All India Engineering / Architecture Entrance Examination (AIEEE)

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AIEEE 2008 MATHEMATICS

Q. 23.

Sol:

Q. 24. AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60^0. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45 ⁰. Then the height of the pole is.

Sol:

Q. 25. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then

1. 1
2. 
3. 
4. 0

Sol:

Q. 26. It is given that the events A and B are such that

Sol:

Q. 27. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is . Then the length of the semi-major axis is

Sol:

Q. 28. 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, 1)
2. (2, 0)
3. (0, 2)
4. (1, 0)

Sol:

Q. 29. The point diametrically opposite to the point P(1, 0) on the circle

1. (- 3, - 4)
2. ( 3, 4)
3. (3, - 4)
4. (- 3, 4)

Sol:

Q. 30. The perpendicular bisector of the line segment joining p (1, 4), and Q (k, 3), has y-intercept –4. Then a possible value of k is

1. - 2
2. - 4
3. 1
4. 2

Sol:

Q. 31. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

1. 12
2. 4
3. - 4
4. - 12

Sol.

Correct choice: (4)

Q. 32. Suppose the cubic x³ - px + qhas three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

Sol:

Correct choice: (3)

Q. 33. How many real solutions does the equation

1. 3
2. 5
3. 7
4. 1

Sol:

Q. 34.

1. f is differentiable at x = 0 but not at x = 1
2. f is differentiable at x = 1 but not at x = 0
3. f is neither differentiable at x = 0 nor at x = 1
4. f is differentiable at x = 0 and at x = 1

Sol:

Q. 35. The solution of the differential equation satisfying the condition y (1) = 1 is

1. 
2. y = x In x +x
3. y = In x +x
4. 

Sol: