1)

ABCD is cyclic quadrilateral with AB as a diameter of the circle. If ∠ADC = 118^o,, then the measure (in degrees) of ∠BAC is:

SSC CHSL 2021

A)

28

B)

32

C)

22

D)

38

2)

A circle touches all four sides of a quadrilateral PQRS. If PQ = 11 cm. QR = 12 cm and PS = 8 cm. then what is the length of RS ?

SSC CHSL 2021

A)

7 cm

B)

15 cm

C)

9 cm

D)

7.3 cm

3)

PQRS is a cyclic quadrilateral. If ∠P is four time ∠R and ∠S is three times ∠Q, then sum of the measures of ∠S and ∠R will be:

SSC CHSL 2021

A)

165°

B)

192°

C)

171°

D)

175°

4)

ABCD is a cyclic quadrilateral whose diagonals intersect at P. If ∠DBC = 72° and ∠BAC = 42°, then the measure of ∠BCD (in degrees) is:

SSC CHSL 2021

A)

66

B)

60

C)

65

D)

57

5)

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°

6)

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°

7)

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

8)

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

9)

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°

10)

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