**AIEEE 2008**

**Sample Questions**

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is

(1) 8/3

(2) 2/3

(3) 4/3

(4) 5/3

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the

parabola is at

(1) (0, 2)

(2) (1, 0)

(3) (0, 1)

(4) (2, 0)

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

(1) a = 0, b = 7 (2) a = 5, b = 2

(3) a = 1, b = 6 (4) a = 3, b = 4

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