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# Maths, X

(Answers may be written neatly on A4 papers.Diagrams are to be drawn neatly)

1.If -4 is a root of the quadratic equation  and  has equal roots, find the value of k.

1. If the root of the quadratic equation 2 is 3, find the other root of the quadratic equation.Also find the value of p.
2. For what value of ‘k’does the equation have equal roots
3. Using quadratic formula solve .

5.Solve

1. Solve + = 3
2. Find the roots of the quadratic equation − 2=0

8.Which of the AP; 121,117,113,…., is its first negative term?

1. The sum of the third and seventh terms of an AP is 6 and their product is 8.Find the sum of first sixteen terms of the AP.
2. The houses of a row are numbered consecutively from 1 to 49.Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it.Find this value of x.
3. If the numbers x-2, 4x-1 and 5x+2 are in AP. Find the value of x.
4. If a, (a-2) and 3a are in AP, then what is the value of a?
5. Which term of the A.P. 72,63,54,….. is 0?
6. How many terms are in the AP.?

7,10,13,…..,151

1. For an AP., the 8th term is 17 and the 14th term is 29. Find its common difference.
2. Write the value of x for which x+2,2x,2x+3 are three consecutive terms of an AP.
3. Draw an equilateral triangle of height 3.6 cm . Draw another triangle similar to it such that its side is of the side of the triangle.
4. Draw a circle of radius 1.5 cm. Take a point ‘P’ outside it. Without using the centre, draw two tangents to the circle from P.
5. As observed from the top of a house, 100 m high above the sea level, the angles of depression of a ship sailing directly towards it changes from 30° to 60°. Determine the distances travelled by the ship during the period of observation.
6. The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 15 seconds the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500 m , find the speed of the aeroplane.

21.The angles  of elevation of the top of a tower from two points on the ground at distances ‘a’ and ‘b’ units from the foot of the tower and in the same straight line with it are complememtary. Prove that the height of the tower is units.

1. A bicycle makes revolutions per minute to maintain a speed of 8.91 km per hour. Find the diameter of the wheel.
2. Find the area of the shaded regionbounded between the circle and the triangle, if AB is the diameter of the circle,AC=6 cm, BC = 8 cm.

C                            ( Use pie=3.14)

A                    B