If PT is tangent to the circle at point T and PAB is secant of this circle. Then which of the following statements is true ?

1. PT² = PA × AB

2. PT² = TB × PA

3. PT² = PA × PB

4. PT² = PB × TB

In the given figure, the angle of depression of point D from point A is :

1. 55°

2. 35°

3. 45°

4. 60°

Assertion (A) : The numbers 8, 10, 12, x and 15 are in ascending order of their values. If the mean of their observations is equal to their median, the value of x is 15.

Reason (R) : If the number of observations is n, their mean = $\dfrac{\text{Sum of observations}}{n}$ and median (if n is odd) = value of the $\Big(\dfrac{n + 1}{2}\Big)^{\text{th}}$ observation

1. A is true, R is true

2. A is true, R is false

3. A is false, R is true

4. A is false, R is false

As shown in the adjoining figure, a wire of uniform thickness is rolled on a cylinder to cover it completely, without any overlapping. If the diameter of the wire is 0.25 cm, find :

(i) the number of turns made by the wire to cover the cylinder completely.

(ii) length of wire used.