Directions (Q. 41 to 44): These questions are based on the following information :

In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. It is given that AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm and PQ = 2 cm.

41. The perimeter of ΔABC is:

1. 12 cm

2. 16 cm

3. 18 cm

4. 24 cm

42. The ratio of the areas of ΔAPQ and ΔABC is:

1. 1 : 3

2. 1 : 4

3. 1 : 9

4. 1 : 16

43. Which of the following holds true?

1. ΔAPQ ∼ ΔABC

2. ΔAQP ∼ ΔABC

3. ΔAPQ ∼ ΔACB

4. none of these

44. Which axiom of similarity applies in the above case?

1. AAA

2. AA

3. SSS

4. SAS

Directions (Q. 45 to 48): Using the given diagram answer the following questions.

In ΔPQR, AB ∥ QR, QP ∥ CB and AR intersects CB at O.

45. The triangle similar to ΔARQ is:

1. ΔORC

2. ΔARP

3. ΔOBR

4. ΔQRP

46. ΔPQR ∼ ΔBCR by axiom:

1. SAS

2. AAA

3. SSS

4. AAS

47. If QC = 6 cm, CR = 4 cm, BR = 3 cm, then the length of RP is:

1. 4.5 cm

2. 5 cm

3. 7.5 cm

4. 8 cm

48. The ratio PQ : BC is:

1. 2 : 3

2. 3 : 2

3. 2 : 5

4. 5 : 2

Directions (Q. 53 to 56): Study the following diagram carefully and answer the given questions:

In ΔABC, D and E are points on AB and AC respectively such that AD = a, DB = 3a, AE = b and EC = 3b. DQ ∥ EA and EP ∥ DA are drawn. QP is joined.

53. ΔADE is similar to which of the following triangles?

I. ΔABC

II. ΔDAQ

III. ΔADQ

IV. ΔEPA

V. ΔEAP

1. I, II and IV only

2. I, III and V only

3. I, II and V only

4. I, III and IV only

54. If DE = 2 cm, then BC is equal to:

1. 4 cm

2. 6 cm

3. 7 cm

4. 8 cm

55. The ratio of the perimeters of ΔADE and ΔABC is:

1. 1 : 2

2. 1 : 3

3. 1 : 4

4. 1 : 6

56. The ratio of the areas of ΔADE and trapezium DBCE is:

1. 1 : 8

2. 1 : 9

3. 1 : 15

4. 1 : 16