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objective Ques (153 results)
1)
SSC CGL Mains 2024
A)

11 : 15

B)

11 : 13

C)

9 : 11

D)

15 : 13

2)

In a triangle HJK, HJ = HK. G is a point on HJ such that HG = GK = JK. What is the degree measure of two-third of (∠HGK + ∠GKJ)?

SSC CGL Mains 2024
A)

90°

B)

84°

C)

136°

D)

96°

3)

∆ABC is inscribed in a circle with Centre O. If AB = 21 cm, BC = 20 cm and AC = 29 cm, then what is the length of the circumradius of the triangle?

SSC CGL Mains 2024
A)

13.5 cm

B)

14.5 cm

C)

32.5 cm

D)

21.5 cm

4)

Let PQR be a right angled triangle, right-angled at R. Let PQ = 29 cm, QR = 21 cm and ∠Q = θ. Find the value of cos 2 θ – sin 2 θ.

SSC CGL Mains 2024
A)
option_A
B)
option_B
C)
option_C
D)
option_D
5)

If the areas of two isosceles triangles are in the ratio of x2 ∶ y2, then the ratio of their corresponding heights is:

SSC CGL 2022
A)

x3 ∶ y3

B)

\(\sqrt{x} : \sqrt{y}\)

C)

x ∶ y

D)

x2 ∶ y2

6)

What is the ASA congruence rule of triangles, where A and S represents angle and side of triangle respectively?

SSC CGL 2022
A)

Two triangles are said to be congruent if 2 sides and the included angle of one triangle are equal to 2 sides and the included angle of the other triangle.

B)

Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.

C)

Two triangles are said to be congruent if all three sides of both the triangles are equal.

D)

Two triangles are said to be congruent if any pair of 2 angles and any 1 pair of sides of both the triangles are equal.

7)

 

△ABC is a right-angle triangle at B and tan A = \(\frac{3}{4} \), then sin A + sin B + sin C will be equal to:

SSC CGL 2022
A)

\(3\frac{1}{5}\)

B)

\(2\frac{2}{5}\)

C)

\(2 \frac{4}{5}\)

D)

\(1\frac{1}{5}\)

8)

If ∆ABC ~ ∆EDF such that AB = 6 cm, DF = 16 cm and DE = 8 cm, then the length of BC is:

SSC CGL 2022
A)

14 cm

B)

10 cm

C)

12 cm

D)

8 cm

9)

In ∆ ABC, D and E are points on sides AB and AC, such that DE ΙΙ BC. If AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2, then the value of x is:

SSC CGL 2022
A)

\({{3} \over 5}\)

B)

\({{1} \over 2}\)

C)

\({{4} \over 5}\)

D)

\({{1} \over 5}\)

10)

In ΔPQR, ∠Q = 90°, PQ = 8 cm and ∠PRQ = 45°. Find the length of QR.

SSC CGL 2022
A)

5 cm

B)

3 cm

C)

6 cm

D)

8 cm

11)

ΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm, respectively. If DE = 6 cm, then what will be the length of AB?

SSC CGL 2022
A)

12 cm

B)

14 cm

C)

16 cm

D)

18 cm

12)

ΔABC and ΔDEF are similar triangles and their areas are 49 cm2 and 144 cm2 respectively. If EF = 16.80 cm, then find BC.

SSC CGL 2022
A)

8.7 cm

B)

9.8 cm

C)

7.5 cm

D)

11.4 cm

13)

If ΔABC ≅ ΔPQR and ∠ABC = (x + 60)°, ∠PQR = (85 - 4x)°, and ∠RPQ = (3x + 65)°, then the value of ∠ABC in degree is:

SSC CGL 2022
A)

45

B)

5

C)

15

D)

65

14)

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

15)

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

16)

'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

17)

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)

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

18)

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)

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

19)

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

SSC CGL 2022
A)

80°

B)

70°

C)

90°

D)

60°

20)

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

21)

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°

22)

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

23)

From the following figure find x+ y + z.

SSC CGL 2022
A)

120°

B)

130°

C)

100°

D)

110°

24)

If the figure, AB = AD = 7 cm and AC = AE and BC = 11 cm, then find the length of ED.

SSC CGL 2022
A)

11

B)

10

C)

12

D)

2

25)

If the angles of a triangle are (x - 46) degrees, (x + 96) degrees and 8x degrees, then what is the value of 2x?

SSC CGL 2022
A)

26 degrees

B)

24 degrees

C)

15 degrees

D)

13 degrees

26)

The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?

SSC CGL 2022
A)

9√3 cm

B)

4√3 cm

C)

6√3 cm

D)

5√3 cm

27)

If areas of similar triangles ΔABC and ΔDEF are x2 cm2 and y2 cm2 respectively, and EF = a cm, then BC (in cm) is:

SSC CGL 2022
A)

\(\frac{a x}{y}\)

B)

\(\frac{y}{a x}\)

C)

\(\frac{y^2}{a^2 x^2}\)

D)

\(\frac{a^2 x^2}{y^2}\)

28)

In the triangle ABC, AB = 12 cm and AC = 10 cm, and ∠BAC = 60°. What is the value of the length of the side BC?

SSC CGL 2022
A)

13.20 cm

B)

7.13 cm

C)

10 cm

D)

11.13 cm

29)

In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, length of the base QR is 8 units, and length of the side PQ is 15 units. If ∠RPQ = α, then sin α + cos α is:

SSC CGL 2022
A)

\(\frac{21}{17}\)

B)

\(\frac{23}{17}\)

C)

\(\frac{18}{17}\)

D)

\(\frac{15}{17}\)

30)

In ∆ABC, the perpendiculars drawn from A, B and C meet the opposite sides at points D, E and F, respectively. AD, BE and CF intersect at point P. If ∠EPD = 110° and the bisectors of ∠A and ∠B meet at point Q, then ∠AQB = ?

SSC CGL 2022
A)

125°

B)

135°

C)

110°

D)

115°

31)

In the following figure, AD bisects angle BAC. Find the length (in cm) of BD.

SSC CGL 2022
A)

5

B)

9

C)

4

D)

6

32)

In a triangle ABC, points P and Q are AB and AC, respectively, such that AP = 4 cm, PB = 6 cm, AQ = 5 cm and QC = 7.5 cm. If PQ = 6 cm, then find BC (in cm).

SSC CGL 2022
A)

10

B)

9

C)

15

D)

12

33)

In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10 cm, AC = 15 cm and BD = 6 cm. Find the length of BC (in cm).

SSC CGL 2022
A)

17

B)

11

C)

15

D)

9

34)

In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6 cm, CA = 18.8 cm and AB = 20.4 cm, what is the perimeter (in cm) of the ΔDEF?

SSC CGL 2022
A)

32.4

B)

36.8

C)

30.6

D)

34.4

35)

In a right-angled triangle PQR, ∠Q = 90°. A and B are the mid-points of PQ and PR, respectively. If PQ = 16 cm, QR = 30 cm and PR = 34 cm, what is perimeter (in cm) of the trapezium ABRQ?

SSC CGL 2022
A)

65

B)

40

C)

80

D)

70

36)

In △ABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:

SSC CGL 2022
A)

124°

B)

56°

C)

68°

D)

112°

37)

In triangle ABC, X and Y are the points on sides AB and AC, respectively, such that  XY is parallel to BC. If XY : BC = 2.5 : 7, what is the ratio of the area of the trapezium BCYX to that of the ΔAXY?

SSC CGL 2022
A)

\(171\over25\)

B)

\(25\over196\)

C)

\(25\over171\)

D)

\(196\over25\)

38)

In ΔPQR, ∠Q = 66° and ∠R = 34. T is a point on QR , and S is a point between Q and T such that PS ⊥ QR and PT is the bisector of ∠QPR. What is the measure of ∠SPT?

SSC CGL 2022
A)

16

B)

20

C)

12

D)

18

39)

A triangle with the lengths of its sides proportional to the numbers 7, 24 and 30 is:

SSC CGL 2022
A)

obtuse angled

B)

acute angled

C)

right angled

D)

not possible

40)

In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm, then find the value of AB2 + BD2 (in cm).

SSC CGL 2022
A)

66

B)

36

C)

96

D)

30

41)

In a right-angled triangle, the lengths of the medians from the vertices of acute angles are 7 cm and \( 4\sqrt 6\) cm. What is the length of the hypotenuse of the triangle (in cm)?

SSC CGL 2022
A)

\(3.5+2\sqrt6\)

B)

\(2\sqrt{29}\)

C)

\(2.5\sqrt{29}\)

D)

\(\sqrt{29}\)

42)

In a triangle ABC, the bisector of angle BAC meets BC at point D such that DC = 2BD. If AC - AB = 5 cm, then find the length of AB (in cm).

SSC CGL 2022
A)

10

B)

7

C)

5

D)

12

43)

A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively: If AB - BC = 4 cm, AB - AC = 2 cm and the perimeter of ΔABC = 32 cm, then \(BC \over 2\) (in cm) = ?

SSC CGL 2022
A)

\(11 \over 3\)

B)

\(13 \over 3\)

C)

\(20 \over 3\)

D)

\(10 \over 3\)

44)

In ΔABC, ∠A = 66°, BD ⊥ AC and CE ⊥ AB. BD and EC intersect at P. The bisectors ∠PBC and ∠PCB meet at Q. What is the measure of ∠BQC?

SSC CGL 2022
A)

143°

B)

132°

C)

127°

D)

147°

45)

The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?

SSC CGL 2022
A)

6.4

B)

7.2

C)

9.6

D)

12.8

46)

Let ΔABC ~ ΔQPR and (Area of ΔABC) : (Area of ΔPQR) = 121 : 64. If QP = 14.4 cm, PR = 12 cm and AC = 18 cm, then what is the length of AB?

SSC CGL 2022
A)

21.6 cm

B)

16.2 cm

C)

19.8 cm

D)

32.4 cm

47)

In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 14.4 cm, CA = 15.2 cm and AB = 12.4 cm, what is the perimeter (in cm) of the ΔDEF?

SSC CGL 2022
A)

35

B)

42

C)

28

D)

21

48)

In Δ PQR, S is a point on the side QR such that PS is the bisector of ∠QPR. If PQ = 12 cm, QS = 3 cm and QR = 7 cm, then what is the length of side PR?

SSC CGL 2022
A)

15 cm

B)

14 cm

C)

18 cm

D)

16 cm

49)

The area of similar triangles PQR and MNT are 196 cm2 and 169 cm2 respectively. If the longest side of the larger Δ PQR be 28 cm then what is the length (in cm) of the longest side of the smaller Δ MNT?

SSC CGL 2022
A)

25

B)

24

C)

26

D)

27

50)

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 \( \frac{DC}{4}\) (in cm) is equal to:

SSC CGL 2022
A)

\(11\over 3\)

B)

\(4\over 3\)

C)

\(14\over 3\)

D)

\(7\over 3\)

51)

The sides AB and AC of ΔABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 88°, the measure of ∠P is :

SSC CGL 2022
A)

51°

B)

56°

C)

46°

D)

61°

52)

In a ΔABC, the bisector of ∠A meets BC at D. If AB = 9.6 cm, AC = 11.2 cm and BD = 4.8 cm, the perimeter (in cm) of ΔABC is:

SSC CGL 2022
A)

30.4

B)

28.6

C)

31.2

D)

32.8

53)

A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively. If AB - BC = 4 cm, AB - AC = 2 cm, and the perimeter of ΔABC = 32 cm, then AC (in cm) = ?

SSC CGL 2022
A)

\(\frac{32}{3}\)

B)

\(\frac{38}{3}\)

C)

\(\frac{35}{3}\)

D)

\(\frac{26}{3}\)

54)

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

55)

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°

56)

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%

57)

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

58)

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)

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

59)

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

60)

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

61)

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°

62)

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

63)

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°

64)

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°

65)

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

66)

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

67)

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

68)

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

69)

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

70)

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

71)

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

72)

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

73)

The sides PQ and PR of ΔPQR are produced to points S and T, respectively. The bisectors of ∠SQR and ∠TRQ meet at U. If ∠QUR = 59°, then the measure of ∠P is:

SSC CPO 2020
A)

41°

B)

31°

C)

49°

D)

62°

74)

In ΔABC, ∠A = 54°. If I is the incentre of the triangle, then the measure of ∠BIC is:

SSC CPO 2020
A)

68°

B)

54°

C)

117°

D)

148°

75)

A circle is inscribed in a triangle ABC. It touches side AB, BC, and AC at points R, P, and Q respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ABC is:

SSC CPO 2020
A)

33.2

B)

16.6

C)

28

D)

30

76)

In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 62° and ∠ EBD = 60°, then the value of x is:

SSC CPO 2020
A)

78°

B)

76°

C)

92°

D)

68°

77)

In ΔABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:

SSC CPO 2020
A)

124°

B)

68°

C)

54°

D)

148°

78)

In ΔABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm. The length of median AD (in cm) is:

SSC CPO 2020
A)

3

B)

4.5

C)

5

D)

4

79)

The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm2) of the triangle?

SSC CPO 2020
A)

96

B)

60

C)

120

D)

90

80)

Let Δ ABC ∼ Δ RPQ and \(\frac{{ar(\Delta ABC)}}{{ar(\Delta RPQ)}} = \frac{4}{9}\) . If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

SSC CPO 2020
A)

4.5 cm

B)

12 cm

C)

5 cm

D)

6 cm

81)

In ΔABC, AB and AC are produced to points D and E, respectively. If the bisectors of ∠CBD and ∠BCE meet at the point O, and ∠BOC = 57°, then ∠A is equal to:

SSC CPO 2020
A)

66°

B)

93°

C)

114°

D)

57°

82)

In ΔABC,∠A = 66°.  AB and AC are produced to points D and E, respectively. If the bisectors of angle CBD and angle BCE meet at the point O, then∠BOC is equal to:

SSC CPO 2020
A)

57°

B)

93°

C)

114°

D)

66°

83)

LetΔABC ~ΔRPQ and \(\frac {ar (\Delta ABC)}{ar(\Delta RPQ)} = \frac 4 9 \). If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:

SSC CPO 2020
A)

12

B)

6

C)

5

D)

4.5

84)

In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 46° and ∠EBD = 60°, then the value of x is:

SSC CPO 2020
A)

76°

B)

72°

C)

78°

D)

68°

85)

In Δ ABC, AC = BC, and the length of the base AB is 10 cm. If CG = 8 cm, where G is the centroid, then what is the length of AC?

SSC CHSL 2021
A)

12 cm

B)

13 cm

C)

15 cm

D)

√91 cm

86)

The sum of all the three sides of an equilateral triangle is 15√3 cm. The height of the triangle is:

SSC CHSL 2021
A)

7.5 cm

B)

7 cm

C)

9 cm

D)

8 cm

87)

The area of an equilateral triangle is 10.24√3 m2. Its perimeter (in m) is:

SSC CHSL 2021
A)

9.6

B)

19.2

C)

6.4

D)

3.2

88)

The side QR of a triangle PQR is extended to a point S. If ∠PRS = 104° and ∠RQP =\(\frac{3}{5}\)∠QPR, then the value of ∠QPR is:

SSC CHSL 2021
A)

55°

B)

65°

C)

45°

D)

58°

89)

In Δ ABC, AD is the bisector of ∠A meeting BC at D. If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC , then the length of AC is:

SSC CHSL 2021
A)

18.5 cm

B)

18 cm

C)

22.5 cm

D)

16 cm

90)

In ΔABC, P and Q are the mid-points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR ∶ RQ = 1 ∶ 3. If PR = 4 cm, then BC is equal to:

SSC CHSL 2021
A)

32 cm

B)

36 cm

C)

24 cm

D)

28 cm

91)

The sum of three sides of an isosceles triangle is 20 cm, and the ratio of an equal side to the base is 3 ∶ 4. The altitude of the triangle is:

SSC CHSL 2021
A)

3√5 cm

B)

4√5 cm

C)

3√3 cm

D)

2√5 cm

92)

In a triangle ABC, the length of side AC is 4 cm less than five times the length of side AB. The length of side BC exceeds four times the length of side AB by 4 cm. If the perimeter of Δ ABC is 90 cm, then its area is:

SSC CHSL 2021
A)

180 cm2

B)

160 cm2

C)

148 cm2

D)

164 cm2

93)

If Δ ABC∼Δ QPR,\( \rm \frac{ar(\Delta ABC)}{ar(\Delta PQR)}=\frac{4}{9}\),  AC = 12 cm, AB = 18 cm and BC = 10 cm, then PR (in cm) is equal to:

SSC CHSL 2021
A)

15

B)

8

C)

10

D)

18

94)

If O is the centroid and RP is the median with length 24 cm of Δ RST , where P is a point on ST, then the value of RO is:

SSC CHSL 2021
A)

20 cm

B)

16 cm

C)

18 cm

D)

14 cm

95)

The sides AB, BC and AC of ΔABC are 12 cm, 8 cm and 10 cm, respectively. A circle is inscribed in the triangle touching AB, BC and AC at D, E and F, respectively. The ratio of the lengths of AD to CE is:

SSC CHSL 2021
A)

10 ∶ 7

B)

5 ∶ 7

C)

7 ∶ 3

D)

3 ∶ 5

96)

In ΔPQR, QT ⊥ PR and S is a point on QR such that ∠PSQ = p°. If ∠TQR = 44° and ∠SPR = 32°, then the value of p is:

SSC CHSL 2021
A)

76°

B)

82°

C)

78°

D)

72°

97)

The sides of a triangle are in the ratio \(\frac{1}{3},\frac{1}{5},\frac{1}{4}\) and its perimeter is 141 cm. The difference between the greatest side and the smallest side is:

SSC CHSL 2021
A)

15 cm

B)

24 cm

C)

18 cm

D)

12 cm

98)

In any triangle, if the angles are in the ratio 1 : 2 : 3, then what will be the ratio of the sides opposite to them?

SSC CHSL 2021
A)

2 : 2 : √3

B)

2 : √3 : 1

C)

1 : √3 : 2

D)

1 : √3 : 1

99)

If S is a point on side QR of a triangle PQR such that QS = 10 cm, QR = 18 cm and ∠PSR = ∠QPR, then the length of PR will be:

SSC CHSL 2021
A)

16 cm

B)

12 cm

C)

15 cm

D)

14 cm

100)

In Δ ABC, points D and E are on AB and AC, respectively, such that DE is parallel to BC. IE AD = 3 cm, BD = 6 cm and AE = 2 cm, then find the length of CE.

SSC CHSL 2021
A)

16 cm

B)

8 cm

C)

6 cm

D)

4 cm

101)

ABC is a triangle inscribed in a circle and ∠ACB is equal to 35°. P is a point on the circle on the side AB, opposite to C. What is the value of ∠APB in degrees?

SSC CHSL 2021
A)

145

B)

70

C)

175

D)

72.5

102)

In triangle ABC, AD is the internal bisector of \(\angle A\) meeting BC at D. If BD = 3.6 cm and BC = 8 cm, then the ratio of AB to AC will be:

SSC CHSL 2021
A)

7 ∶ 13

B)

9 ∶ 11

C)

13 ∶ 7

D)

11 ∶ 9

103)

In a circle, two chords UV and WX intersect each other at a point Z within the circle. If UV = 18 cm, ZV = 6 cm and WZ = 9 cm, then the length of ZX is:

SSC CHSL 2021
A)

8 cm

B)

10 cm

C)

6 cm

D)

4 cm

104)

Chords AB and CD of a circle intersect externally at P. If AB = 8.8 cm, PB = 7.2 cm, PD = 6.4 cm, then CD is equal to:

SSC CHSL 2021
A)

10.8 cm

B)

11.6 cm

C)

10.6 cm

D)

11.4 cm

105)

AB is the diameter of a circle of radius 9 cm. PQ is a chord (not a diameter) that intersects AB at M perpendicularly. If AM : BM = 5 : 4, then the length of chord PQ will be:

SSC CHSL 2021
A)

6√3 cm

B)

5√5 cm

C)

8√5 cm

D)

6√5 cm

106)

AB is 12 cm long chord of a circle with centre O and radius 10 cm. The tangents at A and B intersect at P. What is the length of OP?

SSC CHSL 2021
A)

12 cm

B)

10 cm

C)

12.5 cm

D)

2√61 cm

107)

A circle touches the side BC of ΔABC at P and also touches AB and AC produced at Q and R, respectively. If the perimeter of ΔABC = 14.1 cm, then the length (in cm) of AQ will be:

SSC CHSL 2021
A)

6.25

B)

7.05

C)

9.15

D)

10.3

108)

Two circle touch each other externally. The distance between their centres is 14 cm. If the radius of one circle is 8 cm, then the radius of the other circle is:

SSC CHSL 2021
A)

8 cm

B)

5 cm

C)

6 cm

D)

7 cm

109)

The circumference of a circle is 'aπ' units and the area of the circle is 'bπ' square units. If a ∶ b is equal to 4 ∶ 5, then the radius of the circle is:

SSC CHSL 2021
A)

2.5 cm

B)

2 cm

C)

5 cm

D)

3 cm

110)

Chord AB of a circle with radius 5 cm is at a distance of 4 cm from the centre O. If tangents drawn at A and B intersect at P, then find the length of the tangent AP.

SSC CHSL 2021
A)

7.5 cm

B)

3 cm

C)

3.75 cm

D)

2.4 cm

111)

In a circle with center O, APB is a tangent at P. If MN is a diameter such that ∠ BPN = 52°, then what is the measure of ∠ PNM?

SSC CHSL 2021
A)

38°

B)

48°

C)

90°

D)

52°

112)

Points A, B, C and D are concyclic points of a circle with centre O, such that ∠DOC = 73°. The measure of ∠AOC is 215°. What is the measure of ∠ AOD?

SSC CHSL 2021
A)

145°

B)

72°

C)

87°

D)

273°

113)

PA and PB are tangents drawn to a circle with centre O from an external point P. If A and B are points on the circle and ∠OBA = 42°, then ∠APB is:

SSC CHSL 2021
A)

78°

B)

86°

C)

76°

D)

84°

114)

Two chords PQ and RS of a circle meet at A when produced. AT is a tangent to the circle meeting it at T. The ratio PA : SA is equal to which of the following?

SSC CHSL 2021
A)

AQ : AT

B)

RQ : QT

C)

RA : AQ

D)

AQ : QR

115)

The distance between two equal parallel chords of a circle is 10 cm. If the chords are 24 cm long, then what is the length of the radius?

SSC CHSL 2021
A)

26 cm

B)

13 cm

C)

2√61 cm

D)

17 cm

116)

Two circles of radii 4 cm and 3 cm, respectively, touch each other externally. What is the distance (in cm) between their centres?

SSC CHSL 2021
A)

16

B)

7

C)

5

D)

9

117)

A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 6.5 cm, PC = 7.5 cm and BR = 9 cm, then the perimeter (in cm) of the triangle ABC will be:

SSC CHSL 2021
A)

27.5

B)

46

C)

55

D)

23

118)

If PA and PB are tangents drawn to a circle with centre O at A and B from external point P such that ∠APB = 78°, then ∠OAB is equal to:

SSC CHSL 2021
A)

39°

B)

29°

C)

12°

D)

36°

119)

In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 2.8 cm, PB = 3.15 cm and AB = 3.85 cm, then CD = ?

SSC CHSL 2021
A)

6.975 cm

B)

5.075 cm

C)

4.175 cm

D)

7.875 cm

120)

A chord PQ of a circle C1 of radius 9.25 cm touches another circle C2 that is concentric to C1, and the radius of C2 is 3 cm. What is the length (in cm) of PQ?

SSC CHSL 2021
A)

12

B)

19.5

C)

17.5

D)

15

121)

Chords AB and CD of a circle are produced to meet at the point P, outside the circle, and AD is the diameter of the circle. If ∠DAP = 36° and ∠APC = 30°, then what will be the measure of ∠CBD?

SSC CHSL 2021
A)

34°

B)

26°

C)

24°

D)

16°

122)

Two concentric circles are of radii 15 cm and 6 cm. What is the length (in cm) of the chord of the larger circle that is tangent to the smaller circle?

SSC CHSL 2021
A)

4√21

B)

9√21

C)

6√21

D)

3√21

123)

AB is a chord of a circle with centre O and P is any point on the circle. If  ∠APB = 112°, then what is the measure of ∠OAB ?

SSC CHSL 2021
A)

30°

B)

32°

C)

22°

D)

44°

124)

A and B are two points on a circle with centre O. C is a point on the minor arc of the circle between points A and B. The tangents to the circle at A and B meet each other at a point D. If ∠ ADB = 25°, then ∠ ACB (in degrees) is equal to :

SSC CHSL 2021
A)

102.5

B)

105

C)

100.5

D)

100

125)

AB is a diameter of the circle with centre 0. The tangent at the point C on the circle meets AB produced at Q. If ∠BAC = 34°, then the measures of ∠CQA (in degrees) will be:

SSC CHSL 2021
A)

22

B)

24

C)

36

D)

26

126)

AB is a diameter of a circle with centre O. If C is any point on the circle such that ∠BAC = 42°, then find the measure of ∠BOC.

SSC CHSL 2021
A)

84°

B)

42°

C)

60°

D)

63°

127)

P, Q and R are three points on the circumference of a circle such that QR is a diameter and PQ = PR. If the radius of the circle is 7 cm. then the length of PQ is:

SSC CHSL 2021
A)

7 cm

B)

14√2 cm

C)

7√2 cm

D)

7√3 cm

128)

AB and CD are two chords of a circle that intersects at E inside the circle. If ∠BEC = 125° and ∠EBD = 28°, then what is the measure of ∠BAC?

SSC CHSL 2021
A)

87°

B)

55°

C)

56°

D)

97°

129)

Let O be the centre of a circle. PA and PB are tangents to the circle from a point P outside the circle and A and B are points on the circle. If angle APB = 50°, then angle OAB is equal to:

SSC CHSL 2021
A)

25° 

B)

40°

C)

50°

D)

20°

130)

AB and AC are tangents to a circle with centre O from an external point A. The tangents AB and AC touch the circle at B and C, respectively, such that ∠BAC = 118°. Find the measures of ∠OCB.

SSC CHSL 2021
A)

59° 

B)

62°

C)

60°

D)

54°

131)

In a circle with centre O, a 6 cm long chord is at a distance 4 cm from the centre. Find the length of the diameter.

SSC CHSL 2021
A)

5 cm

B)

10 cm

C)

14 cm

D)

7 cm

132)

Chord AB and diameter CD of a circle meet at the point P, outside the circle when the produced, If PB = 8 cm, AB = 12 cm and distance of P from the centre of the circle is 18 cm, the radius (in cm) of the circle is closest to:

SSC CHSL 2021
A)

12

B)

12.8

C)

12.4

D)

13

133)

Two chords AB and CD of a circle with centre O intersect each other at P. If \(\angle APC = 95^0\) and \(\angle AOD = 110^0\) , then \(\angle BOC\) is:

SSC CGL 2020
A)

\(70^0\)

B)

\(60^0\)

C)

\(65^0\)

D)

\(55^0\)

134)

Diameter AB of a circle with centre O is produced to a point P such that PO = 16.8 cm. PQR is a secant which intersects the circle at Q and R, such that PQ = 12 cm and PR = 19.2 cm.The length of AB (in cm.) is :

SSC CGL 2020
A)

15.8

B)

14.4

C)

15.2

D)

14.2

135)

In the given figure, \(\angle KLN = 58^0\), then \(\angle KMN=\space?\)

SSC CGL 2020
A)

\(26^0\)

B)

\(42^0\)

C)

\(32^0\)

D)

\(58^0\)

136)

In the figure, two circles with centres P and Q touch externally at R. Tangents AT and BT meet the common tangent TR at T. If AP = 6 cm and PT = 10 cm, then BT = ?

SSC CGL 2020
A)

8 cm

B)

12 cm

C)

10 cm

D)

6 cm

137)

Two tangents PA and PB are drawn to a circle with centre O from an external point P. If \(\angle OAB = 30^0\), then \(\angle APB\) is:

SSC CGL 2020
A)

\(120^0\)

B)

\(30^0\)

C)

\(60^0\)

D)

\(15^0\)

138)

In the given figure, if \(\angle APO = 35^0\), then which of the following options is correct?

SSC CGL 2020
A)

\(\angle BPO = 35^0\)

B)

\(\angle APB = 80^0\)

C)

\(\angle APB = 60^0\)

D)

\(\angle BPO = 55^0\)

139)

In the given figure, if AB = 10 cm, CD = 7 cm, SD = 4 cm and AS = 5 cm, then BC = ?

SSC CGL 2020
A)

8 cm

B)

7.5 cm

C)

9 cm

D)

6 cm

140)

A, B and C are three points on a circle such that the angle subtended by the chords AB and AC at the centre O are \(80^0\) and \(120^0\), respectively. The value of \(\angle BAC\) is:

SSC CGL 2020
A)

\(70^0\)

B)

\(85^0\)

C)

\(80^0\)

D)

\(75^0\)

141)

In the given figure, MP is a tangent to a circle with center A and NQ is a tangent to a circle with center B. If MP = 15 cm, NQ = 8 cm, PA = 17 cm and BQ = 10 cm, then AB is:

SSC CGL 2020
A)

28 cm.

B)

14 cm.

C)

13.5 cm.

D)

23 cm.

142)

AB is a diameter of a circle with centre O. The tangent at a point C on the circle meets AB produced at Q. If \(\angle CAB=42^0\), then what is the measure of \(\angle CQA\)?

SSC CGL 2020
A)

\(17^0\)

B)

\(5^0\)

C)

\(6^0\)

D)

\(7^0\)

143)

PAQ is a tangent to circle with centre O, at a point A on it. AB is a chord such that \(\angle BAQ=x^0 (x<90)\). C is a point on the major arc AB such that \(\angle ACB = y^0\). If \(\angle ABO = 32^0\), then the value of x + y is:

SSC CGL 2020
A)

112

B)

98

C)

110

D)

116

144)

In a circle, AB is a the diameter and CD is a chord. AB and CD produced meet at a point P, outside the circle. If PD = 15.3 cm, CD = 11.9 cm and AP = 30.6 cm,then the radius of the circle is is:

SSC CGL 2020
A)

7.5 cm

B)

8.5 cm

C)

9 cm

D)

8 cm

145)

From an external point P, a tangent PQ is drawn to a circle, with the centre O, touching the circle at Q. If the distance of P from the centre is 13 cm and length of the tangent PQ is 12 cm, then the radius of the circle is:

SSC CGL 2020
A)

3 cm

B)

12.5 cm

C)

5 cm

D)

10 cm

146)

In a circle, chords PQ and TS are produced to meet at R. If RQ = 14.4 cm, PQ = 11.2 cm, and SR = 12.8 cm, then the length of chord TS is:

SSC CGL 2020
A)

18 cm

B)

14.2 cm

C)

12.4 cm

D)

16 cm

147)

In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is:

SSC CGL 2019
A)

8.35 cm.

B)

9 cm.

C)

10.15 cm.

D)

9.25 cm.

148)

In circle with centre O, AC and BD are two chords. AC and BD meet at E when produced. If AB is the diameter and \(\angle AEB=68^0\), then the measure of \(\angle DOC\) is :

SSC CGL 2019
A)

\(32^0\)

B)

\(30^0\)

C)

\(22^0\)

D)

\(44^0\)

149)

A circle touches the side BC of \(\triangle ABC\) at D and AB and AC are produced to E and F, respectively. If AB = 10 cm, AC = 8.6 cm and BC =6.4 cm, then BE =?

SSC CGL 2019
A)

3.2 cm

B)

3.5 cm

C)

2.2 cm

D)

2.5 cm

150)

Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is \(5\sqrt{13}cm\). What is the distance (in cm) between the chords?

SSC CGL 2019
A)

2

B)

3

C)

2.5

D)

1.5

151)

Chord AB of a circle is produced to a point P, and is a point on the circle such that PC is a tangent to the circle. If PC = 18 cm, and BP = 15 cm, then AB is equal to:

SSC CGL 2019
A)

5.8 cm

B)

6.2 cm

C)

6.6 cm

D)

8.5 cm

152)

If angle of sector is 60°, radius is 3.5 cm then length of the arc is

Class 10 Maths
A)

3.66 cm

B)

3.56 cm

C)

1.66 cm

D)

3 cm

153)

In the figure, PA is a tangent from an external point P to the circle with centre O. If \(\angle POB = 110 ^{\circ}\), then measure of \(\angle APO\) is:

SSC CGL 2020
A)

\(30 ^{\circ}\)

B)

\(25^{\circ}\)

C)

\(20 ^{\circ}\)

D)

\(40 ^{\circ}\)

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