21)

PQRS is a cyclic quadrilateral with QR as the diameter of the circle. If ∠SQR = 24°, then what will be the measure of ∠QPS?

SSC CHSL 2021

A)

114°

B)

126°

C)

104°

D)

116°

22)

In triangle ABC, if BD and CD bisect ∠B and ∠C , respectively, and ∠BDC = 135°, then find the measure of ∠BAC .

SSC CHSL 2021

A)

90°

B)

45°

C)

65°

D)

75°

23)

Two chords AB and CD of a circle intersect at O. If CO = 4 cm, OD = 3.75 cm, and AB = 8 cm, then what is the length (in cm) of the smaller among AO and OB?

SSC CHSL 2021

A)

3

B)

5

C)

2.75

D)

5.25

24)

A rhombus of side 28 cm has one angle of 60°. What is the length of the larger diagonal?

SSC CHSL 2021

A)

28√2 cm

B)

28(1 + √3) cm

C)

28√3 cm

D)

28 cm

25)

In a circle with centre O, PA and PB are the tangents at A and B, respectively, from an external point P. If ∠APB = 42° then what will be the measure of ∠AOB ?

SSC CHSL 2021

A)

121°

B)

138°

C)

142°

D)

159°

26)

BD and CE are the medians of Δ ABC, right angled at A. If \(CE =\frac{{5\sqrt {13} }}{2}\) cm, BC = 10 cm, then the length of BD is:

SSC CHSL 2021

A)

\(3\sqrt 5\) cm

B)

\(3\sqrt 7\) cm

C)

\(\sqrt {13}\) cm

D)

\(\frac{5}{2}\sqrt {7}\) cm

27)

Chords AB and CD of a circle intersect externally at P. If CD = 11.6 cm, PD = 6.4 cm and PB = 7.2 cm, then AB (in cm) is equal to:

SSC CHSL 2021

A)

8.8

B)

16

C)

12

D)

4.8

28)

In a circle with centre O, chord AB and diameter CD intersect each other at point E, inside the circle. If ∠AOD = 42° and ∠BOC = 104°, then what is the measure (in degrees) of ∠AED? 

SSC CHSL 2021

A)

58

B)

73

C)

84

D)

62

29)

The in-radius and circumradius of a right-angled triangle is 3 cm and 12.5 cm, respectively. The area of the triangle is:

SSC CHSL 2021

A)

84 cm²

B)

88 cm²

C)

48 cm²

D)

64 cm²

30)

The sum of the square of the sides of a rhombus is 1600 cm². What is the side of the rhombus?

SSC CHSL 2021

A)

25 cm

B)

10 cm

C)

15 cm

D)

20 cm