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

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

• 1

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

• 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 

• (0, 2)

• (1, 0)

• (0,1)

• (0,1)

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)

The conjugate of a complex number is . Then the complex number is

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

• -2

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

• y = ln x + x

• y = x ln x + x²

•  y = xe^(x−1)

•  y = xe^(x−1)

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?

• a = 0, b = 7 

• a = 5, b = 2

• a = 1, b = 6

• a = 1, b = 6

10.

Statement − 1: For every natural number n ≥ 2 

Statement −2: For every natural number n ≥ 2,

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.