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**Miscellaneous Exercise**

**Solve the inequalities:**

**1. **

**Ans. **Given:

**2. **

**Ans. **Given:

**3. **

**Ans. **Given:

**4. **

**Ans. **Given:

**5. **

**Ans. **Given:

**6. **

**Ans. **Given:

**Solve the inequalities in Exercises 7 to 10 and represent the solution graphically on number line:**

**7. **

**Ans. **Given: and

and

and

**8. **

**Ans. **Given: and

and

and

and

**9. **

**Ans. **Given: and

and

and

and

**10. **

**Ans. **Given: and

and

and

and

and

**11. A solution is to be kept between ****F and ****F. What is the range of temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) convension formula is given by ****?**

**Ans. **Given: F < F < F.

Therefore, the range of temperature between C and C.

**12. 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 liters of the 8% solution, have many liters of the 2% solution will have to be added?**

**Ans. **Let litre of 2% boric acid solution be added to 640 litres of 8% boric acid solution. Then,

Total quantity of mixture = litres

And Total boric acid in litres of mixture = =

According to question,

and

and

Therefore 2% boric acid solution must be more than 320 liters but less than 1280 liters.

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

**Ans. **Let liters of water to be added to 1125 liters of 45% acid solution.

Then Total quantity of mixture = liters

According to question,

and

and

and

and

and

Therefore, minimum 562.5 liters and maximum 900 liters of water need to be added.

**14. IQ of a person is given by the formula IQ = **** 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.**

**Ans. **Given: and CA = 12

IQ =

Therefore, minimum MA is 9.6 and maximum 16.8.