1. I. 3x2 – 4x – 15 = 0,
II. 3y2 + 11y + 10 = 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:
3x2 – 4x – 15 = 0
3x2 – 9x + 5x – 15 = 0
Gives x = -5/3, 3
3y2 + 11y + 10 = 0
3y2 + 6y + 5y + 10 = 0
Gives y = -2. -5/3
2. I. 3x2 + 17x + 24 = 0,
II. 3y2 – 4y – 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 + 17x + 24 = 0
3x2 + 17x + 24 = 0
Gives x = -3, -8/3
3y2 – 4y – 32 = 0
3y2 – 12y + 8y – 32 = 0
Gives y = -8/3, 4
3. 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 – 2x – 16 = 0
Gives x = -2, 8/3
3y2 – 20y + 32 = 0
3y2 – 20y + 32 = 0
Gives y = 8/3, 4
4. I. 2x2 + 5x – 12 = 0,
II. 4y2 – 19y – 30 = 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:
2x2 + 5x – 12 = 0
2x2 + 8x – 3x – 12 = 0
Gives x = -4, 3/2
4y2 – 19y – 30 = 0
4y2 – 24y + 5y – 30 = 0
Gives y= -5/4, 6
5. I. 2x2 – 17x + 36 = 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 A
Solution:
2x2 – 17x + 36 = 0
2x2 – 8x – 9x + 36 = 0
Gives x = 4, 9/2
3y2 – 2y – 8 = 0
3y2 – 6y + 4y – 8 = 0
Gives y= -4/3, 2
6. I. 3x2 + 19x + 30 = 0,
II. 2y2 + 3y – 2 = 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 + 19x + 30 = 0
3x2 + 9x + 10x + 30 = 0
Gives x = -10/3, -3
2y2 + 3y – 2 = 0
2y2 + 4y – y – 2 = 0
Gives y = -2, 1/2
7. I. 5x2 + 11x – 12 = 0,
II. 3y2 + 7y – 6 = 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:
5x2 + 11x – 12 = 0
5x2 + 15x – 4x – 12 = 0
Gives x = -3, 4/5
3y2 + 7y – 6 = 0
3y2 + 9y – 2y – 6 = 0
So y = -3, 2/3
8. I. 3x2 + x – 10 = 0,
II. 2y2 + 11y + 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 C
Solution:
3x2 + x – 10 = 0
3x2 + 6x – 5x – 10 = 0
Gives x = -2, 5/3
2y2 + 11y + 14 = 0
2y2 + 4y + 7y + 14 = 0
So y = -7/2, -2
9. I. 3x2 + 19x + 30 = 0,
II. 2y2 – 3y – 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 B
Solution:
3x2 + 19x + 30 = 0
3x2 + 9x + 10x + 30 = 0
Gives x = -3, -10/3
2y2 – 3y – 20 = 0
2y2 – 8y + 5y – 20 = 0
So y = -5/2, 4
10. I. 2x2 – x – 36 = 0,
II. 2y2 – 21y + 54 = 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:
2x2 – x – 36 = 0
2x2 + 8x – 9x – 36 = 0
Gives x = -4, 9/2
2y2 – 21y + 54 = 0
2y2 – 12y – 9y + 54 = 0
So y = 9/2, 6