1. I. 3x2 – 8x – 28 = 0,
II. 3y2 – 44y + 140 = 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 – 8x – 28 = 0
3x2 – + 6x – 14x – 28 = 0
Gives x = -2, 14/3
3y2 – 44y + 140 = 0
3y2 – 30y -14y + 140 = 0
Gives y = 14/3, 10
2. I. 2x2 – 27x + 81 = 0,
II. 3y2 – 50y + 168 = 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 – 27x + 81 = 0
2x2 – 18x – 9x + 81 = 0
Gives x = 9/2, 9
3y2 – 50y + 168 = 0
3y2 – 36y – 14y + 168 = 0
Gives y = 14/3, 12
3. I. 2x2 – 3x – 54 = 0,
II. 3y2 – 32y + 80 = 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 – 54 = 0
2x2 – 12x + 9x – 54 = 0
Gives x = -9/2, 6
3y2 – 32y + 80 = 0
3y2 – 12y – 20y + 80 = 0
Gives y = 4, 20/3
4. I. 3x2 – 14x – 24 = 0,
II. 3y2 + 32y + 64 = 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 – 14x – 24 = 0
3x2 – 18x + 4x – 24 = 0
Gives x = -4/3, 6
3y2 + 32y + 64 = 0
3y2 + 24y + 8y + 64 = 0
Gives y= -8, -8/3
5. I. 4x2 + x – 18 = 0,
II. 4y2 – 11y – 45 = 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 + x – 18 = 0
4x2 – 8x + 9x – 18 = 0
Gives x = -9/4, 2
4y2 – 11y – 45 = 0
4y2 – 20y + 9y – 45 = 0
Gives y= -9/4, 5
6. I. 3x2 – 26x + 48 = 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 C
Solution:
3x2 – 26x + 48 = 0
3x2 – 18x – 8x + 48 = 0
Gives x = 8/3, 6
3y2 – 25y + 52 = 0
3y2 – 12y – 13y + 52 = 0
Gives y = -4, 8/3
7. I. 4x2 + 39x + 77 = 0,
II. 4y2 – y – 33 = 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:
4x2 + 39x + 77 = 0
4x2 + 28x + 11x + 77 = 0
Gives x = -7, -11/4
4y2 – y – 33 = 0
4y2 – 12y + 11y – 33 = 0
Gives y = -11/4, 3
8. I. 3x2 + 7x – 40 = 0,
II. 3y2 – 38y + 112 = 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 + 7x – 40 = 0
3x2 + 15x – 8x – 40 = 0
Gives x = -5, 8/3
3y2 – 38y + 112 = 0
3y2 – 24y – 14y + 112 = 0
Gives y = 14/3, 8
9. I. x2 = 1849,
II. y = √2116
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:
x2 = 1849
x = -43, 43
y = √2116
y = 46 (root is always positive)
-43……….43………….46
If
a2 = 1849, then a = -43, 43
and if a = √1849, then a = 43
10. I. x2 – 565 = 1284,
II. y = √1521
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 = 1849
x = -43, 43
y = √1521
y = 39
-43……….39………..43