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Directions (01-10): In each question, two equations numbered I and II are given. You have to solve both the equations and mark an appropriate answer.
1) I) 5x – 4y = 83
II) 6x + 3y = 45
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
2) I) x2Â + 26x + 153=0
II) y2+ 117=406
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
3) I) 2x2 – 28x + 96=0
II)y2– 22y + 96=0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
4) I) 2x2 – 30x + 88=0
II)3y2– 30y + 48=0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
5) I) 5x – 6y = -3
II) 3x + 4y = -17
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
6) I)Â x2 + 21x + 54 = 0
II)2y2 + 25y + 23 = 0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
7) I) 6x² + 7x + 2 = 0
II) 2y² – 3y – 2 = 0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
8) I) 3x2 – 24x + 48=0
II)y2– 14y + 45=0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
9) I)Â x2Â + 36x + 323=0
II)y2+ 43y + 462=0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
10) I) x2 + 6x – 27=0
II)3y2-18y + 27=0
a)Â Â x < y
b)  x ≥ y
c)Â Â x > y
d)  x ≤ y
e)  Relation between x and y can’t be established
Answers :
1) Answer: C
I) 5x – 4y = 83    ..(i)
II) 6x + 3y = 45     …(ii)
Solving equation (i)×3 + (ii)×4, we get
(15x – 12y = 249) + (24x + 12y = 180)
x = (429/39) = 11
Putting the value of x in equation (i), we get
55 – 4y = 83
-4y = 83-55
y = -28/4 = -7
Hence x> y
2) Answer: E
x2Â + 26x + 153 = 0
x2Â + 17x + 9x + 153 = 0
x(x + 17) + 9(x + 17) = 0
(x + 9)(x + 17) = 0
x = -17, -9
y2Â + 117 = 406
y2Â = 289
y = -17, 17
Relationship cannot be established between x and y.
3) Answer: E
2x2 – 28x + 96=0
2x2 – 16x – 12x + 96=0
2x(x – 8) – 12(x – 8)=0
(2x – 12)(x – 8)=0
X=6, 8
y2 – 22y + 96=0
y2 – 16y – 6y + 96=0
y(y – 16) – 6(y – 16)=0
(y – 6)(y – 16)=0
Y = 6, 16
Relationship between x and y cannot established.
4) Answer: E
2x2 – 30x + 88=0
2x2 – 22x – 8x + 88=0
2x(x – 11) – 8(x – 11)=0
(2x – 8) (x – 11)=0
x=4, 11
3y2 – 30y + 48=0
3y2 – 24y – 6y + 48=0
3y(y – 8) – 6(y – 8)=0
(3y – 6) (y – 8)=0
y=2, 8
Hence Relationship between x and y cannot be established.
5) Answer: A
5x – 6y = -3 —-> (1)
3x + 4y = -17 —> (2)
By solving the equation (1) and (2), we get,
x = -3, y = -2
x < y
6) Answer: E
x2+21x+54=0
x2+18x+3x+54=0
x(x+18)+3(x+18)=0
(x+3)(x+18)=0
x=-3, -18
2y2+25y+23=0
2y2+23y+2y+23=0
y(2y+23)+1(2y+23)=0
(y+1)(2y+23)=0
y=-1, -11.5
Relation between x and y can’t be established
7) Answer: D
I) 6x² + 7x + 2 = 0
6x² + 4x + 3x + 2 = 0
2x(3x + 2) + 1(3x + 2) = 0
(3x + 2) (2x + 1) = 0
x = -2/3, 1/2 = -0.66, -0.5
II) 2y² – 3y – 2 = 0
2y² – 4y + y + 2 = 0
2y(y – 2) + 1(y – 2) = 0
(2y+1) (y-2) = 0
y=-1/2, 2 = 2, -0.5
Hence, x ≤y
8) Answer: A
3x2 – 24x + 48=0
3x2 –12x – 12x + 48=0
3x(x – 4) – 12(x – 4)=0
(3x – 12)(x – 4)=0
x=4, 4
y2 – 14y + 45=0
y2 – 9y – 5y + 45=0
y(y – 9) – 5(y – 9)=0
(y – 5)(y – 9)=0
y=5, 9
x < y
9) Answer: C
x2Â + 36x + 323=0
x2Â + 17x + 19x + 323=0
x(x + 17) + 19(x + 17)=0
(x + 19) (x + 17)=0
x=-19, -17
y2Â + 43y + 462=0
y2Â + 21y + 22y + 462=0
y(y + 21) + 22(y + 21)=0
(y + 22)(y + 21)=0
y=-22, -21
x > y
10) Answer: D
x2 + 6x – 27=0
x2 + 9x – 3x – 27=0
x(x + 9) – 3(x + 9)=0
(x – 3)(x + 9)=0
x=3, -9
3y2Â -18y + 27=0
3y2 – 9y – 9y + 27=0
3y(y – 3) – 9(y – 3)=0
(3y – 9)(y – 3)=0
y=3, 3
x ≤ y
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