D and E are points on the sides AB and AC respectively of ΔABC. In which of the following cases DE ∥ BC?

1. AD = 3 cm, BD = 8 cm, AC = 8 cm, AE = 3 cm

2. AD = 5 cm, BD = 6 cm, AE = 6 cm, CE = 5 cm

3. AB = 18 cm, AD = 8 cm, AE = 12 cm, EC = 15 cm

4. none of these

In ΔABC, DE ∥ BC so that AD = (7x − 4) cm, AE = (5x − 2) cm, DB = (3x + 4) cm and EC = (3x) cm.
Then x equals:

1. 2.5

2. 3

3. 4

4. 5

It is given that ΔABC ∼ ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then which of the following is true?

1. DE = 12 cm, ∠F = 50°

2. DE = 12 cm, ∠F = 100°

3. EF = 12 cm, ∠D = 100°

4. EF = 12 cm, ∠D = 30°