# Class 10 - Formative Assessment 3 - Mathematics (2016-2017)

**Section A [1 x 4 = 4M]**

**1.) Check whether the following equation is quadratic or not:**

\( (x + 1)^2 = 2 ( x + 3) \)

**2.)**** What will be the nature of roots of the following quadratic equation:**

\( x^2 + x + 1 \)

**3.) Find a _{n}, where a = 10, d = 4 and n = 7.**

**4.) Find whether the following are in A.P. or not?**

\( \sqrt{2} \), \( \sqrt{8} \), \( \sqrt{18} \), \( \sqrt{32} \), ............ etc

**Section B [ 2 x 5 = 10M]**

**5.) **Find the two numbers whose sum is 25 and the product is 156?

**6.) Find the value of k for the following quadratic equaltion, so that the roots are equal:**

\(2x^2 + kx + 3 = 0 \)

**7.)** Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

**8.)** A tower stands verticaaly on the ground. From a point on the ground which is 15m away from the foot of the tower is found to be 60°. Find the height of the tower. (The angle of elevation of top of the tower is 60°)

**9.)** Find the missing terms: 18, ____, ____, 3

**SECTION - C [3 x 6 = 18M)**

**10.)** A train travels 360km at uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for same journey. Find the speed of the train.

**11.)** Find the sum of the first 24 terms of the list of numbers (which are in A.P.) whose nth term is given by **a _{n} = 3 + 2n**

**12.)** How many three digit numbers are divisible by 3?

**13.)** Find the sum of first ten multiples of 7.

**14.)** Find the roots of the quadratic equation by using completing square method: \( 3x^2 - 5x + 2 = 0 \)

**15.)** An observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney.?

**SECTION - D [4 x 2 = 8M]**

**16.)** From the top of 100m tall building above sea level, the angles of depressions of two ships are 45° and 60°. If one ship is behind the other on the same side of the tower, find the distance between them.

**17.)** In the centre of a rectangular lawn of dimensions 50m x 40m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m^{2}. Find the length and breadth of the pond.