SSC CGL Geometry and Mensuration Practice Test 8

15 fresh SSC CGL geometry questions on similar triangles, tangents, inscribed circles, and 3D mensuration.

Timer-based practiceDetailed answer reviewMobile-friendly flow

SSC CGL Sponsor

High Intent Competitive Exam Traffic

Leaderboard slot above the practice session for revision tools, test series, books, and career products.

SSC CGL Practice Session

SSC CGL Geometry and Mensuration Practice Test 8

15 fresh SSC CGL geometry questions on similar triangles, tangents, inscribed circles, and 3D mensuration.

Questions

Marking

+2 correct, -0.5 wrong

Format

15-question ad-supported session

Preview all 15 questions in SSC CGL Geometry and Mensuration Practice Test 8 (no login required)

Similar Triangles
1. Two similar triangles have sides 6 and 10. Ratio of their areas:
- A. 6:10
- B. 18:50
- C. 9:25 (Correct)
- D. 36:100
Explanation: Ratio of areas = (6/10)² = 36/100 = 9:25.
Tangent
2. A tangent from external point P to circle of radius 5 cm. Distance of P from centre is 13 cm. Tangent length:
- A. 10 cm
- B. 11 cm
- C. 12 cm (Correct)
- D. 13 cm
Explanation: Tangent=√(13²−5²)=√(169−25)=√144=12 cm.
Quadrilateral
3. In a trapezium, parallel sides are 8 cm and 12 cm. Height is 6 cm. Area:
- A. 54 sq cm
- B. 58 sq cm
- C. 60 sq cm (Correct)
- D. 66 sq cm
Explanation: Area=1/2×(8+12)×6=60 sq cm.
Triangle
4. In triangle ABC, angle bisector from A meets BC at D. If AB=6, AC=9, BC=10, find BD.
- A. 3 cm
- B. 4 cm (Correct)
- C. 5 cm
- D. 6 cm
Explanation: By angle bisector theorem: BD/DC=AB/AC=6/9=2/3. BD=10×2/5=4 cm.
Angles
5. Vertically opposite angles are always:
- A. Supplementary
- B. Complementary
- C. Equal (Correct)
- D. Reflex
Explanation: Vertically opposite angles are always equal.
Cylinder
6. Total surface area of a cylinder with r=7 cm and h=10 cm:
- A. 726 cm²
- B. 748 cm² (Correct)
- C. 760 cm²
- D. 776 cm²
Explanation: TSA=2πr(r+h)=2×22/7×7×17=748 cm².
Circle
7. Angle subtended by an arc at centre is 120°. Angle at any point on the major arc:
- A. 30°
- B. 40°
- C. 50°
- D. 60° (Correct)
Explanation: Angle at major arc=120°/2=60°.
Similar Triangles
8. In similar triangles, perimeters are 12 and 20. If smallest side of smaller triangle is 3, smallest side of larger is:
- A. 4
- B. 5 (Correct)
- C. 6
- D. 7
Explanation: Ratio=12:20=3:5. Smallest side of larger=3×20/12=5.
Cone
9. Slant height of cone with r=5 and h=12 is:
- A. 11 cm
- B. 12 cm
- C. 13 cm (Correct)
- D. 14 cm
Explanation: l=√(r²+h²)=√(25+144)=13 cm.
Triangle
10. Pythagoras theorem applies to:
- A. All triangles
- B. Acute triangles
- C. Right triangles (Correct)
- D. Obtuse triangles
Explanation: Pythagorean relation holds only for right-angled triangles.
Quadrilateral
11. Diagonals of a rhombus are 24 cm and 10 cm. Side of rhombus:
- A. 11 cm
- B. 12 cm
- C. 13 cm (Correct)
- D. 14 cm
Explanation: Side=√(12²+5²)=√169=13 cm.
Angles
12. In a cyclic quadrilateral, opposite angles sum to:
- A. 90°
- B. 120°
- C. 180° (Correct)
- D. 360°
Explanation: Opposite angles of a cyclic quadrilateral are supplementary.
Hemisphere
13. Curved surface area of hemisphere of radius 14 cm:
- A. 1144 cm²
- B. 1232 cm² (Correct)
- C. 1344 cm²
- D. 1432 cm²
Explanation: CSA=2πr²=2×22/7×196=1232 cm².
Tangent
14. Two tangents from external point make angle 60° between them. Angle subtended at centre by chord joining tangent points:
- A. 100°
- B. 110°
- C. 120° (Correct)
- D. 130°
Explanation: Angle at centre = 180°−60°=120°.
Triangle
15. In a 45-45-90 triangle, hypotenuse is 10 cm. Legs are:
- A. 5 cm each
- B. 5√2 cm each (Correct)
- C. 7 cm each
- D. 8 cm each
Explanation: Leg=hyp/√2=10/√2=5√2 cm.