1. I. 4x2 – 29x + 45 = 0,
II. 4y2 – 17y + 18 = 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 – 29x + 45 = 0
4x2 – 20x – 9x + 45 = 0
Gives x = 9/4, 5
4y2 – 17y + 18 = 0
4y2 – 8y – 9y + 18 = 0
Gives y = 2, 9/4
2. I. 3x2 – 13x – 30 = 0,
II. 2y2 – 25y + 78 = 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 – 13x – 30 = 0
3x2 – 18x + 5x – 30 = 0
Gives x = -5/3, 6
2y2 – 25y + 78 = 0
2y2 – 12y – 13y + 78 = 0
Gives y = 6, 13/2
3. I. 3x2 – 20x + 32 = 0,
II. 3y2 – 29y + 56 = 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 – 20x + 32 = 0
3x2 – 12x – 8x + 32 = 0
Gives x = 8/3, 4
3y2 – 29y + 56 = 0
3y2 – 21y – 8y + 56 = 0
Gives y = 8/3, 7
4. I. 3x2 – 16x – 35 = 0,
II. 3y2 – 23y + 40 = 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 – 16x – 35 = 0
3x2 – 21x + 5x – 35 = 0
Gives x = -5/3, 7
3y2 – 23y + 40 = 0
3y2 – 15y – 8y+ 40 = 0
Gives y= 8/3, 5
5. I. 2x2 – 23x + 65 = 0,
II. 3y2 + 2y – 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 A
Solution:
2x2 – 23x + 65 = 0
2x2 – 10x – 13x + 65 = 0
Gives x = 5, 13/2
3y2 + 2y – 16 = 0
3y2 – 6y + 8y – 16 = 0
Gives y= -8/3, 2
6. I. x2 – 78 = 91,
II. √3 y = √432
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:
x2 – 78 = 91
x2 = 169
Gives x = -13, 13
√3 y = √432
y = √432/√3 = √144
Gives y = 12
Now when x = -13, y > x
and when x = 13, y < x
So relation cannot be established
7. I. 3x2 + 17x + 10 = 0,
II. 3y2 + 14y – 5 = 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 + 17x + 10 = 0
3x2 + 15x + 2x + 10 = 0
Gives x = -5, -2/3
3y2 + 14y – 5 = 0
3y2 + 15y – y – 5 = 0
Gives y = -5, 1/3
8. I. 2x2 – 13x + 15 = 0,
II. 2y2 + 5y – 12 = 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:
2x2 – 13x + 15 = 0
2x2 – 10x – 3x + 15 = 0
Gives x = 3/2, 5
2y2 + 5y – 12 = 0
2y2 + 8y -3y – 12 = 0
Gives y= -4, 3/2
9. I. 2x2 – 3x – 35 = 0,
II. 3y2 + 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 E
Solution:
2x2 – 3x – 35 = 0
2x2 – 10x + 7x – 35 = 0
Gives x = -7/2, 5
3y2 + 11y + 6 = 0
3y2 + 9y +2y + 6 = 0
Gives y= -3, -2/3
10. I. 3x2 + 19x + 20 = 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 B
Solution:
3x2 + 19x + 20 = 0
3x2 + 15x + 4x + 20 = 0
Gives x = -5, -4/3
3y2 – 7y – 6 = 0
3y2 – 9y + 2y – 6 = 0
Gives y= -2/3, 3