This are most repeated questions in board exam which will help you to score more in board exam.

1.The ratio of the areas of two similar triangles are equal to the ratio of the squares of any two corresponding sides.prove.

2.If A line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.prove.

3.If the diagonals of a quadrilateral divide each other proportionally, then it is a trapezium.prove.

4.Show that the square of any positive integer is of the form 3m or 3m +1 for some integer m.

5.Find all the zeros of the polynomial x4+ x3 - 34x² - 4x + 120, if two of its zeros are 2 and -2.

6.If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.

7.ABC is an isosceles triangle in which AB = AC, circumscribed about a circle, as shown in
Fig. 10.16. Prove that the base is bisected by the point of contact.

8.A circle is touching the side BC of triangle  ABC at P and touching AB and AC produced at Q and R respectively. Prove that
AQ=1 ( Perimeter of triangle ABC)
2

9.If all the side of a parallelogram touch a circle, show that the parallelogram is a rhombus.

10.The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.