Geometry Questions for SSC CGL

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Q1. If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is: 
(a) Equal to 1/4
(b) Equal to 1/2
(c) Equal to 1
(d) Greater than 1

Q2. If ABCD is a rhombus, then:
(a) AC²+BD²=4AB²
(b) AC²+BD²=AB²
(c) AC²+BD²=2AB²
(d) 2(AC²+BD² )=3AB²

Q3. The length of one side of a rhombus is 6.5 cm and its altitude is 10 cm. if the length of one of its diagonal be 26 cm, the length of the other diagonal will be: 
(a) 5 cm
(b) 10 cm
(c) 6.5 cm
(d) 26 cm

Q4. The diagonals of a rhombus are 32 cm and 24 cm respectively. The perimeter of the rhombus is :
(a) 80 cm
(b) 72 cm
(c) 68 cm
(d) 64 cm

Q5. In ∆ ABC, AD is the internal bisector of A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is:
(a) 2 : 1
(b) 1 : 2
(c) 4 : 5
(d) 3 : 5

Q6. I is the incentre of ABC, ABC = 60° and ACB = 50°. Then BIC is
(a) 55°
(b) 125°
(c) 70°
(d) 65°

Q7. Two chords AE and BC intersect each other at D at right angles, if AB = 5 cm, BD = 4 cm, CD = 9 cm find AE.
(a) 15 cm
(b) 6 cm
(c) 9 cm
(d) 10 cm

Q8. Water flows in a tank 150 m × 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm, at the speed of 15 km/h. In what time will the water be 3 m deep?
(a) 100 hours
(b 120 hours
(c) 140 hours
(d) 150 hours

Q9. The length of all median of ∆ABC are 18 cm, 24 cm, & 30 cm. Then find the area of ∆ABC. 
(a) 288 cm²
(b) 384 cm²
(c) 278 cm²
(d) 286 cm²

Q10. In ∆ABC, AB = 16 cm, BC = 36 cm and AC = 28 cm, then find the length of median AD.

(a) 12
(b) 13
(c) 24
(d) 14

Q11. ABCD is a trapezium in which AB || DC and AB = 2 CD. The diagonals AC and BD meet at O. The ratio of area of triangles AOB and COD is 
(a) 1 : 1
(b) 1∶√2
(c) 4 : 1
(d) 1 : 4

Q12. In ∆ABC, D and E are the points of sides AB and BC respectively such that DE || AC and AD : BD =3 : 2. The ratio of area of trapezium ACED  to that of ∆BED is 
(a) 4 : 15
(b) 15 : 4
(c) 4 : 21
(d) 21 : 4

Q13. At each corner of a triangular field of sides 26 cm, 28 m and 30 m, a cow is tethered by a rope of length 7  m, the area (in m) ungrazed by the cows is 
(a) 336
(b) 259
(c) 154
(d) 77

Q14. A godown is 15 m long and 12 m broad. The sum of the area of the floor and the celling is equal to the sum of areas of the four walls. The volume (in m³) of the godown is : 
(a) 900
(b) 1200
(c) 1800
(d) 720

Q15. If the altitude of a triangle is increased by 10% while its area remains same, its corresponding base will have to be decreased by 
(a) 10%
(b) 9%
(c) 9 (1/11)%
(d) 11 (1/9)%

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