# NCERT Mathematics Class 10 Exemplar Ch 4 Quadratic Equations Part 4

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**EXERCISE 4.4**

1. Find whether the following equations have real roots. If real roots exist, find them.

(i)

(ii)

(iii)

(iv)

(v)

Answer: (i) Real roots exist; roots are

(ii) Real roots exist; roots are

(iii) Real roots exist; roots are

(iv) Real roots exist; roots are

(v) Real roots exist; roots are

2. Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

Answer: The natural number is 12

3. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Answer: The natural number is 8

4. A train, travelling at a uniform speed for , would have taken 48 minutes less to travel the same distance if its speed were more. Find the original speed of the train.

Answer: Original speed of the train is

5. If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

Answer: Zeba’s age now is 14 years

6. At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Answer: Nisha’s age is 5 years and Asha’s age are 27 years

7. In the centre of a rectangular lawn of dimensions , a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be [see Fig. 4.1]. Find the length and breadth of the pond.

Answer: Length of the pond is and breadth are

8. At t minutes past , the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than minutes. Find t.

Answer: 14