11)

In quadrilateral PQRS, \(RM\perp QS\), \(PN\perp QS\) and QS = 6 cm. If RM = 3 cm and PN = 2 cm, then the area of PQRS is

SSC CGL 2020

A)

\(15cm^2\)

B)

\(14cm^2\)

C)

\(13cm^2\)

D)

\(11cm^2\)

Correct Option: A

\(15cm^2\)

---

Area of quadrilateral PQRS = Area of \(\triangle PQS\) + Area of \(\triangle QRS\) =\({1\over2}\times QS\times PN + {1\over2}\times QS\times RM={1\over2}\times QS(PN + RM)={1\over2}\times6(2+3)=15 cm^2\)

12)

In the figure. if \(\angle A = 100^0\) then \(\angle C = ?\)

SSC CGL 2020

A)

\(50^0\)

B)

\(90^0\)

C)

\(80^0\)

D)

\(100^0\)

13)

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Its area is :

SSC CGL 2020

A)

\(96\space cm^2\)

B)

\(48\space cm^2\)

C)

\(69\space cm^2\)

D)

\(28\space cm^2\)

14)

In a trapezium ABCD, AB || CD, AB < CD, CD = 6 cm and distance between the parallel sides is 4 cm. If the area of ABCD is 16 cm2, then AB is

SSC CGL 2016

A)

10 cm

B)

5 cm

C)

2 cm

D)

1 cm

15)

ABCD is a cyclic quadrilateral which sides AD and BC are produced to meet at P, and sides DC and AB meet at Q when produced. If \(\angle A = 60^\circ\) \( and\space \angle ABC = 72^\circ,\)\( then\space \angle DPC - \angle BQC = ?\)

SSC CGL 2020

A)

\(40^0\)

B)

\(36^0\)

C)

\(24^0\)

D)

\(30^0\)

Correct Option: B

\(36^0\)

---

Since ABCD is a cyclic quadrilateral.  \(\angle A+\angle C = 180 \) & \(\angle B +\angle D = 180^0\) ; 

\(\therefore \angle C = 120^0\)  & \(\angle D = 108^0\) ; 

In \(\triangle PDC\) ⇒ \(\angle PDC = 180-108=72^0\) & \(\angle PCD = 180-120=60^0\) ;  

\(\therefore \angle P = 180-72-60=48^0\) ;

Similarly, In \(\triangle BCQ\) ⇒ \(\angle Q = 12^0\) ;  Now \(\angle P-\angle Q= 48^0-12^0=36^0\)

16)

Sides AB and DC of cyclic quadrilateral ABCD are produced to meet at E, and sides AD and BC are produced to meet at F. If \(\angle ADC = 75^\circ\) and \(\angle BEC =52^\circ\), then the difference between \(\angle BAD\) and \(\angle AFB \) is:

SSC CGL 2020

A)

\(23^0\)

B)

\(22^0\)

C)

\(21^0\)

D)

\(31^0\)

Correct Option: D

\(31^0\)

---

ABCD is a cyclic quadrilateral.  \(\angle ADC = 75^\circ\) ;
 ∴\(\angle ABC + ∠ADC=180^0\) ;
⇒ \(∠ABC = 180^0 − 75^0=105^0\) ;
⇒ \(∠CBE = 180^0 − 105^0=75^0\)  ;
\(\therefore ∠BCE = 180-(52+75)=53^0\); 
\(\angle BCD=180-53=127^0\) ;
\(\because \angle BCD+\angle BAD=180^0\) ; ⇒ \(\angle BAD = 53^0\); 
\(\angle AFB = 180-(105+53)=22^0\) ;
Required difference = \(53^0-22^0=31^0\)

17)

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

18)

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

19)

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°

20)

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