51)

In ΔABC, ∠A = 135°, CA = 5√2 cm and AB = 7 cm. E and F are midpoints of sides AC and AB, respectively. The length of EF (in cm) is:

SSC CHSL 2021

A)

5.5

B)

6.5

C)

6

D)

5

52)

The altitude AD of a triangle ABC is 9 cm. If AB = 6√3 cm and CD = 3√3 cm, then what will be the measure of ∠A?

SSC CHSL 2021

A)

45°

B)

30°

C)

90°

D)

60°

53)

In ΔABC, AD is a median. If points E, F and G are midpoints of AD, AE and DE, respectively, then what will be the area ΔBFG ?

SSC CHSL 2021

A)

\(\frac{1}{4}\) (Area of ΔABC)

B)

\(\frac{1}{2}\)  (Area of ΔBGC)

C)

\(\frac{1}{2}\)  (Area of ΔABC)

D)

\(\frac{1}{8} \) (Area of ΔABC)

54)

The centroid of an equilateral triangle ΔABC is O. If AB = 27 cm, then the length of AO is:

SSC CHSL 2021

A)

9√3 cm

B)

6√3 cm

C)

7√3 cm

D)

8√3 cm

55)

ΔPQR is an isosceles triangle with PQ = PR = 25 cm. If PS is the median on QR from P such that PS = 7 cm, then the length of QR is:

SSC CHSL 2021

A)

42 cm

B)

48 cm

C)

45 cm

D)

38 cm

56)

Two circles touch internally. Their diameters are, respectively, 8 cm and 4 cm. What is the distance (in cm) between their centres?

SSC CHSL 2021

A)

3

B)

1

C)

2

D)

4

57)

If a and b are the lengths of two sides of a triangle such that the product ab = 24, where a and b are integers, then how many such triangles are possible?

SSC CHSL 2021

A)

16

B)

15

C)

18

D)

12

58)

ΔPQR is inscribed in a circle with center O. PO is produced to meet QR at U and the circle at S, and PT ⊥ QR, where T lies between Q and U. if ∠Q = 70° and ∠R = 55°, then what is the measure (in degrees) of ∠TPS?

SSC CHSL 2021

A)

30

B)

15

C)

20

D)

25

59)

If ΔABC, DE || AB, where D and E are points on sides AC and BC, respectively. F is a point between C and D such that EF || BD. If AD = 15 cm, DC = 10 cm, then the length of CF is:

SSC CHSL 2021

A)

7.5 cm

B)

5 cm

C)

3 cm

D)

4 cm

60)

Two sides of a triangle are 12.8 m and 9.6 m. If the height of the triangle is 12 m, corresponding to 9.6 m then what its height (in m) corresponding to 12.8 m?

SSC CHSL 2021

A)

12

B)

9

C)

10

D)

8