1)

In a ΔABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ∠BAC = 75º, what is the measure of ∠PQR (in degrees)?

SSC CGL 2022

A)

75

B)

50

C)

30

D)

40

2)

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ∠CBD = 40º. Find the measure of ∠BCD.

SSC CGL 2022

A)

40º

B)

30º

C)

50º

D)

20º

3)

The lengths of the three sides of a right-angled triangle are (x - 1) cm, (x + 1) cm and (x + 3) cm, respectively. The hypotenuse of the right-angled triangle (in cm) is:

SSC CGL 2022

A)

6

B)

12

C)

7

D)

10

4)

What is the height (in cm) of an equilateral triangle whose each side is 8 cm?

SSC CGL 2022

A)

4√3

B)

4√2

C)

3√5

D)

3√2

5)

In ΔACD, B and E are two points on side AC and AD respectively, such that BE is parallel to CD. CD = 9 cm, BE = 6 cm, AB = 5 cm and ED = 2 cm. What are the measures of the lengths (in cm) of AE and BC?

SSC CGL 2022

A)

3, 4

B)

4, 3

C)

4, 2.5

D)

2.5, 4

6)

In Δ LMN, the bisector of ∠L and ∠N intersect at and angle of 112°. What is the measure (in degree) of ∠M?

SSC CGL 2022

A)

72

B)

44

C)

62

D)

60

7)

The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm². What is the perimeter (in cm) of the triangle?

SSC CGL 2022

A)

56

B)

49

C)

36

D)

40

8)

The bisector of ∠B in ΔABC meets AC at D. If AB = 12 cm, BC = 18 cm and AC = 15 cm, then the length of AD (in cm) is:

SSC CGL 2022

A)

12

B)

6

C)

9

D)

5

9)

In ∆ ABC, ∠A = 88°. If I is the incentre of the triangle, then the measure of ∠BIC is:

SSC CGL 2022

A)

56°

B)

134°

C)

112°

D)

68°

10)

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°