Inequalities Test

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Inequalities Test - 2

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Question 1
3 / -1

3x² - 7x + 4 ≤ 0

A
x > 0

B
x < 0

C
All x

D
None of these

Solution

At x = 0, inequality is not satisfied. Thus, option (c) is rejected. Also x = 0 is not a solution of the equation. Since, this is a continuous function, the solution cannot start from 0. Thus options (a) and (b) are not right. Further, we see that the given function is quadratic with real roots. Hence, option (d) is also rejected.
Question 2
3 / -1

3x² - 7x + 6 < 0

A
0.66 <x< 3

B
-0.66 <x< 3

C
-1 < x < 3

D
None of these

Solution

At x = 0, inequality is not satisfied.
Hence, options (b), (c) and (d) are rejected. At x = 2, inequality is not satisfied. Hence, option (a) is rejected.
Thus, option (d) is correct.
Question 3
3 / -1

X² - 14x - 15 > 0

A
x < -1

B
15 < x

C
Both (a) and (b)

D
-1 < x < 15

Solution

At x = 0 inequality is not satisfied. Thus option (d) is rejected. x = -1 and x = 15 are the roots of the quadratic equation. Thus, option (c) is correct.
Question 4
3 / -1

For all integral values of x,
|x - 4| x< 5

A
-1 ≤x≤5

B
1 ≤x≤5

C
-1 ≤ x ≤ 1

D
x<5

Solution

At x = 0 inequality is satisfied, option (b) is rejected.
At x = 2, inequality is satisfied, option (c) is rejected.
At x = 5, LHS = RHS.
Thus, option (d) is correct.
Question 5
3 / -1

|x² - 2x| < x

A
l < x < 3

B
—1 < x < 3

C
0 < x < 4

D
x > 3

Solution

At x = 1 and x = 3 LHS = RHS.
At x = 2 inequality is satisfied.
At x = 0.1 inequality is not satisfied.
At x = 2.9 inequality is satisfied.
At x = 3.1 inequality is not satisfied.
Thus, option (a) is correct.
Question 6
3 / -1

x² - 7x + 12 < | x - 4 |

A
x < 2

B
x > 4

C
2 < x < 4

D
2 ≤ x ≤ 4

Solution

At x = 0, inequality is not satisfied, option (a) is rejected.
At x = 5, inequality is not satisfied, option (b) is rejected.
At x = 2 inequality is not satisfied.
Options (d) are rejected.
Option (c) is correct.
Question 7
3 / -1

|x - 6| > x² - 5x + 9

A
1 ≤ x < 3

B
1 < x < 3

C
2 < x < 5

D
-3 < x < 1

Solution

At x = 2, inequality is satisfied.
At x = 0, inequality is not satisfied.
At x = 1, inequality is not satisfied but LHS = RHS. At x = 3, inequality is not satisfied but LHS = RHS. Thus, option (b) is correct.
Solve other questions of LOD I and LOD II in the same fashion.
Question 8
3 / -1

3x² – 7x – 6 < 0

A
–0.66 < x < 3

B
x < – 0.66 or x > 3

C
3 < x < 7

D
–2 < x < 2

Solution

At x = 0, inequality is satisfied. Hence, options (b) and (c) are rejected. x = 3 gives LHS = RHS.
and x = – 0.66 also does the same. Hence. roots of the equation are 3 and – 0.66.
Thus, option (a) is correct.
Question 9
3 / -1

x² – 14x – 15 > 0

A
x < –1

B
15 < x

C
Both (a) and (b)

D
–1 < x < 15

Solution

At x = 0 inequality is not satisfied. Thus option (d) is rejected.
x = –1 and x = 15 are the roots of the quadratic equation. Thus, option (c) is correct.
Question 10
3 / -1

|x² + x| – 5 < 0

A
x < 0

B
x > 0

C
None of these

D
All values of x
Question 11
3 / -1

|x² – 2x – 3| < 3x – 3

A
2 < x < 5

B
–2 < x < 5

C
x > 5

D
1 < x < 3

Solution

x² - 2x - 3 ≥ 0
(x-3) (x+1) ≥ 0
x belongs to (-∞,-3]∪[3,∞)
Therefore, x belongs to (-1,3)
=> x² - 2x - 3 > 0
x² - 2x - 3< 3x - 3
x² - 5x < 0
x(x-5) < 0
x belongs to (0,5)........(1)
x² - 2x - 3 < 0
x² - 2x - 3 < 3x - 3
x² + x - 6 > 0
(x+3)(x-2) > 0
x belongs to (-∞,-3]∪[2,∞)
x belongs to (2,3)........(2)
Taking intersection of (1) and (2)
we get,
x belongs to (2,5)
Question 12
3 / -1

x² – 7x + 12 < |x – 4|

A
x < 2

B
x > 4

C
2 < x < 4

D
2 £ x £ 4

Solution

At x = 0, inequality is not satisfied, option (a) is rejected.
At x = 5, inequality is not satisfied, option (b) is rejected.
At x = 2 inequality is not satisfied.
Options (d) are rejected.
Option (c) is correct
Question 13
3 / -1

|x – 6| > x² – 5x + 9

A
1 £ x < 3

B
1 < x < 3

C
2 < x < 5

D
–3 < x < 1

Solution

At x = 2, inequality is satisfied.
At x = 0, inequality is not satisfied.
At x = 1, inequality is not satisfied but LHS = RHS.
At x = 3, inequality is not satisfied but LHS = RHS.
Thus, option (b) is correct.
Solve other questions of LOD I and LOD II in the same fashion.

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Inequalities Test - 2

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Inequalities Test - 2

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Question 1

x > 0

x < 0

All x

None of these

Solution

Question 2

0.66 <x< 3

-0.66 <x< 3

-1 < x < 3

None of these

Solution

Question 3

x < -1

15 < x

Both (a) and (b)

-1 < x < 15

Solution

Question 4

-1 ≤x≤5

1 ≤x≤5

-1 ≤ x ≤ 1

x<5

Solution

Question 5

l < x < 3

—1 < x < 3

0 < x < 4

x > 3

Solution

Question 6

x < 2

x > 4

2 < x < 4

2 ≤ x ≤ 4

Solution

Question 7

1 ≤ x < 3

1 < x < 3

2 < x < 5

-3 < x < 1

Solution

Question 8

–0.66 < x < 3

x < – 0.66 or x > 3

3 < x < 7

–2 < x < 2

Solution

Question 9

x < –1

15 < x

Both (a) and (b)

–1 < x < 15

Solution

Question 10

x < 0

x > 0

None of these

All values of x

Question 11

2 < x < 5

–2 < x < 5

x > 5

1 < x < 3

Solution

Question 12

x < 2

x > 4

2 < x < 4

2 £ x £ 4

Solution

Question 13