The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of the first triangle is 9cm, find the length of the corresponding side of the second triangle.

OR

In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9 AD² = 7 AB².

If one root of the quadratic equation 3x² + px + 4 = 0 is 2/3, then find the value of p and the other root of the equation.

OR

The roots α and β of the quadratic equation x² - 5x + 3(k - 1) = 0 are such that α – β = 1. Find the value of k.

In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.

The median of the following data is 16. Find the missing frequencies a and b, if the total of the frequencies is 70.

If the angles of elevation of the top of the candle from two coins distant ‘a’ cm and ‘b’ cm (a>b) from its base and in the same straight line from it are 30° and 60°, then find the height of the candle.