# NCERT Solutions class-11 Maths Miscellaneous

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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.