Two equal circles intersect such that each pass through the center of the other. If the length of the common chord of the circle is 10√3 cm, then what is the diameter of the circle?

ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If <BEC = 128° and <ECD = 25°, then what is the measure of <BAC?

$${\sqrt{4×?}}={160\over 10}$$

Directions: The pie– chart shows the proposed outlay for different sectors during a Five–Year plan of Government of India. Total outlay is Rs. 40,000 crores. By reading the pie–chart answer the following three questions.

If the proposed outlay of Irrigation is x% of the proposed outlay of Agriculture, then x is equal to 

cosA(sec A – cosA)(cotA+tanA)=?

The length of the diagonal of a square is ‘a’ cm. Which of the following represents the area of the square (in sq. cm.)?

$$\left({?-0.5\over 0.2} \right)={120\over 2}$$

What should come in place of the question mark '?' in the following number series?

9, 19, 40, 83, ?, 345, 696