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##### objective Ques (161 results)
41)

ABC is an equilateral triangle. P, Q and R are the midpoints of sides AB, BC and CA, respectively. If the length of the side of the triangle ABC is 8 cm, then the area of $$\triangle PQR$$ is:

SSC CGL 2020
A)

$${\sqrt3\over3}\space cm^2$$

B)

$${8\sqrt3}\space cm^2$$

C)

$${4\sqrt3}\space cm^2$$

D)

$${\sqrt3\over4}\space cm^2$$

42)

In the given figure, if $$​ DE \parallel BC ​$$, AD = 2.5 cm, DB = 3.5 cm and EC = 4.2 cm, then the measure of AC is: SSC CGL 2020
A)

7.4 cm

B)

3 cm

C)

3.2 cm

D)

7.2 cm

43)

If angles of a triangle are in the ratio of 2 : 3 : 4, then the measure of the smallest angle is:

SSC CGL 2020
A)

$$40^0$$

B)

$$20^0$$

C)

$$50^0$$

D)

$$30^0$$

44)

The centroid of a triangle is the point where

SSC CGL 2016
A)

the medians meet

B)

the altitudes meet

C)

the right bisectors of the sides of the triangle meet

D)

the bisectors of the angles of the triangle meet

45)

In a triangle PQR, the side QR is extended to S. ∠QPR = 72° and ∠PRS = 110°, then the value of ∠PQR is:

SSC CGL 2016
A)

18°

B)

28°

C)

D)

38°

46)

In ΔABC, ∠B = 70°and ∠C = 60°. The internal bisectors of the two smallest angles of ΔABC meet at O. The angle so formed at O is

SSC CGL 2016
A)

15°

B)

125°

C)

100°

D)

25°

47)

In $$\triangle ABC$$$$\angle B=90^0$$. If the points D and E are on the side BC such that BD = DE = EC, then which of the following is true?

SSC CGL 2020
A)

$$8AE^2 = 5AC^2 + 3AD^2$$

B)

$$8AE^2 = 3AC^2 + 5AD^2$$

C)

$$5AE^2 = 3AC^2 + 2AD^2$$

D)

$$5AE^2 = 2AC^2 + 3AD^2$$

48)

In $$\triangle PQR$$, PQ = 24 cm. and $$\angle Q = 58^\circ$$. S and T are the points on the sides PQ and PR, respectively, such that $$\angle STR = 122^\circ$$. If PS = 14 cm and PT = 12 cm, then the length of RT is :

SSC CGL 2020
A)

14.8 cm

B)

15 cm

C)

16 cm

D)

16.4 cm

49)

D is the midpoint of side BC of $$\triangle ABC$$. Point E lies on AC such that $$CE={1\over3}AC$$. BE and AD intersect at G. What is $$AG\over GD$$ ?

SSC CGL 2020
A)

8 : 3

B)

5 : 2

C)

4 : 1

D)

3 : 1

50)

In $$\triangle ABC$$, $$\angle C = 90^\circ$$, AC = 5 cm and BC = 12 cm. The bisector of $$\angle A$$ meets BC at D. What is the length of AD ?

SSC CGL 2020
A)

$$\frac{2}{3}\sqrt{13}$$ cm

B)

$$2\sqrt{13}$$ cm

C)

$$\frac{4}{3}\sqrt{13}$$ cm

D)

$$\frac{5\sqrt{13}}{3}$$ cm

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