Important Questions for CBSE Class 11 Maths Chapter 6 - Linear Inequalities
CBSE Class 11 Maths Chapter-6 Important Questions - Free PDF Download
1 Marks Questions
1. Solve 
Ans. 
2. Solve 
when 
is a real no.
Ans.
3. Solve the inequality 
Ans. 
4. If 
then 
Ans. 
5. Solve the inequality 
Ans.
6. Solution set of the in inequations 
and 
is.
Ans. 
7. Solve
. Show the graph of the solution on number line.
Ans.
8. Solve the inequality. 
Ans. 
9. Solve 
when is an integer.
Ans.
10. Solve 
when is a natural no.
Ans.
Solution set of the inequality 
11. Solve the inequality 
Ans. 
12. Solve 
when is an integer.
Ans.
When is an integer the solutions of the given inequality are……-4,-3,-2,-1, 0, 1
4 Marks Questions
1. Solve 
graphically
Ans. 
Put (0,0)in eq. (i)
false.
2. Ravi obtained 70 and 75 mark in first unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks.
Ans. Let Ravi secure 
marks in third test
ATQ 
3. Find all pairs of consecutive odd natural no. both of which are larger than 10 such that their sum is less than 40.
Ans. Let and 
be consecutive odd natural no.
ATQ
From (i) and (ii)
4. A company manufactures cassettes and its cost equation for a week is C=300+1.5and its revenue equation is R=2, where is the no. of cassettes sold in a week. How many cassettes must be sold by the company to get some profit?
Ans. Profit = revenue-cost
5. The longest side of a
is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of theis at least 61 cm find the minimum length of the shortest side.
Ans. Let shortest side be cm then the longest side is 
cm and the third side 
cm.
ATQ 
Length of shortest side is 9 cm.
6. In drilling world’s deepest hole it was found that the temperature T in degree Celsius, km below the surface of earth was given by 
At what depth will the tempt. Be between 
c and 
Ans. Let km is the depth where the tempt lies between 
and 
7. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second.
Ans. Let the shortest length be cm, then second length is (+3) cm and the third length is 2 cm.
ATQ 
Again ATQ
8. The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8 If the first pH reading are 7.48 and7.85, find the range of pH value for the third reading that will result in the acidity level being normal.
Ans. Let third reading be then
9. A plumber can be paid under two schemes as given below.
I: Rs 600 and Rs 50 per hr.
II: Rs 170 per hr.
If the job takes n hr. for what values of n does the scheme I gives the plumber the better wages.
Ans. For better wages earning should be more then
Thus for better wages scheme working hr. should be less than 5 hr.
| 0 | 15 |
| 20 | 0 |
| 0 | 20 |
| 0 | 40 |
10. Solve the inequalities 
graphically
Ans. 
| 0 | 4 |
| 3 | 0 |
Put 
in eq. ………
false
11. Solve graphically 
Ans. 
Put (1,0) in eq. (i)
false
12. Solve 
graphically
Ans. 
| 0 | 2 |
| 3 | 0 |
Put in eq. ……….
which is false
6 Marks Questions
1. IQ of a person is given by the formula 
Where MA is mental age and CA is chronological age. If 80 
IQ140 for a group of 12yr old children, fond the range of their mental age.
Ans. 
IQ
(Given)
MA
MA
2. Solve graphically 
Ans. 
| 0 | 15 |
| 20 | 0 |
| 0 | 20 |
| 0 | 40 |
3. A manufacturer has 600 litre of a 12% sol. Of acid. How many litres of a 30% acid sol. Must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%.
Ans. Let 
litres of 30% acid sol. Is required to be added.
of 
of 
and
of 
of
and 
i.e. 
4. Solve graphically 
Ans. 
| 3 | 5 |
| 0 | 1 |
| 0 | 4 |
| 3 | 0 |
5. A sol. Of 8% boric acid is to be diluted by adding a 2% boric acid sol. to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% sol. how many litre of the 2% sol. will have to be added.
Ans. Let be added
ATQ 
of 
of
of 
And 
of of 
of
From (i) and (ii)
6. Solve graphically 
Ans. 
| 0 | 10 |
| 5 | 0 |
| 0 | 1 |
| 1 | 0 |
| 0 | 2 |
| 0 | 2 |
7. How many litres of water will have to be added to 1125 litres of the 45% sol. Of acid so that the resulting mixture will contain more than 25%but less than 30% acid content.
Ans. Let litre of water be added to 1125 litre of 45 acid sol.
of 
of 
of 
of
8. Solve graphically 
Ans. 
| 0 | 50 |
| 75 | 0 |
| 0 | 80 |
| 20 | 0 |