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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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
Answer & Explanation 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