**SSC Mathematics Topic Wise Solved Papers – Geometry**

SSC Mathematics Previous Year Question Papers English Reasoning General Awareness

**1. ABCD is a quadrilateral in which diagonal BD = 64 cm, AL ⊥ BD and CM ⊥ BD, such that AL = 13.2 cm and CM = 16.8 cm. The area of the quadrilateral ABCD in square centimetres is (SSC Sub. Ins. 2012)**

(a) 537.6

(b) 960.0

(c) 422.4

(d) 690.0

**2. In ∆ABC, ∠B = 60°, ∠C = 40° If AD bisects ∠BAC and AE ⊥ BC, then ∠EAD is (SSC Sub. Ins. 2012)**

(a) 40°

(b) 80°

(c) 10°

(d) 20°

**3. In the figure below, if AB || CD and CE ⊥ED then the value of x is (SSC Sub. Ins. 2012)**

(a) 37

(b) 45

(c) 53

(d) 63

**4. PA and PB are two tangents drawn from an external point P to a circle with centre O where the points A and B are the points of contact. The quadrilateral OAPB must be (SSC Sub. Ins. 2012) **

(a) a square

(b) concylic

(c) a rectangle

(d) a rhombus

**5. G is the centroid of ∆ABC. If AG = BC, then ∠BGC is (SSC Sub. Ins. 2012) **

(a) 60°

(b) 120°

(c) 90°

(d) 30°

**6. In the following figure, if OA = 10 and AC = 16, then OB must be (SSC Sub. Ins. 2012)**

(a) 3

(b) 4

(c) 5

(d) 6

**7. If in ∆ABC, ∠A = 90°, BC = a, AC = b and AB = c, then the value of tan B + tan C is (SSC Sub. Ins. 2012)**

**8. ABC is a right angled triangle, right angled at C and p is the length of the perpendicular from C on AB. If a, b and c are the lengths of the sides BC, CA and AB respectively, then (SSC CHSL 2012)**

**9. If ∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm, then AB is: (SSC CHSL 2012)**

(a) 5 cm

(b) 10 cm

(c) 5√2 cm

(d) 2.5 cm

**10. The length of the two sides forming the right angle of a right-angled triangle are 6 cm and 8 cm. The length of its circum-radius is: (SSC CHSL 2012)**

(a) 5 cm

(b) 7 cm

(c) 6 cm

(d) 10 cm

**11. The length of radius of a circumcircle of a triangle having sides 3 cm, 4 cm and 5 cm is: (SSC CHSL 2012)**

(a) 2 cm

(b) 2.5 cm

(c) 3 cm

(d) 1.5 cm

**12. A, O, B are three points on a line segment and C is a point not lying on AOB. If ∠AOC = 40° and OX, OY are the internal and external bisectors of ∠AOC respectively, then ∠BOY is (SSC CGL 1st Sit. 2012)**

(a) 70°

(b) 80°

(c) 72°

(d) 68°

**13. In the following figure, O is the centre of the circle and XO is perpendicular to OY. If the area of the triangle XOY is 32, then the area of the circle is (SSC CGL 1st Sit. 2012)**

(a) 64 π

(b) 256 π

(c) 16 π

(d) 32 π

**14. The side BC of ∆ ABC is produced to D. If ∠ACD = 108° and ∠B = 1/2 ∠A then ∠A is 2 (SSC CGL 1st Sit. 2012)**

(a) 36°

(b) 72°

(c) 108°

(d) 59°

**15. Two circles of radii 4 cm and 9 cm respectively touch each other externally at a point and a common tangent touches them at the points P and Q respectively. They the area of a square with one side PQ, is (SSC CGL 1st Sit. 2012)**

(a) 97 sq. cm

(b) 194 sq. cm

(c) 72 sq.cm

(d) 144 sq.cm

**16. Two tangents are drawn from a point Pto a circle at A and B. 0 is the centre of the circle. If ∠AOP = 60°, then ∠ APB is (SSC CGL 1st Sit. 2012)**

(a) 120°

(b) 90°

(c) 60°

(d) 30°

**17. If each intetior angle is double of each exterior angle of a regular polygon with n sides, then the value of n is (SSC CGL 1st Sit. 2012)**

(a) 8

(b) 10

(c) 5

(d) 6

**18. If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR= 120°, then the length of QS, in cm, is**

**(SSC CGL 1st Sit. 2012)**

(a) 4

(b) 6

(c) 3

(d) 5

**19. The angle formed by the hour-hand and the minute-hand of a clock at 2:15 p.m. is (SSC CGL 1st Sit. 2012)**

(a) 27°

(b) 45°

(c) 22

(d) 30°

**20. Two sides of a triangle are of length 4 cm and 10 cm. If the length of the third side is ‘a’ cm. then (SSC CGL 1st Sit. 2012)**

(a) a>5

(b) 6≤a≤12

(c) a<5

(d) 6<a< 14

**21. In ∆ABC, AD is the median and AD = 1/2 BC.If ∠BAD = 30°, then measure of ∠ACB is (SSC CGL 1st Sit. 2012)**

(a) 90°

(b) 45°

(c) 30°

(d) 60°

**22. The perimeter of an isosceles, right-angled triangle is 2p unit. The area of the same triangle is: (SSC CGL 2nd Sit. 2012)**

**23. ∆ABC and ∆DEF are similar and their areas be respectively 64 cm ^{2} and 121 cm^{2}. If EF = 15.4 cm, BC is: (SSC CGL 2nd Sit. 2012)**

(a) 12.3 cm

(b) 11.2 cm

(c) 12.1 an

(d) 11.0 cm

**24. If G is the centroid of ∆ABC and AG = BC, then ∠BGC is: (SSC CGL 2nd Sit. 2012)**

(a) 75°

(b) 45°

(c) 90°

(d) 60°

**25. By decreasing 15° of each angle of a triangle, the ratios of their angles are 2 : 3 : 5. The radian measure of greatest angle is: (SSC CGL 2nd Sit. 2012)**

**26. O is the circum centre of the triangle ABC with circumradius 13 cm. Let BC = 24 cm and OD is perpendicular to BC. Then the length of OD is: (SSC CGL 2nd Sit. 2012)**

(a) 7 cm

(b) 3 cm

(c) 4 cm

(d) 5 on

**27. D and E are the mid-points of AB and AC of ∆ABC; BC is produced to any point P; DE, DP and EP are joined. Then, (SSC CGL 2nd Sit. 2012)**

**28. The length of the common chord of two circles of radii 15 cm and 20 cm whose centres are 25 cm apart is (in cm): (SSC CGL 2nd Sit. 2012)**

(a) 20

(b) 24

(c) 25

(d) 15

**29. AB is a diameter of a circle with centre O. CD is a chord equal to the radius of the circle. AC and BD are produced to meet at P. Then the measure of ∠APB is: (SSC CGL 2nd Sit. 2012)**

(a) 120°

(b) 30°

(c) 60°

(d) 90°

**30. R and r are the radius of two circles (R > r). If the distance between the centre of the two circles be d, then length of common tangent of two circles is: (SSC CGL 2nd Sit. 2012)**

**31. P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersect the circle at points A and B in such a way that PA = 9 cm and AB = 7 cm. The radius of the circle is: (SSC CGL 2nd Sit. 2012)**

(a) 5.5 on

(b) 5 cm

(c) 4 cm

(d) 4.5 cm

**32. The perimeters of two similar triangle ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is: (SSC CGL 2nd Sit. 2012) **

(a) 25 cm

(b) 10 cm

(c) 15 cm

(d) 20 cm

**33. In an obtuse-angled triangle ABC, ∠A is the obtuse angle and O is the orthocenter. If ∠BOC = 54°, then ∠BAC is (SSC CGL 1st Sit. 2012)**

(a) 108°

(b) 126°

(c) 136°

(d) 116°

**34. If the ratio of areas of two similar triangles is 9:16, then the ratio of their corresponding sides is (SSC CGL 1st Sit. 2012)**

(a) 3:5

(b) 3:4

(c) 4:5

(d) 4:3

**35. Let BE and CF the two medians of a ∆ABC and G be their intersection. Also let EF cut AG at O. Then AO : OG is (SSC CGL 1st Sit 2012)**

(a) 1:1

(b) 1:2

(c) 2:1

(d) 3:1

**36. If S is the circumcentre of ∆ABC and ∠A = 50°, then the value of ∠BCS is (SSC CGL 1st Sit. 2012)**

(a) 20°

(b) 40°

(c) 60°

(d) 80°

**37. AC and BC are two equal chords of a circle. BA is produced to any point P and CP, when joined cuts the circle at T. Then (SSC CGL 1st Sit. 2012)**

(a) CT: TP=AB : CA

(b) CT:TP = CA:AB

(c) CT: CB = CA: CP

(d) CT:CB = CP:CA

**38. PQ is a direct common tangent of two circles of radii r _{1} and r_{2} touching each other externally at A. Then the value of **

**39. BC is the chord of a circle with centre O. A is a point on major arc BC as shown in the above figure. What is the value of ∠BAC + ∠OBC ? (SSC CGL 1st Sit 2012)**

(a) 120°

(b) 60°

(c) 90°

(d) 180°

**40. Two circles with radii 5 cm and 8 cm touch each other externally at a point A. If a straight line through the point A cuts the circles at points P and Q respectively, then AP: AQ is (SSC CGL 1st Sit 2012)**

(a) 8:5

(b) 5:8

(c) 3:4

(d) 4:5

**41. If I is the In-centre of ∆ABC and ∠A = 60°, then the value of ∠BIC is (SSC CGL 1st Sit. 2012)**

(a) 100°

(b) 120°

(c) 150°

(d) 110°

**42. The external bisectors of ∠B and ∠C of ∆ABC meet at point P. If ∠BAC = 80°, then ∠BPC is (SSC CGL 1st Sit 2012)**

(a) 50°

(b) 40°

(c) 80°

(d) 100°

**43. When a pendulum of length 50 cm oscillates, it produces an arc of 16 cm. The angle so formed in degree measure is (approx) (SSC CGL 1st Sit 2012)**

(a) 18°25′

(b) 18°35′

(c) 18°20′

(d) 18°08′

**44. A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres? (SSC CGL 1st Sit 2012)**

(a) 91.64 metres

(b) 90.46 metres

(c) 89.64 metres

(d) 93.64 metres

**45. The radius of the circumcircle of the triangle made by x-axis, y-axis and 4x + 3y = 12 is (SSC CGL 2nd Sit 2012)**

(a) 2 unit

(b) 2.5 unit

(c) 3 unit

(d) 4 unit

**46. The length of the circum-radius of a triangle having sides of lengths 12 cm, 16 cm and 20 cm is (SSC CGL 2nd Sit. 2012)**

(a) 15 cm

(b) 10 cm

(c) 18 cm

(d) 16 cm

**47. If D is the mid-point of the side BC of ∆ABC and the area of ∆ABD is 16 cm2, then the area of ∆ABC is (SSC CGL 2nd Sit 2012) **

(a) 16 cm2

(b) 24 cm2

(c) 32 cm2

(d) 48 cm2

**48. ABC is a triangle. The medians CD and BE intersect each other at O. Then A ODE: ∆ABC is (SSC CGL 2nd Sit. 2012)**

(a) 1:3

(b) 1:4

(c) 1:6

(d) 1:12

**49. If P, R, Tare the area of a parallelogram, a rhombus and a triangle standing on the same base and between the same parallels, which of the following is true? (SSC CGL 2nd Sit. 2012)**

(a) R<P<T

(b) P>R>T

(c) R = P = T

(d) R = P = 2T

**50. AB is a diameter of the circumcircle of ∆APB; N is the foot of the perpendicular drawn from the point P on AB. If AP = 8 cm and BP = 6 cm, then the length of BN is (SSC CGL 2nd Sit. 2012)**

(a) 3.6 cm

(b) 3 cm

(c) 3.4 cm

(d) 3.5 cm

**51. Two circles with same radius r intersect each other and one passes through the centre of the other. Then the length of the common chord is (SSC CGL 2nd Sit. 2012)**

**52. The bisector of ∠A of ∆ABC cuts BC at D and the circumcircle of the triangle at E. Then (SSC CGL 2nd Sit. 2012)**

(a) AB: AC = BD: DC

(b) AD: AC = AE: AB

(c) AB:AD=AC:AE

(d) AB: AD =AE:AC

**53. Two circles intersect each other at P and Q. PA and PB are two diameters. Then ∠AQB is (SSC CGL 2nd Sit. 2012)**

(a) 120°

(b) 135°

(c) 160°

(d) 180°

**54. O is the centre of the circle passing through the points A, B and Csuch that ∠BAO= 30°, ∠BCO= 40° and ∠AOC = x°. What is the value of x ? (SSC CGL 2nd Sit. 2012)**

(a) 70°

(b) 140°

(c) 210°

(d) 280°

**55. A and B are centres of the two circles whose radii are 5 cm and 2 cm respectively. The direct common tangents to the circles meet AB extended at P. Then P divides AB. (SSC CGL 2nd Sit. 2012)**

(a) externally in the ratio 5:2

(b) internally in the ratio 2:5

(c) . internally in the ratio 5:2

(d) externally in the ratio 7:2

**56. A wheel rotates 3.5 times in one second. What time (in seconds) does the wheel take to rotate 55 radian of angle? (SSC CGL 2nd Sit. 2012)**

(a) 1.5

(b) 2.5

(c) 3.5

(d) 4.5

**57. If area of an equilateral triangle is A and height b, then**

**58. Triangle PQR circumscribes a circle with centre O and radius rcm such that ∠PQR = 90°. If PQ = 3 cm, QR= 4 cm, then the value of r is : (SSC Sub. Ins. 2013)**

(a) 2

(b) 1.5

(c) 2.5

(d) 1

**59. In the following figure. AB be diameter of a circle whose centre is O. If ∠AOE = 150°. ∠DAO = 51° then the measure of∠CBE is: (SSC Sub. Ins. 2013)**

**60. The areas of two similar triangles ABC and DEF are 20 cm ^{2} and 45 cm^{2} respectively. If AB = 5 cm. then DE is equal to: (SSC Sub. Ins. 2013)**

(a) 6.5 cm

(b) 7.5 cm

(c) 8.5 cm

(d) 5.5 cm

**61. In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ ACB = 80°, then the measure of ∠ABC is: (SSC Sub. Ins. 2013)**

(a) 31°

(b) 33°

(c) 35°

(d) 29°

**62. In∆ABC ∠A+∠B = 145° and ∠C+2∠B= 180°. Statewhich one of the following relations is true? (SSC Sub. Ins. 2013)**

(a) CA=AB

(b) CA<AB

(c) BC>AB

(d) CA>AB

**63. From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to diameter of the circle, then ∠APB is (SSC CHSL 2013)**

(a) 60°

(b) 45°

(c) 90°

(d) 30°

**64. A chord 12 cm long is drawn in a circle of diameter 20 cm. The distance of the chord from the centre is (SSG CHSL 2013)**

(a) 16 cm

(b) 8 cm

(c) 6 cm

(d) 10 cm

**65. 360 sq. cm and 250 sq. cm are the areas of two similar triangles. Ifthe length of one of the sides of the first triangle be 8 cm, then the length of the corresponding side of the 2nd triangle is (SSC CHSL 2013)**

**66. If in ∆ABC, ∠ABC = 5∠ACB and ∠ BAC = 3 ∠ACB, then ∠ABC= (SSC CHSL 2013)**

(a) 120°

(b) 130°

(c) 80°

(d) 100°

**67. The perpendiculars, drawn from the vertices to the opposite sides of a triangle, meet at the point whose name is (SSC CHSL 2013)**

(a) orthocentre

(b) incentre

(c) circumcentre

(d) centroid

**68. If ∆ABC is similar to ADEF such that BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 cm2, then the area of ADEF is: (SSC CGL 1st Sit 2013)**

(a) 54 cm2

(b) 66 cm2

(c) 78 cm2

(d) 96 cm2

**69. A chord AB of a circle C _{1} of radius (√3 +1) cm touches a circle C_{2} which is concentric to C_{1}. If the radius of C_{2} is**

**70. In a triangle ABC, AB = AC, ∠BAC = 40°. Then the external angle at B is: (SSC CGL 1st Sit 2013)**

(a) 80°

(b) 90°

(c) 70°

(d) 110°

**71. A chord of length 30 cm is at a distance of 8 cm from the centre of a circle. The radius of the circle is: (SSC CGL 1st Sit. 2013)**

(a) 19

(b) 17

(c) 23

(d) 21

**72. If ABCD be a rectangle and P, Q, R, S be the mid points**

**73. P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet eahc other at the point S. If ∠PSQ = 20°, ∠PRQ = ? (SSC CGL 1st Sit 2013)**

(a) 100°

(b) 80°

(c) 200°

(d) 160°

**74. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is: (SSC CGL 1st Sit 2013)**

(a) 10cm

(b) 11cm

(c) 12 cm

(d) 13 cm

**75. ABC is an isosceles triangle such that AB = AC and ∠B = 35°. AD is the median to the base BC. Then ∠BAD is: (SSC CGL 1st Sit 2013)**

(a) 55°

(b) 70°

(c) 35°

(d) 110°

**76. ABCD is a cyclic trape∠ium with AB || DC and AB = and diameter of the circle. If ∠CAB = 30° then ∠ADC is (SSC CGL 2nd Sit. 2013)**

(a) 60°

(b) 120°

(c) 150°

(d) 30°

**77. ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect atD. If∠BDC = 50°, then ∠A is (SSC CGL 2nd Sit. 2013)**

(a) 100°

(b) 90°

(c) 120°

(d) 60°

**78. AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting, AB produced at C such that BC = OD. If ∠BCD = 20°, then ∠AOD = ? (SSC CGL 2nd Sit. 2013)**

(a) 20°

(b) 30°

(c) 40°

(d) 60°

**79. In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is (SSC CGL 2nd Sit. 2013)**

(a) 9 cm

(b) 7 cm

(c) 23 cm

(d) 11cm

**80. ABC is a right angled triangle, B being the right angle. Mid points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’ B’B to the area of the triangle ABC is (SSC CGL 2nd Sit. 2013)**

(a) 1:2

(b) 2:3

(c) 3:4

(d) None of the above

**81. In a triangle ABC, the side BC is extended up to D. Such that CD = AC, if ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is (SSC CGL 2nd Sit. 2013)**

(a) 35°

(b) 60°

(c) 40°

(d) 45°

**82. Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the greater circle which is outside the inner circle of length.**

**83. ABCD is a cyclic quadrilateral AB and DC are produced to meet at P. If ∠ADC = 70° and ∠DAB = 60°, then the ∠PBC + ∠PCB is (SSC CGL 2nd sit. 2013)**

(a) 130°

(b) 150°

(c) 155°

(d) 180°

**84. From a point P which is at a distance of 13 cm from center O of a circle of radius 5 cm, in the same plane, a pair of tangents PQ and PR are drawn to the circle. Area of quadrilateral PQOR is (SSC CGL 2nd Sit. 2013)**

(a) 65 cm2

(b) 60 cm2

(c) 30 cm2

(d) 90 cm2

**85. If the arcs of square length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is (SSC CGL 2nd Sit. 2013)**

(a) 3:4

(b) 4:5

(c) 5:4

(d) 3:5

**86. N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is (SSC CGL 1st Sit. 2013)**

**87.**

**88. If G is the centroid of ∆ABC and ∆ABC = 48cm2, then the area of ∆BGC is (SSC CGL 1st Sit. 2013)**

(a) 16 cm2

(b) 24 cm2

(c) 32 cm2

(d) 8 cm2

**89. The diagonals AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that (SSC CGL 1st Sit. 2013)**

(a) AP.BP = CP.DP

(b) AP.CD = AB.CP

(c) BP. AB = CD. CP

(d) AP. CP = BP. DP

**90. If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)**

(a) 55°

(b) 60°

(c) 65°

(d) 50°

**91. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is (SSC CGL 1st Sit. 2013)**

(a) 65 m

(b) 70 m

(c) 72 m

(d) 60 m

**92. A, B, C, D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. ∠BAC = 130° and ∠ECD= 20°. ∠BAC is (SSC CGL 1st Sit. 2013)**

(a) 100°

(b) 110°

(c) 120°

(d) 90°

**93. In a triangle, if three altitudes are equal, then the triangle is (SSC CGL 1st Sit. 2013)**

(a) Right

(b) Isoceles

(c) Obtuse

(d) Equilateral

**94. A, B, P are three points on a circle having centre O. If ∠OAP = 25° and ∠OBP = 35°, then the measure of ∠AOB is (SSC CGL 1st Sit. 2013)**

(a) 120°

(b) 60°

(c) 75°

(d) 150°

**95.**

**96. The length of tangent (upto the point of contact) drawn from an external point P to a circle of radius 5 cm is 12 cm. The distance of P from the centre of the circle is (SSC CGL Ist. Sitt 2013) **

(a) 11cm

(b) 12cm

(c) 13 cm

(d) 14 cm

**97. ABCD is a cyclic quadrilateral, AB is a diameter of the circle. If ∠ACD = 50°, the value of ∠BAD is (SSC CGL 1st Sit. 2013)**

(a) 30°

(b) 40°

(c) 50°

(d) 60°

**98. Two circles of equal radikouch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. The relation of TQ and TR is (SSC CGL 1st Sit. 2013)**

(a) TQ<TR

(b) TQ>TR

(c) TQ = 2TR

(d) TQ = TR

**99. When two circles touch externally, the number of common tangents are (SSC CGL 1st Sit. 2013)**

(a) 4

(b) 3

(c) 2

(d) 1

**100. D and E are the mid-points of AB and AC of ∆ABC.If ∠A= 80°, ∠C = 35°, then ∠EDB is equal to (SSC CGL 1st Sit. 2013)**

(a) 100°

(b) 115°

(c) 120°

(d) 125°

**101. If the inradius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle in sq. cm is (SSC CGL 1st Sit. 2013)**

(a) 48

(b) 64

(c) 100

(d) 96

**102. The sum of three altitudes of a triangle is (SSCCGL 1st Sit. 2013)**

(a) equal to the sum of three sides

(b) less than the sum of sides

(c) greater than the sum of sides

(d) twice the sum af sides

**103. In ∆ABC, ∠A+ ∠B = 65°, ∠B + ∠C = 140°, then find ∠B. (SSC CGL 1st Sit. 2013)**

(a) 40°

(b) 25°

(c) 35°

(d) 20°

**104. The length of the tangent drawn to a circle of radius 4 cm from a point 5 cm away from the centre of the circle is (SSC CGL 1st Sit 2013)**

(a) 3 cm

(b) 4√2 on

(c) 5√2 cm

(d) 3√2 an

**105. A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC ⊥ BD, ∠CAD = θ. Then the angle ∠ABC = (SSC CGL 1st Sit 2013)**

**106. The height of an equilateral triangle is 15 cm. The area of the triangle is (SSC CGL 1st Sit. 2013)**

(a) 50√3 sq.cm.

(b) 70√3 sq. cm.

(c) 75√3 sq.cm.

(d) 150√3 sq.cm.

**107. Two parallel chords of a circle, of diameter 20 cm lying on the opposite sides ofthe centre are of lengths 12 cm and 16 cm. The distance between the chords is (SSC CGL 1st Sit. 2013) **

(a) 16 cm

(b) 24 cm

(c) 14 cm

(d) 20 cm

**108. In ∆ABC, DE || AC. D and E are two points on AB and CB respectively. IfAB= 10 cm and AD 24 cm, then BE: CE is (SSC CGL 1st Sit 2013)**

(a) 2:3

(b) 2:5

(c) 5:2

(d) 3:2

**109. A, B and C are the three points on a circle such that the an gles subtended by the chords AB and AC at the centre O are 90° and 110° respectively. ∠BAC is equal to (SSC CGL 1st Sit. 2013)**

(a) 70°

(b) 80°

(c) 90°

(d) 100°

**110.**

**111. In a ∆ABC, AD, BE and CF are three medians. The perimeter of ∆ABC is always (SSC Sub. Ins. 2014)**

**112.**

**113. Two circles with radii 25 cm and 9 cm touch each other externally. The length of the direct common tangent is (SSC Sub. Ins. 2014)**

(a) 34 cm

(b) 30 cm

(c) 36 cm

(d) 32 cm

**114. IfAB= 5 cm, AC = 12 and AB ⊥ AC then the radius of the circumcircle of ∆ABC is (SSC Sub. Ins. 2014)**

(a) 6.5 cm

(b) 6 cm

(c) 5 cm

(d) 7 cm

**115. The sum of the interior angles of a polygon is 1444°. The number of sides of the polygon is (SSC CHSL 2014) **

(a) 6

(b) 9

(c) 10

(d) 12

**116. In ∆ABC, D and E are two points on the sides AB and AC**

**117. The perimeters of two similar triangles ∆ABC and APQR are 3 6 cm and 24 cm respectively. If PQ = 10 cm, the AB is (SSC CHSL 2014)**

(a) 15 cm

(b) 12 cm

(c) 14 cm

(d) 26 cm

**118. If the sides of a right angled triangle are three consecutive integers, then the length ofthe smallest side is (SSC CHSL 2014)**

(a) 3 units

(b) 2 units

(c) 4 units

(d) 5 units

**119. Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)**

(a) 1.50 cm

(b) 2.25 cm

(c) 4.50 cm

(d) 9.00 cm

**120. In a quadrilateral ABCD, the bisectors of ∠A and ∠B meet at O. If ∠C = 70° and ∠D =130°, then measure of ∠AOB is (SSC CGL 1st Sit. 2014)**

(a) 40°

(b) 60°

(c) 80°

(d) 100°

**121. In ∆ABC, E and D are points on sides AB and AC respectively such that ∠ABC = ∠ADE. If AE = 3 cm, AD = 2 cm and EB = 2 cm, then length of DC is (SSC CGL 1st Sit. 2014)**

(a) 4 cm

(b) 4.5 cm

(c) 5.0 cm

(d) 5.5 cm

**122. In a circle with centre O, AB is a chord, and AP is a tangent to the circle. If ∠AOB = 140°, then the measure of ∠PAB is (SSC CGL 1st Sit. 2014)**

(a) 35°

(b) 55°

(c) 70°

(d) 75°

**123. In ∆ABC, ∠A<∠B. The altitude to the base divides vertex**

**124. If O is the in-centre of ∆ABC; if ∠BOC = 120°, then the measure of ∠BAC is (SSC CGL 1st Sit. 2014)**

(a) 30°

(b) 60°

(c) 150°

(d) 75°

**125. Two parallel chords of a circle of diameter 20 cm are 12 cm and 16 cm long. If the chords are in the same side of the centre, then the distance between them is (SSC CGL 1st Sit. 2014)**

(a) 28 cm

(b) 2 cm

(c) 4 cm

(d) 8 cm

**126. The interior angle of a regular polygon is 140°. The number of sides of that polygon is (SSC CGL 1st Sit. 2014)**

(a) 9

(b) 8

(c) 7

(d) 6

**127. If two circles ofradii 9 cm and 4 cm touch externally, then the length of a common tangent is (SSC CGL 1st Sit. 2014)**

(a) 5 cm

(b) 7 cm

(c) 8 cm

(d) 12 cm

**128. If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB=19 cm and AC=22 cm then the length of BC is : (SSC Sub. Ins. 2015)**

(a) 20.5 cm

(b) 19.5 cm

(c) 13 cm

(d) 26 cm

**129. Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Then the distance between their centres is: (SSC Sub. Ins. 2015)**

(a) 15 cm

(b) 10 cm

(c) 8 cm

(d) 13.3 cm

**130. Two isosceles triangles have equal vertical angles and their areas are in the ratio 9:16. Then the ratio of their corresponding heights is: (SSC Sub. Ins. 2015)**

(a) 4.5:8

(b) 8:4.5

(c) 3:4

(d) 4:3

**131. The perimetres oftwo similar triangles are 30 cm and 20cm respectively. If one side ofthe first triangle is 9cm. Determine the corresponding side of the second triangle: (SSC Sub. Ins. 2015)**

(a) 15 cm

(b) 5 cm

(c) 6 cm

(d) 13.5 cm

**132. The diagonal of a quadrilateral shaped field is 24m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 13m. The area of the field is: (SSC Sub. Ins. 2015)**

(a) 252 m^{2}

(b) 1152 m^{2}

(c) 96 m^{2}

(d) 156 m^{2}

**133. In ∆ABC, ∠B = 60°, and ∠C = 40°; AD and AE are respectively the bisector of ∠A and perpendicular on BC. The measure of ∠EAD is: (SSC CHSL 2015)**

(a) 9°

(b) 11°

(c) 12°

(d) 10°

**134. ABCD is a square. Draw a triangle QBC on side BC considering BC as base and draw a triangle PAC on AC as its base such that ∆QBC ~ ∆PAC.**

**135. The distance between centres of two circles of radii 3 cm and 8 cm is 13 cm. Ifthe points of contact of a direct common tangent to the circles are P and Q, then the length of the lien segment PQ is: (SSC CHSL 2015)**

(a) 11.9 cm

(b) 11.5 cm

(c) 12 cm

(d) 11.58 cm

**136. In ∆ABC, AB = BC = K, AC = √2 K, then ∆ABC is a: (SSC CHSL 2015)**

(a) Isosceles triangle

(b) Right angled triangle

(c) Equilateral triangle

(d) Right isosceles triangle

**137. Two circles of radii 5 cm and 3 cm touch externally, then the ratio in which the direct common tangent to the circles divides externally the line joining the centres of the circles is: (SSC CHSL 2015)**

(a) 2.5:1.5

(b) 1.5:2.5

(c) 3:5

(d) 5:3

**138. In ∆ABC, a line through A cuts the side BC at D such that BD: DC = 4 :5. If the area of ∆ABD = 60 cm2, then the area of ∆ADC is (SSC CGL 1st Sit. 2015)**

(a) 50 cm^{2}

(b) 60 cm^{2}

(c) 75 cm^{2}

(d) 90 cm^{2}

**139. A tangent is drawn to a circle of radius 6cm from a point situated at a distance of 10 cm from the centre of the circle. The length of the tangent will be (SSC CGL 1st Sit. 2015)**

(a) 4 cm

(b) 5 on

(c) 8 cm

(d) 7 cm

**140. Two poles of height 7 m and 12 m stand on a plane ground. If the distance between their feet is 12 m, the distance between their top will be (SSC CGL 1st Sit. 2015) **

(a) 13m

(b) 19m

(c) 17m

(d) 15m

**141. The measure of an angle whose supplement is three times as large as its complement, is (SSC CGL 1st Sit. 2015)**

(a) 30°

(b) 45°

(c) 60°

(d) 75°

**142. The sides of a triangle having area 7776 sq. cm are in the ratio 3:4:5. The perimeter of the triangle is (SSC CGL 1st Sit. 2015)**

(a) 400cm

(b) 412cm

(c) 424 cm

(d) 432 cm

**143. Two chords of length a unit and b unit of a circle make angles 60° and 90° at the centre of a circle respectively, then the correct relation is (SSC CGL 1st Sit. 2015)**

**144. In a parallelogram PQRS, angle P is four times of angle Q, then the measure of ∠R is (SSC CGL 1st Sit. 2015)**

(a) 36°

(b) 72°

(c) 130°

(d) 144°

**145. If a clock started at noon, then the angle turned by hour hand at 3.45 PM is (SSC CGL 1st Sit. 2015)**

**146. Let C, and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm and 5 cm then area of C1 to area of C2 is (SSC CGL 1st Sit. 2015)**

**147. If the three angles of a triangle are:**

(a) scalene

(b) isosceles

(c) right angled

(d) equilateral

**148. If the number of vertices, edges and faces of a rectangular parallelopiped are denoted by v, e and f respectively, the value of (v – e + f) is (SSC CGL 1st Sit. 2015)**

(a) 4

(b) 2

(c) 1

(d) 0

**149. If the altitude of an equilateral triangle is 12√3 cm, then its area would be: (SSC CGL 1st Sit. 2015)**

**150. Internal bisectors of ∠Q and ∠R of APQR intersect at O. If ∠ROQ = 96° then the value of ∠RPQ is: (SSC CGL 1st Sit. 2015)**

(a) 12°

(b) 6°

(c) 36°

(d) 24°

**151. If the measure of three angles ofa triangle are in the ratio 2 : 3 : 5, then the triangle is : (SSC CGL 1st Sit. 2015)**

(a) equilateral

(b) isocsceles

(c) Obtuse angled

(d) right angled

**152. G is the centroid of ∆ABC. The medians AD and BE intersect at right angles. If the lengths of AD and BE are 9 cm and 12 cm respectively; then the length of AB (in cm) is ? (SSC CGL 1st Sit. 2015)**

(a) 10

(b) 10.5

(c) 9.5

(d) 11

**153. If a person travels from a point L towards east for 12 km and then travels 5 km towards north and reaches a point M, then shortest distance from L to M is : (SSC CGL 1st Sit. 2015)**

(a) 14

(b) 12

(c) 17

(d) 13

**154. If D,E and Fare the mid points of BC, CA and AB respectively of the ∆ABC then the ratio of area of the parallelogram DEFB and area of the trapezium CAFD is: (SSC CGL 1st Sit. 2015)**

(a) 1:3

(b) 1:2

(c) 3:4

(d) 2:3

**155. O is the orthocentre of ∆ABC , and if ∠BOC = 110° then ∠BAC will be (SSC CGL 1st Sit. 2016)**

(a) 110°

(b) 70°

(c) 100°

(d) 90°

**156. BE and CF are two altitudes of a triangle ABC. If AB = 6 cm , AC = 5 cm and CF = 4 cm , then the length of BE(SSC CGL 1st Sit. 2016)**

(a) 4.8 cm

(b) 7.5cm

(c) 3.33 cm

(d) 5.5 cm

**157. In a A ABC, BC is extended upto D (SSC CGL 1st Sit. 2016)**

(a) 60°

(b) 75°

(c) 80°

(d) 90°

**158. O is the centre of a circle and AB is the tangent to it touching at B. If OB = 3 cm. and OA = 5 cm, then the measure of AB in cm is (SSC CGL 1st Sit. 2016)**

(a) √34

(b) 2

(c) 8

(d) 4

**159. X and Y are the mid points of sides AB and AC of a triangle ABC. If BC + XY=12 units, then BC – XY is (SSC CGL 1st Sit. 2016)**

(a) 8 units

(b) 4 units

(c) 6 units

(d) 2 units

**160. In ∆PQR, L and M are two points on the sides PQ and PR respectively such that LM || QR. If PL = 2cm; LQ = 6cm and PM= 1.5 cm, then MR in cm is (SSC CGL 1st Sit. 2016)**

(a) 0.5

(b) 4.5

(c) 9

(d) 8

**161. The length of the radius of a circle with centre O is 5 cm and the length of the chord AB is 8 cm. The distance of the chord AB from the point O is (SSC CGL 1st Sit. 2016)**

(a) 2cm

(b) 3cm

(c) 4 cm

(d) 15 cm

**162. In a triangle ABC, if∠A+ ∠C = 140° and∠A+ 3∠B= 180°, then ∠A is equal to (SSC CGL 1st Sit. 2016)**

(a) 80°

(b) 40°

(c) 60°

(d) 20°

**163. If PA and PB are two tangents to a cirlce with centre O such that ∠APB = 80°. Then, ∠AOP =? (SSC CGL 1st Sit. 2016)**

(a) 40°

(b) 50°

(c) 60°

(d) 70°

**164. Which of the set of three sides can’t form a triangle? (SSC CGL 1st Sit. 2016)**

(a) 5 cm, 6 cm, 7 cm

(b) 5 cm, 8 cm, 15 cm

(c) 8 cm, 15 cm, 18 cm

(d) 6 cm, 7 cm, 11cm

**165. AB is the diameter of a circle with centre O and P be a point on its circumference, If ∠POA =120°, then the value of ∠PBO is: (SSC CGL 1st Sit. 2016)**

(a) 30°

(b) 60°

(c) 50°

(d) 40°

**166. An arc of 30° in one circle is double an arc in a second circle, the radius of which is three times the radius of the first. Then the angles subtended by the arc of the second circle at its centre is (SSC CGL 1st Sit. 2016)**

(a) 3°

(b) 4°

(c) 5°

(d) 6°

**167. Which of the following ratios can be the ratio of the sides of a right angled triangle? (SSC CGL 1st Sit. 2016)**

(a) 9:6:3

(b) 13:12:5

(c) 7:6:5

(d) 5:3:2

**168. Number of circles that can be drawn through three non-colinear points is (SSC CGL 1st Sit 2016)**

(a) exactly one

(b) two

(c) three

(d) more than three

**169. Two circles touch each other internally. The radius of the smaller circle is 6 cm and the distance between the centre of two circles is 3 cm. The radius of the larger circle is (SSC CGL 1st Sit. 2016)**

(a) 7.5 cm

(b) 9 cm

(c) 8 cm

(d) 10 cm

**170. PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is (SSC CGL 1st Sit. 2016)**

(a) 3 cm

(b) 6 cm

(c) 12 cm

(d) 4.5 cm

**171. In the triangle ABC, ∠B AC = 50° and the bisectors of ∠ABC and ∠ACB meets at P. What is the value (in degrees) of ∠BPC? (SSC CGL2017)**

(a) 100

(b) 105

(c) 115

(d) 125

**172. Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles? (SSC CGL 2017)**

(a) 25

(b) 25√2

(c) 50

(d) 50√2

**173. In the given figure, ∠QRN = 40°, ∠PQR = 46° and MN is a tangent at R. What is the value (in degrees) of x, y and z respectively? (SSC CGL 2017)**

(a) 40, 46, 94

(b) 40, 50, 90

(c) 46, 54, 80

(d) 50 ,40, 90

**174. In ∆PQR, ∠R= 54°, the perpendicular bisector of PQ at S meets QR at T. If ∠TPR = 46°, then what is the value (in degrees) of ∠PQR? (SSC CGL 2017)**

(a) 25

(b) 40

(c) 50

(d) 60

**175. The perimeter of an isosceles triangle is 32 cm and each of the equal sides is 5/6 times of the base. What is the area (in cm2) ofthe triangle? (SSC CGL 2017)**

(a) 39

(b) 48

(c) 57

(d) 64

**176. If length of each side of a rhombus PQRS is 8 cm and ∠PQR = 120°, then what is the length (in cm) ofQS? (SSC CGL 2017)**

(a) 4√5

(b) 6

(c) 8

(d) 12

**177. In the given figure, ABC is a triangle. The bisectors of internal ∠B and external ∠C intersect at D. If ∠BDC = 48°, then what is the value (in degrees) of ∠A ? (SSC CGL 2017)**

(a) 48

(b) 96

(c) 100

(d) 114

**178. In the given figure, O is the centre ofthe circle and ∠DCE = 45°. If CD = 10√2 cm, then what is the length (in cm) of AC. (CB = BD): (SSC CGL 2017)**

(a) 14

(b) 15.5

(c) 18.5

(d) 20

**179. In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively? (SSC CGL 2017)**

(a) 1:1

(b) 2:1

(c) 3:1

(d) 4:1

**180. PQR is a right angled triangle in which ∠R= 90°. If RS ⊥ PQ, PR = 3 cm and RQ = 4 cm, then what is the value of RS (in cm)? (SSC CGL 2017)**

(a) 12/5

(b) 36/5

(c) 5

(d) 2.5

**181. In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR = 105°, then what is the value of ∠PAR (in degrees)? (SSC CGL 2017)**

(a) 60

(b) 100

(c) 105

(d) 115

**182. If there are four lines in a plane, then what cannot be the number of points of intersection of these lines? (SSC CGL 2017)**

(a) 0

(b) 5

(c) 4

(d) 7

**183. In ∆ABC, ∠BAC = 90° and AD is drawn perpendicular to BC. If BD = 7 cm and CD = 28 cm, then what is the length (in cm) of AD? (SSC CGL 2017)**

(a) 3.5

(b) 7

(c) 10.5

(d) 14

**184. A chord of length 60 cm is at a distance of 16 cm from the centre of a circle. What is the radius (in cm) of the circle? (SSC CGL 2017)**

(a) 17

(b) 34

(c) 51

(d) 68

**185. In the given figure, a smaller circle touches a larger circle at P and passes through its centre O. PR is a chord of length 34 cm, then what is the length (in cm) of PS? (SSC CGL 2017)**

(a) 9

(b) 17

(c) 21

(d) 25

**186. In the given figure, ABC is a triangle in which, AB = 10 cm, AC = 6 cm and altitude AE = 4 cm. If AD is the diameter of the circum-circle, then what is the length (in cm) of circum- radius? (SSC CGL 2017)**

(a) 3

(b) 7.5

(c) 12

(d) 15

**187. Find the sum of interior angles of a dodecagon? (SSC CHSL 2017)**

(a) 1620°

(b) 1800°

(c) 1440°

(d) 1260°

**188. In ∆PQR, ∠P:∠Q:∠R = 2:2:5. A line parallel to QR is drawn which touches PQ and PR at A and B respectively. What is the value of ∠PBA – ∠PAB? (SSC Sub. Ins. 2017) **

(a) 60

(b) 30

(c) 24

(d) 36

**189. In the given figure, O is the centre of the circle, ∠DAB = 110°and ∠BEC = 100° . What is the value (in degrees) of ∠OCB? (SSC Sub. Ins. 2017)**

(a) 5

(b) 10

(c) 15

(d) 20

**190. If ADEF is right angled at E, DE = 15 and ∠DFE = 60 °, then what is the value of EF? (SSC Sub. Ins. 2017)**

(a) 5√3

(b) 5

(c) 15

(d) 30

**191. In the given figure, area of isosceles triangle PQT is 128 cm2 and QT = PQ and PQ = 4 PS, PT || SR, then what is the area (in cm2) of the quadrilateral PTRS? (SSC Sub. Ins. 2017)**

(a) 80

(a) 64

(c) 124

(d) 72

**192. In the given figure, BD passes through centre O, AB = 12 and AC = 8. What is the radius of the circle? (SSC Sub. Ins. 2017)**

**Hints & Solutions**

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