GAT General (NTS) chapter 7: Quantitative · Geometry and trigonometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

50 exam-style questions on Quantitative · Geometry and trigonometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

50 questions · 4 topics · 10 per test

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What chapter 7 covers

Ten Quantitative · Geometry and trigonometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A cube has total surface area 150 cm2. Its volume is

  1. A
    25 cm3
  2. B
    216 cm3
  3. C
    125 cm3
  4. D
    150 cm3
Show answer

Answer: C. 6a2 = 150 gives a = 5 cm, so volume = 53 = 125 cm3. 25 is the area of one face.

2. Taking π = 22/7, the curved surface area of a hemisphere of radius 7 cm is

  1. A
    308 cm2
  2. B
    616 cm2
  3. C
    154 cm2
  4. D
    462 cm2
Show answer

Answer: A. Curved surface = 2πr2 = 2 × 22/7 × 49 = 308 cm2. 616 is the whole sphere, and 462 (3πr2) includes the flat base.

3. A cylinder has radius 7 cm and height 10 cm. Taking π = 22/7, its volume is

  1. A
    1540 cm3
  2. B
    440 cm3
  3. C
    220 cm3
  4. D
    3080 cm3
Show answer

Answer: A. V = πr2h = 22/7 × 49 × 10 = 1540 cm3. 440 is the curved surface area 2πrh.

4. An exterior angle of a triangle is 110° and one of the two interior opposite angles is 45°. The other interior opposite angle is

  1. A
    70°
  2. B
    65°
  3. C
    55°
  4. D
    45°
Show answer

Answer: B. An exterior angle equals the sum of the two interior opposite angles: 110° − 45° = 65°. 70° is the interior angle next to the exterior angle.

5. In an isosceles triangle the angle between the two equal sides is 50°. Each base angle is

  1. A
    65°
  2. B
    50°
  3. C
    130°
  4. D
    40°
Show answer

Answer: A. The two base angles are equal and the three angles add to 180°: (180° − 50°)/2 = 65°. 130° is the total of the two base angles.

6. A triangle has sides 3 cm, 4 cm and 5 cm. A similar triangle has its shortest side 9 cm. The perimeter of the larger triangle is

  1. A
    27 cm
  2. B
    36 cm
  3. C
    15 cm
  4. D
    45 cm
Show answer

Answer: B. The scale factor is 9/3 = 3, so the sides are 9, 12 and 15 cm and the perimeter is 36 cm. 27 cm adds 6 to each side instead of scaling.

7. Each interior angle of a regular octagon is

  1. A
    120°
  2. B
    140°
  3. C
    150°
  4. D
    135°
Show answer

Answer: D. Exterior angle = 360°/8 = 45°, so the interior angle is 180° − 45° = 135°. 120° is a hexagon and 140° a nonagon.

8. A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre is

  1. A
    6 cm
  2. B
    8 cm
  3. C
    4 cm
  4. D
    12 cm
Show answer

Answer: A. The perpendicular from the centre bisects the chord, giving a right triangle with hypotenuse 10 and one side 8: distance = √(100 − 64) = 6 cm.

9. A rectangular lawn 20 m by 15 m has a path 2 m wide around the outside. The area of the path is

  1. A
    156 m2
  2. B
    140 m2
  3. C
    300 m2
  4. D
    456 m2
Show answer

Answer: A. Outer rectangle 24 m × 19 m = 456 m2; subtract the lawn 300 m2 to get 156 m2. Perimeter × width (70 × 2 = 140) misses the four corner squares.

10. PA and PB are tangents from an external point P to a circle with centre O. If angle APB = 50°, then angle AOB =

  1. A
    130°
  2. B
    50°
  3. C
    100°
  4. D
    65°
Show answer

Answer: A. Angles OAP and OBP are 90° (radius ⟂ tangent), so in quadrilateral OAPB angle AOB = 360° − 90° − 90° − 50° = 130°.

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Ways to practise this chapter

Quantitative · Geometry and trigonometry: questions students ask

How many Quantitative · Geometry and trigonometry MCQs are there?

50, each with the answer and a short explanation, across 4 topics: Lines, angles and triangles, Circles and polygons, Mensuration, Trigonometry and coordinate geometry. Every chapter test draws ten of them, so you can take it many times.

Is the GAT General (NTS) chapter 7 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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