131)

From the following figure find x+ y + z.

SSC CGL 2022

A)

120°

B)

130°

C)

100°

D)

110°

132)

In triangle ABC, the bisector of angle BAC cuts the line BC at D. If BD = 6 and BC = 14 then what is the value of AB : AC?

SSC CGL 2022

A)

3 : 10

B)

7 : 3

C)

3 : 4

D)

3 : 7

133)

In the given triangle, CD is the bisector of ∠BCA. CD = DA. If ∠BDC = 76°, What is the degree measure of ∠CBD? 

SSC CGL 2022

A)

80°

B)

76°

C)

32°

D)

66°

134)

The area of a triangle is 480 cm² and the ratio of its sides is 10 ∶ 24 26. What is the perimeter of the triangle?

SSC CGL 2022

A)

150 cm

B)

30 cm

C)

120 cm

D)

60 cm

135)

In a Δ ABC, ∠B + ∠C = 110°, then find the measure of ∠A.

SSC CGL 2022

A)

80°

B)

70°

C)

90°

D)

60°

136)

Find the area of the shaded portion of an equilateral triangle with sides 6 units shown in the following figure. A circle of radius 1 unit is centred at midpoint of a side of the triangle.

SSC CGL 2022

A)

\(\frac{1}{2}\left( {6\sqrt 3 - \frac{{11}}{7}} \right)~\)\(unit^{2}\)

B)

\(\frac{1}{4}\left( {9\sqrt 3 - \frac{{11}}{7}} \right)~\)\(unit^{2}\)

C)

\(\frac{1}{2}\left( {9\sqrt 3 - \frac{{11}}{7}} \right)\)  \(unit^{2}\)

D)

\(\frac{1}{2}\left( {9\sqrt 3 - \frac{{22}}{7}} \right)~\)\(unit^{2}\)

137)

ΔPQR is right-angled at Q. The length of PQ is 5 cm and ∠PRQ = 30°. Determine the length of side QR.

SSC CGL 2022

A)

\(\frac{1}{\sqrt3}\)\(cm\)

B)

\(3\sqrt3\)\(cm\)

C)

\(5\sqrt3 cm\)

D)

\(\frac{5}{\sqrt3}\)\(cm\)

138)

'O' is a point in the interior of an equilateral triangle. The perpendicular distance from 'O' to the sides are\( \sqrt3 cm\), 2 cm, 5 cm. The perimeter of the triangle is :

SSC CGL 2022

A)

24 cm

B)

32 cm

C)

48 cm

D)

64 cm

139)

The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?

SSC CGL 2022

A)

\(4 \sqrt{3}\) cm

B)

\(5\sqrt{3}\) cm

C)

\(2 \sqrt{3}\) cm

D)

\(3 \sqrt{3}\) cm

140)

An airplane goes 14 km due east and then 48 km due north. How far is it from its initial position?

SSC CGL 2022

A)

50 km

B)

48 km

C)

14 km

D)

28 km