91)

Sides AB and AC of ∆ ABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 78°, then the measure of ∠P is:

SSC CGL 2022

A)

55°

B)

61°

C)

51°

D)

56°

92)

The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?

SSC CGL 2022

A)

15

B)

16

C)

12

D)

18

93)

In Δ ABC, AD is perpendicular to BC and AE is the bisector of ∠ BAC. If ∠ABC = 58° and ∠ACB = 34°, then find the measure of ∠DAE.

SSC CGL 2022

A)

22°

B)

11°

C)

12°

D)

15°

94)

In Δ ABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CD = 8 cm, then CB (in cm) = ?

SSC CGL 2022

A)

12

B)

15

C)

18

D)

10

95)

In a triangle ABC, D and E are points on BC such that AD = AE and ∠BAD = ∠CAE. If AB = (2p + 3), BD = 2p, AC = (3q - 1) and CE = q, then find the value of (p + q).

SSC CGL 2022

A)

3.6

B)

2

C)

3

D)

4.5

96)

In ΔABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then DC (in cm) = ?

SSC CGL 2022

A)

\(\frac{16}{3}\)

B)

\(\frac{17}{3}\)

C)

\(\frac{14}{3}\)

D)

\(\frac{11}{3}\)

97)

In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 15 cm and CD = 9 cm, then CB (in cm) = ?

SSC CGL 2022

A)

25

B)

15

C)

10

D)

12

98)

The base of a triangle is increased by 40%. By what percentage (correct to two decimal places) should its height be increased so that the area increases by 60%?

SSC CGL 2022

A)

20.01%

B)

18.62%

C)

15.54%

D)

14.29%

99)

The sides PQ and PR of ΔPQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at point U. If ∠QUR = 69°, then the measure of ∠P is:

SSC CGL 2022

A)

42°

B)

21°

C)

69°

D)

31°

100)

Let ΔABC ~ ΔPQR and \(\frac{\operatorname{ar}(\triangle \mathrm{ABC})}{\operatorname{ar}(\triangle \mathrm{QPR})}=\frac{64}{169} \text { }\). If AB = 10 cm, BC = 7 cm and AC = 16 cm, then PR (in cm) is equal to:

SSC CGL 2022

A)

15

B)

21

C)

13

D)

26