TM
Rational Inequations
RACE -1
Path to success KOTA (RAJASTHAN )
Solve the following inequalities
Q.1
(x - 1) (3 - x) (x - 2)2 > 0.
Q.2
( x 1)(x 2) 2
1 x
Q.3
x 2 6x 7
x2 1
Q.4
x2 9
3x x 2 24
Q.5
x2 x 6
x 2 6x
Q.6
2x 2
Q.7
14 x 9 x 30
x 1 x 4
Q.8
(2 x 2 ) (x 3)3
( x 1) ( x 2 3x 4)
Q.9
2( x 4)
( x 1) ( x 7)
Q.10
( x 2) ( x 2 2 x 1)
4 3x x 2
1
x
0.
2 .
0.
0.
0.
0.
0.
1
x 2.
0.
JEE (Main + Advanced) 2018
NURTURE COURSE
TM
Path to success KOTA (RAJASTHAN )
Rational Inequations
RACE -2
Solve the following inequalities :
Q.1
4
1 x
+
2
1 x
<1
Q.2
x 4 3x 3 2 x 2
x 2 x 30
Q.3
x 1 x 1
–
<2
x
x 1
Q.4
7
9
+
+1<0
( x 2)(x 3)
x 3
Q.5
20
10
+1>0
+
( x 3)(x 4)
x 4
Q.6
( x 1)(x 2)(x 3)
>1
( x 1)(x 2)(x 3)
Q.7
1+
Q.8
x 1
x 1
Q.9
30x 9
x 2
Q.10
0
12
7
2 <
x
x
1
x 2
x 5
x 1
–
25 (x + 2)
1
x
2
x 2
JEE (Main + Advanced) 2018
NURTURE COURSE
TM
Rational Inequations
RACE -3
Path to success KOTA (RAJASTHAN )
Solve the following inequalities
Q.1
x 1
( x 1) 2
Q.2
1 3x 2
2 x 21x 40
Q.3
1.
0.
2
1
1
x 1
x 2
0
Q.4
20
10
1 0.
(x 3) (x 4) x 4
Q.5
( x 2) ( x 4) ( x 7 )
1.
( x 2) ( x 4) ( x 7 )
Q.6
( x 2 3x 1) ( x 2 3x 3) 5 .
Q.7
( x 2 x 1) ( x 2
Q.8
(x 2
Q.9
( x 2 3x ) ( 2 x 3) 16
Q.10
1
x 7)
2 x ) ( 2 x 2) 9
3x 2 7 x 8
x2 1
2.
5.
2x 2
x 2 2x
0.
2x 3
x 2 3x
0.
JEE (Main + Advanced) 2018
NURTURE COURSE
ANSWER -KEY-1
1. (1, 2) ( 2, 3)
2. (
,
2) ( 2, 1) (1,
4. (
,
5. (
,
6) [ 2, 0) [3, )
6. (
, 1 / 3 2 ) (0, )
7. ( 1, 1) ( 4, 6)
8. [
2 , 1) ( 1,
9. (1, 2) (7, )
10. (
3) (3, )
,
2 ] [3, 4)
3. R
)
2] ( 1, 4)
ANSWER –KEY-2
1.
(– , –1)
(1, )
3.
(– , –1)
(0,
5.
7.
(– , –2)
(3, 4)
9.
(–
1
)
2
(–1, 3)
–1.4]
2.
(–
(1, )
4.
(–5, 1)
(4, )
6.
8.
(– – )
(– , –1)
10.
(–2, (3– 17 )/2]
(2, 2.6]
–5)
(1, 2)
(6, )
(2, 3)
(–2, –1)
(1, 3]
(0, 2)
[(3 + 17 )/2, )
ANSWER -KEY-3
1. (
, 0)
4. (
,
2)
(3,
( 1, 3)
7. ( 2, 1)
( 2, 3)
9. [ 4,
[ 3 / 2, 0)
3)
2.
)
( 4,
[1,
)
)
5
, 8
2
5. (
,
7)
( 4,
2)
8. (
, 1]
(0, 1]
( 2, 3]
10. [1, 6]
3. ( 2,
3 / 2]
6. (
4] [ 2, 1] [1,
,
( 1,
)
)