**Q1 (4) ** Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. 13 cm, 12 cm, 5 cm

In case of a right triangle, the length of its hypotenuse is highest.
hypotenuse be h.
Taking, 5cm, 12 cm
By Pythagoras theorem,
= given third side.
Hence, it is a right triangle with h=13 cm.

**Q14. **IQ of a person is given by the formula

where MA is mental age and CA is chronological age. If for a group of 12 years old children, find the range of their mental age.

Given that group of 12 years old children.
For a group of 12 years old children, CA =12 years
Putting the value of IQ, we obtain
Thus, the range of mental age of the group of 12 years old children is

**Q13. **How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Let x litres of water is required to be added.
Total mixture = (x+1125) litres
It is evident that amount of acid contained in the resulting mixture is 45% of 1125 litres.
The resulting mixture contain more than 25 % but less than 30% acid.
and
and
...

**Q12. **A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution 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% solution, how many litres of the 2% solution will have to be added?

Let x litres of 2% boric acid solution is required to be added.
Total mixture = (x+640) litres
The resulting mixture is to be more than 4% but less than 6% boric acid.
and
and
...

**Q11. **A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by

?

Since the solution is to be kept between 68° F and 77° F.
Putting the value of , we have
the range in temperature in degree Celsius (C) is between 20 to 25.

Solve the inequality and represent the solution graphically on number line.

**Q10. **

Solve the inequality and represent the solution graphically on number line.

**Q9. **

Solve the inequality and represent the solution graphically on number line.

**Q8. **

Solve the inequality and represent the solution graphically on number line.

**Q7.**** **

Solve the inequality

**Q6. **

Solve the inequality

**Q5. **

Solve the inequality

**Q4. **

Solve the inequality

**Q3. **

Solve the inequality

**Q2. **

Solve the inequality

**Q1. **

Given :
Thus, all the real numbers greater than equal to 2 and less than equal to 3 are solutions to this inequality.
Solution set is

Solve the following system of inequality graphically:

**Q15. **

Graphical representation of is given in graph below.
For
The solution to this inequality is region below the line including points on this line because points on line also satisfy the inequality.
For ,
The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.
For ,
The solution to this inequality...

Solve the following system of inequality graphically:

**Q14. **

Graphical representation of is given in graph below.
For
The solution to this inequality is region below the line including points on this line because points on the line also satisfy the inequality.
For ,
The solution to this inequality is region below the line including points on this line because points on the line also satisfy the inequality.
For ,
The solution to this...

Solve the following system of inequalities graphically:

**Q13. **

Graphical representation of is given in graph below.
For
The solution to this inequality is region below the line including points on this line because points on the line also satisfy the inequality.
For ,
The solution to this inequality is region above the line including points on this line because points on the line also satisfy the inequality.
For ,
The solution to this...

Solve the following system of inequalities graphically:

** Q12. **

Graphical representation of is given in graph below.
For ,
The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.
For ,
The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.
For
The solution to this inequality is...

Solve the following system of inequalities graphically:

**Q11. **

Graphical representation of and is given in graph below.
For ,
The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.
For ,
The solution to this inequality is region below the line including points on this line because points on line also satisfy the inequality.
For
The solution to this...

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