31)

In a trapezium ABCD, DC || AB, AB = 16 cm and DC = 11.2 cm. What is the length (in cm) of the line segment joining the mid points of its diagonals?

SSC CHSL 2021

A)

1.8

B)

1.2

C)

2.4

D)

2.8

32)

The sides of a triangle are 24 cm, 26 cm and 10 cm. At each of its vertices, circles of radius 4.2 cm are drawn. What is the area (in sqcm ) of the triangle, excluding the portion covered by the section of the circles?

SSC CPO 2020

A)

120

B)

27.72

C)

92.28

D)

105.86

33)

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and∠ADC = 148°. What is the measure of the∠BAC?

SSC CPO 2020

A)

45°

B)

60°

C)

58°

D)

32°

34)

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 118°. What is the measure of ∠BAC?

SSC CPO 2020

A)

32°

B)

28°

C)

45°

D)

30°

35)

PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:

SSC CPO 2020

A)

45.7°

B)

81°

C)

90°

D)

40.5°

36)

A cyclic quadrilateral ABCD is drawn in a circle with center O. A and C are joined O. If ∠ABC = 2p and ∠ADC = 3p, what is the measure (in degrees) of the ∠AOC reflex?

SSC CGL 2022

A)

210

B)

245

C)

200

D)

216

37)

In a quadrilateral ABCD, the bisectors of ∠C and ∠D meet at point E. If ∠CED = 57° and ∠A = 47°, then the measure of ∠B is:

SSC CGL 2022

A)

77°

B)

67°

C)

47°

D)

57°

38)

A circle is circumscribed on a quadrilateral ABCD. If ∠DAB = 100°, ∠ADB = 35° and ∠CDB = 40°, then find the measure of ∠DBC.

SSC CGL 2022

A)

60°

B)

40°

C)

45°

D)

35°

39)

PQRS is a cyclic quadrilateral and PQ is a diameter of the circle. If ∠RPQ = 23°, then what is the measure of ∠PSR?

SSC CGL 2022

A)

123°

B)

113°

C)

157°

D)

147°

40)

The value of 80° in radian is 

A)

\(( {2 \pi \over 9})^c\)

B)

\(( {4 \pi \over 9})^c\)

C)

\(( {6 \pi \over 9})^c\)

D)

\(( {8 \pi \over 9})^c\)