The shadow of a 5 m long stick is 2 m long. At the same time the length of the shadow of a 12.5 m high tree is:

1. 3 m

2. 3.5 m

3. 4.5 m

4. 5 m

In a right-angled ΔABC, right-angled at A, if AD ⟂ BC such that AD = p, BC = a, CA = b and AB = c, then:

1. $\dfrac{p}{a} = \dfrac{p}{b}$

2. p² = b² + c²

3. p² = b² c²

4. $\dfrac{1}{p^{2}} = \dfrac{1}{b^{2}} + \dfrac{1}{c^{2}}$

In the adjoining figure, XY is parallel to BC. If XY divides the triangle into two equal parts, then $\dfrac{AX}{AB}$ equals:

1. $\dfrac{1}{\sqrt{2}}$

2. $\dfrac{1}{2}$

3. $\dfrac{\sqrt{2} + 1}{\sqrt{2}}$

4. $\dfrac{\sqrt{2} - 1}{\sqrt{2}}$

Which of the following is true in the given figure, where AD is the altitude to the hypotenuse of a right-angled ΔABC?

(I) ΔABD ∼ ΔCAD

(II) ΔADB ≅ ΔCDA

(III) ΔADB ∼ ΔCAB

1. I and II

2. II and III

3. I and III

4. I, II and III