# Aptitude Questions (Inequality) for AAO and Upcoming Exams

Aptitude Questions (Inequality) for AAO and Upcoming Exams 2016 Set-69:
Dear Readers, Important Practice Aptitude Questions for Upcoming AAO Exams was given here with Solutions. Aspirants those who are preparing for the examination can use this.

Directions (1-5):  In each question two equations numbered I and II are given. You have  to solve both the equations and mark answer
a)   If x< y
b)   If x> y
c)   If x โฅ y
d)   if x โค y
e)   if x = y or relation between x and y cannot be established.
1). I. 6x2 + 5x + 1 = 0
II. 15y2 + 8y + 1 =0

2). I. x2 + 5x + 6 = 0
II. 4y2 + 24 y +35 = 0

3). I . 2x2 + 5x + 3 = 0
II. y2 + 9y + 14 =0

4). I. 88x2 โ 19x +1 = 0
II. 132y2 โ 23y +1 = 0

5)I. 6x2 โ 7x + 2 = 0
II. 20yโ 31y +12 = 0

Directions (6 -10):  In the following questions, two equations I and II have been given. You have to solve both equations and
a)    x> y
b)    x โฅ y
c)    x< y
d)     x โค y
e)    X = y or the relation cannot be established.
6). I. 6x2 + 23x + 20 = 0
II. 6y2 + 31y +35 = 0

7). I. x2 =81
II. y2 โ 18y + 81 = 0

8). I. 4x2 + 20x + 21 =0
II. 2y+17y + 35 =0

9). I. x2 -14x + 48 = 0
II. y2 + 6 = 5y

10). I. 38x2 โ 3x โ 11 =0
II. 28y2 + 32y+9 =0
1). a)  2). e)  3). b)  4). c)  5). a)  6). c)  7). d)  8). b)  9). a)  10). b)

Solutions:
1). I.  6x2 + 5x + 1 = 0
ร 6x2 + 3x + 2x + 1 = 0
ร 3x (2x + 1) + 1 (2x + 1) = 0
ร (3x + 1)(2x + 1) =0
ร  x = -1/3  or โ 1 /2
II. 15y2 + 8y + 1 =0
ร 15y2 + 5y +3y +1 =0
ร  5y(3y + 1) + 1(3y +1) =0
ร (5y +1)(3y + 1) =0
ร y= -1/5  or -1/3

2). I. x2 + 5x + 6 = 0
ร  x+3x + 2x +6 =0
ร x(x+3) + 2(x+3) = 0
ร (x+2)(x+3)=0
ร x= -2 or -3
II.  4y2 + 24 y +35 = 0
ร 4y2 + 14y + 10y + 35 = 0
ร 2y(2y + 7) + 5(2y + 7) =0
ร (2y + 7)(2y +5) =0
ร y = -7/2  or  -5/2 = – 3.5 or โ 2.5

3). I. 2x2 + 5x + 3 = 0
ร 2x2 + 2x + 3x +3 = 0
ร 2x(x+1) + 3(x+ 1) = 0
ร (x +1) (2x+3)=0
ร x = -1 or โ 3/2
II. y2 + 9y + 14 =0
ร  y2 + 2y + 7y +14 = 0
ร y (y+2) + 7(y +2) =0
ร (y +7)(y+2) =0
ร y = -2 or โ 7

4). I. 88x2 โ 19x +1 = 0
ร  88x2 โ11x โ 8x + 1=0
ร 11x(8x – 1) -1(8x -1) =0
ร (11x – 1)(8x -1) =0
ร  x=1/11 or 1 /8
II. 132y2 โ 23y +1 = 0
ร  132y2 โ12y โ 11y + 1=0
ร 12y (11y – 1) โ 1 (11y – 1) =0
ร (12y – 1)(11y – 1) =0
ร y = 1/12 or 1 /11

5). I. 6x2 โ 7x + 2 = 0
ร  6x2 โ 4x-3x +2 =0
ร 2x (3x -2) -1 (3x – 2) =0
ร  (2x – 1)(3x -2)=0
ร x = 1/2    or    2/3
II. 20yโ 31y +12 = 0
ร 20y2  – 15y โ 16y + 12 = 0
ร 5y (4y – 3) -4 (4y – 3) =0
ร  (4y -3)(5y -4)=0
ร y =3/4 or 4/5

6). I. 6x2 + 23x + 20 = 0
ร  6x2 + 15x+ 8x+ 20 = 0
ร 3x (2x + 5) + 4(2x +5) =0
ร (2x +5)(3x+4)=0
ร x= -5/2  or   -4/3
II. 6y2 + 31y +35 = 0
ร  6y2 + 10y+ 21y +35 = 0
ร 2y (3y +5) + 7(3y +5)=0
ร (2y+7)(3y+5)=0
ร y = -7/2 or -5/3

7). I. x2 =81
ร x =โ81 = ยฑ9
II. y2 โ 18y + 81 = 0
ร (y – 9) = 0 ร (y – 9) = 0
ร y=9

8). I. 4x2 + 20x + 21 =0
ร 4x2   +14x + 6x +21 =0
ร 2x(2x +7) + 3(2x +7) =0
ร (2x+7)(2x+3)=0
ร x=-7/2  or  -3/2
II. 2y+17y + 35 =0
ร 2y+10y+7y+35 =0
ร 2y(y+5) + 7(y +5)=0
ร (2y+7) (y+5)=0
ร y= -5 or -7/2

9). I. x2 -14x + 48 = 0
ร  x2 -8x โ 6x+ 48 = 0
ร x(x-8) โ 6(x-8) =0
ร (x-6)(x-8)=0
ร x=6  or 8
II. y2 + 6 = 5y
ร  y2  – 5y + 6 =0
ร y2 -3y โ 2y+ 6 =0
ร y(y -3)-2(y-3)=0
ร (y-3)(y-2)=0
ร y= 3  or 2

10). I. 38x2 โ 3x โ 11 =0
ร 38x2 โ 22x + 19x โ 11 =0
ร 2x(19x -11) +1(19x -11)=0
ร (2x+1)(19x-11)=0
ร x = -1/2 or 11/9
II. 28y2 + 32y+9 =0
ร 28y2 + 14y+ 18y+9 =0
ร 14y(2y +1)+9(2y+1) =0
ร (14y+9)(2y+1)=0
ร y =- 9/14  or -1/2