 3y² – 2y – 8 = 0
   A) If x > y
   B) If x < y
   C) If x ≥ y
   D) If x ≤ y
   E) If x = y or relation cannot be established
   
   View Answer

    Option C
   Solution: 
   4x² – 17x + 18 = 0
   4x² – 8x – 9x + 18 = 0
   Gives x = 2, 9/4
   3y² – 2y – 8 = 0
   3y² – 6y + 4y – 8 = 0
   Gives y = -4/3, 2
   
7. I. 2x² – 5x – 12 = 0,
   II. 3y² – 17y + 10 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relationship cannot be determined
   
   View Answer

    Option E
   Solution: 
   2x² – 5x – 12 = 0
   2x² – 8x + 3x – 12 = 0
   Gives x = -3/2, 4
   3y² – 17y + 10 = 0
   3y² – 15y – 2y + 10 = 0
   So y = 2/3, 5
   
8. I. 3x² + 2x – 16 = 0,
   II. y² + 11y + 24 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relationship cannot be determined
   
   View Answer

    Option A
   Solution: 
   3x² + 2x – 16 = 0
   3x² – 6x + 8x – 16 = 0
   Gives x = -8/3, 2
   y² + 11y + 24 = 0
   y² + 8y + 3y + 24 = 0
   So y = -8, -3
   
9. I. 3x² + 10x + 8 = 0,
   II. 3y² – 11y – 20 = 0
   A) x > y
   B) x < y
   C) x ≥ y
   D) x ≤ y
   E) x = y or relationship cannot be determined
   
   View Answer

    Option D
   Solution: 
   3x² + 10x + 8 = 0
   3x² + 6x + 4x + 8 = 0
   Gives x = -2, -4/3
   3y² – 11y – 20 = 0
   3y² – 15y + 4y – 20 = 0
   So y = -4/3, 5
   
10. I. 4x² + 23x + 15 = 0,
    II. 3y² – 19y – 14 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    
    View Answer

     Option B
    Solution: 
    4x² + 23x + 15 = 0
    4x² + 20x + 3x + 15 = 0
    Gives x = -5, -3/4
    3y² – 19y – 14 = 0
    3y² – 21y + 2y – 14 = 0
    So y = -2/3, 7
    

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