1. I. 5x2 – 18x + 9 =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 A
Solution:
5x2 – 18x + 9 = 0
=> 5x2 – 15x – 3x + 9 =0
=> (5x – 3 )(x-3 )= 0
=> x= 3/ 5 or x= 3
3y2 + 5y – 2 = 0
=> 3y2 + 6y – y -2 = 0
=> (3y-1)(y + 2) = 0
=> y = 1/3 or -2
2. I. √x – √6 / √x = 0
II. y3 – 63/2 = 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:
√x – √6 / √x = 0
x – √6 = 0
x = √6
y3 – 6 (3/2 ) = 0
=>y3 = (√6)3
=> y = √6
3. I. (625)1/4x + √1225 = 155
II. √196y + 13 = 279
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:
5x + 35 = 155
=> 5x = 155 – 35
=> x = 120/ 5 = 24√196 y + 13 = 279
=> 14y = 279 -13
=> y = 266/14 =19
4. I. 3x2 – 17x + 24 =0
II. 4y2 – 15y + 14 = 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 -17x + 24 =0
=> 3x2 – 9x – 8x +24 = 0
=> (3x- 8)(x-3) = 0
=> x= 8/3 or 3
4y2 – 15y + 14 = 0
=> 4y2 – 8y -7y +14 = 0
=> (4y -7 )(y-2)=0
=> y = 7 /4 or 2
5. I. x2 – 2x – √5 x + 2√5 = 0
II. y2 – √3 y – √2 y + √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 A
Solution:
x2 – 2x- √5 x + 2√5 = 0
=> x(x-2 ) – √5 (x-2 )= 0
=> (x-2)(x-√5)=0
=> x= 2 0r √5
y2 – √3 y – √2 y + √6 =0
=> y(y-√3) – √2(y – √3) = 0
=> (y – √2)(y- √3) =0
=> y = √2 or √3
6. I. 5x2 – 23x + 12 = 0,
II. 5y2 – 28y + 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:
x = 3/5, 4
y = 3/5, 5
7. I. 6x2 + 5x – 6 = 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 D
Solution:
x = 2/3, 3
y = -3/2, 2/3
8. I. 3x2 – 5x – 12 = 0,
II. 2y2 – 17y + 36 = 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:
x = -4/3, 3
y = 4, 9/2
9. I. 8x2 – (4 + 4√3)x + 2√3 = 0,
II. 3y2 – (4 + 3√3)y + 4√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 B
Solution:
8x2 – (4 + 4√3)x + 2√3 = 0
(8x2 – 4x) – (4√3x – 2√3) = 0
4x (2x- 1) – 2√3 (2x – 1) = 0,
So x = 1/2 (0.5), 2√3/4 (0.87)
3y2 – (4 + 3√3)y + 4√3 = 0
(3y2 – 4y) – (3√3y – 4√3) = 0
y (3y – 4) – √3 (3y – 4) = 0
So, y = √3 (1.732), 4/3
put on number line
0.5………..0.87……..4/3………1.732
10. I. x2 + (4 + 2√2)x + 8√2 = 0
II. 3y2 – (3 + √3)y + √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:
x2 + (4 + 2√2)x + 8√2 = 0
(x2 + 4x) + (2√2x + 8√2) = 0
x (x + 4) + 2√2 (x + 4) = 0
So x = -4, -2√2 (-2.8)
3y2 – (3 + √3)y + √3 = 0
(3y2 – 3y) – (√3y – √3) = 0
3y (y – 1) – √3 (y – 1) = 0
So y = 1, √3/3 (0.57)