Math ore board exam

The axis of the hyperbola which is parallel to its directrices is known as:

Fund the minimum distance from the point (4, 2) to the parabola y^2 = 8x.

From past experience, it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year old is given this voice recognation test. Let the random variable X denote the number of children who do not recognize their mother's voice. Find the variance of X

A groupt consists of n engineers and n nurses. if two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n.

Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft. high if the height is increasing at 2 in/min.

An unlimited sequence of squares are inscribed one within another by joining the midpoints of the sides of each preceding square. If the initial square is 8 cm on a side, find the sum of the perimeters of these squares

The area enclosed by the elipse 4x² + 9y² =36 is revolved about fhe line x = 3, what is the volume generated?

Solve ( x+y) dy = ( x-y) dx?

If in the Fourier series of a periodic function, the coefficient ao = 10, then it must be having _____ symmetry.

A ball bounces 2/3 of the altitude from which it falls. Suppose the ball is dropped from a height of 18 ft. How far will it travel at the instant it strikes the ground for the 5th time?