1. I. 3x2 – 5x – 12 = 0,
II. 3y2 + 22y + 24 = 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 – 5x – 12 = 0
3x2 – 9x + 4x – 12 = 0
Gives x = -4/3, 3
3y2 + 22y + 24 = 0
3y2 + 18y + 4y + 24 = 0
Gives y = -6, -4/3
2. I. 3x2 – 2x – 8 = 0,
II. 3y2 – 8y – 16 = 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 – 8 = 0
3x2 – 6x + 4x – 8 = 0
Gives x = -4/3, 2
3y2 – 8y – 16 = 0
3y2 – 12y + 4y – 16 = 0
Gives y = -4/3, 1
3. I. 3x2 – 7x – 6 = 0,
II. 3y2 + 20y + 25 = 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:
3x2 – 7x – 6 = 0
3x2 – 9x + 2x – 6 = 0
Gives x = -2/3, 3
3y2 + 20y + 25 = 0
3y2 + 15y + 5y + 25 = 0
Gives y = -5, -5/3
4. I. 4x2 + 13x – 12 = 0,
II. 3y2 – 7y – 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 E
Solution:
4x2 + 13x – 12 = 0
4x2 + 16x – 3x – 12 = 0
Gives x = -4, 3/4
3y2 – 7y – 6 = 0
3y2 – 9y + 2y – 6 = 0
Gives y= -2/3, 3
5. I. 3x2 + 20x + 32 = 0,
II. 3y2 + 14y + 16 = 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 + 20x + 32 = 0
3x2 + 12x + 8x + 32 = 0
Gives x = -4, -8/3
3y2 + 14y + 16 = 0
3y2 + 6y + 8y + 16 = 0
Gives y= -8/3, -2
6. I. 2x2 – x – 15 = 0,
II. 3y2 – 25y + 52 = 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:
2x2 – x – 15 = 0
2x2 – 6x + 5x – 15 = 0
Gives x = -5/2, 3
3y2 – 25y + 52 = 0
3y2 – 12y – 13y + 52 = 0
Gives y = 4, 13/3
7. I. 4x2 – 9x – 28 = 0,
II. 4y2 + 19y + 21 = 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 – 28 = 0
4x2 – 16x + 7x – 28 = 0
Gives x = -7/4, 4
4y2 + 19y + 21 = 0
4y2 + 12y +7y + 21 = 0
Gives y = -3, -7/4
8. I. 2x2 + (4 + 2√2)x + 4√2 = 0
II. y2 + (3 + √2)y + 3√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 E
Solution:
2x2 + (4 + 2√2)x + 4√2 = 0
(2x2 + 4x) + (2√2x + 4√2) = 0
2x (x + 2) + 2√2 (x + 2) = 0
So x = -2, -√2 (-1.4)
y2 + (3 + √2)y + 3√2 = 0
(y2 + 3y) + (√2y + 3√2) = 0
y (y + 3) + √2 (y + 3) = 0
So, y = -3 (-0.4), -√2 (-1.4)
9. I. 3x2 – (1 + 6√3)x + 2√3 = 0,
II. 4y2 – (2 + 2√3)y + √3 = 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:
3x2 – (1 + 6√3)x + 2√3 = 0
(3x2 – x) – (6√3x – 2√3) = 0
x (3x- 1) – 2√3 (3x – 1) = 0,
So x = 1/3, 2√3 (3.5)
4y2 – (2 + 2√3)y + √3 = 0
(4y2 – 2y) – (2√3y – √3) = 0
2y (2y – 1) – √3 (2y – 1) = 0
So, y = 1/2, √3/2 (0.86)
10. I. 8x2 + (4 + 2√2)x + √2 = 0
II. y2 – (3 + √3)y + 3√3 = 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:
8x2 + (4 + 2√2)x + √2 = 0
(8x2 + 4x) + (2√2x + √2) = 0
4x (2x + 1) + √2 (2x + 1) = 0
So x = -1/2 (-0.5), -√2/4 (-0.35)
y2 – (3 + √3)y + 3√3 = 0
(y2 – 3y) – (√3y – 3√3) = 0
y (y – 3) – √3 (y – 3) = 0
So y = 3, √3 (1.73)