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°. 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°.
Then the height of the pole is

• 
• 
• 
• 

B.

BD = AB = 7 + x
Also AB = x tan 60° = x√3
∴ x√3 = 7+x

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 P (A ∪ B) is 

• 3/5

• 0

• 1

• 2/5

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 

• 8/3

• 2/3

• 5/3

• 4/3

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

• (0, 2)

• (1, 0)

• (0,1)

• (2,0)

The point diametrically opposite to the point P (1, 0) on the circle x²+ y² + 2x + 4y − 3 = 0 is 

• (-3,4)

• (-4,3)

• (-3,-4)

• (3,4)