1. I. 20x2 – 31x + 12 = 0,
II. 3y2 – 5y + 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:
20x2 – 31x + 12 = 0
20x2 – 16x – 15x + 12 = 0
So x = 3/4, 4/5
3y2 – 5y + 2 = 0
3y2 – 3y – 2y + 2 = 0
So y = 1, 2/3
2. I. 3x2 – 19x + 30 = 0,
II. 3y2 – 10y + 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 C
Solution:
3x2 – 19x + 30 = 0
3x2 – 9x – 10x + 30 = 0
So x = 3, 10/3
3y2 – 10y + 3 = 0
3y2 – 9y – y + 3 = 0
So y = 1/3, 3
3. I. 3x2 – 25x + 52 = 0,
II. 5y2 – 18y + 9 = 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 – 25x + 52 = 0
3x2 – 12x – 13x + 52 = 0
So x = 4, 13/3
5y2 – 18y + 9 = 0
5y2 – 15y – 3y + 9 = 0
So y = 3/5, 3
Put on number line
-1/2 …. 3/5 ….2/3 …. 3
4. I. 4x2 – 5x – 6 = 0,
II. 5y2 – 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 – 5x – 6 = 0
4x2 – 8x + 3x – 6 = 0
So x = -3/4, 2
5y2 – 7y – 6 = 0
5y2 – 10y + 3y – 6 = 0
So y = -3/5, 2
5. I. 3x2 – 10x + 8 = 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 – 10x + 8 = 0
3x2 – 6x – 4x + 8 = 0
So x = 2, 4/3
3y2 – 14y + 16 = 0
3y2 – 6y – 8y + 16 = 0
So y = 2, 8/3
6. I. 2x2 + 17x + 30 = 0,
II. 4y2 – 7y – 15 = 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 + 17x + 30 = 0
2x2 + 12x + 5x + 30 = 0
So x = -6, -5/2
4y2 – 7y – 15 = 0
4y2 – 12y + 5y – 15 = 0
So y = -5/4, 3
7. I. 3x2 + 16x + 20 = 0,
II. 5y2 + 8y – 4 = 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 + 16x + 20 = 0
3x2 + 6x + 10x + 20 = 0
So x = -10/3, -2
5y2 + 8y – 4 = 0
5y2 + 10y – 2y – 4 = 0
So y = -2, 2/5
8. I. 2x2 + 17x + 21 = 0,
II. 2y2 + 13y + 15 = 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 + 17x + 21 = 0
2x2 + 14x + 3x + 21 = 0
So x = -7, -3/2
2y2 + 13y + 15 = 0
2y2 + 10y + 3y + 15 = 0
So y = -5, -3/2
9. I. 5x2 – 7x – 6 = 0,
II. 3y2 – 19y + 28 = 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:
5x2 – 7x – 6 = 0
5x2 – 10x + 3x – 6 = 0
So x = -3/5, 2
3y2 – 19y + 28 = 0
3y2 – 12y – 7y + 28 = 0
So y = 7/3, 4
10. I. 8x2 + 6x – 5 = 0,
II. 2y2 + 7y – 4 = 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:
8x2 + 6x – 5 = 0
8x2 – 4x + 10x – 5 = 0
So x = -5/4, 1/2
2y2 + 7y – 4 = 0
2y2 + 8y – y – 4 = 0
So y = -4, 1/2