Constructions Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test are covered in this Article. Constructions Class 10 MCQ Test contains 17 questions. Answers to MCQ on Constructions Class 10 are available after clicking on the answer. MCQ Questions for Class 10 with Answers have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.
| Board | CBSE |
| Textbook | Maths (NCERT) |
| Class | Class 10 |
| Chapter | Chapter 11 Constructions |
| Category | MCQ Questions for Class 10 Maths with Answers |
Constructions Class 10 MCQ with Answers
1.To divide a line segment AB in the ratio a: b,( a and b are two positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is
(a) a +b +1
(b) a + b
(c) a + b -1
(d) ab + 1
Answer
Answer: (b) a + b
Explanation: To divide a line segment AB in the ratio a : b, where a and b are two positive integers, draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is a + b
2. To construct a pair of tangents to a circle at an angle of 30° to each other, it is needed to draw tangents at endpoints of those two radii of the circle, the angle between them should be
(a) 150°
(b) 140°
(c) 130°
(d) 120°
Answer
Answer: (a) 150°
Explanation: The angle should be 150°.
the figure produced by the intersection point of pair of tangents and the two endpoints of those two radii and the centre of the circle, is a quadrilateral.
We know that the sum of the opposite angles should be 180°.
30° + 150° = 180°
3. By geometrical construction, which one of the following ratios is not possible to divide a line segment?
(a) 2:5
(b) √1:√4
(c) 2+√5: 2 -√5
(d) All of these
Answer
Answer: (c) 2+√5: 2 -√5
Explanation: 2+√5 : 2 – √5 can not be simplified in the form of integers.
4. To divide a line segment AB in the ratio m: n,( m and n are two positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is 17, then the possible ratio of m : n is
(a) 15: 2
(b) 3: 14
(c) 12: 5
(d) All of these
Answer
Answer: (d) All of these
Explanation: To divide a line segment AB in the ratio m: n, draw a ray AX so that ∠BAX is an acute angle and then mark m + n points at equal distances from each other.
For option (a)
m + n = 15 +2 = 17
For option (b)
m + n = 3 + 14 = 17
For option (c)
m + n = 12 + 5 = 17
All ratios satisfy m + n = 17.
5. In division of a line segment PQ, any ray PX makes an ……. angle with PQ
(a) An acute
(b) An obtuse
(c) A right angle
(d) None of these
Answer
Answer: (a) An acute
6. To divide a line segment AB in the ratio 7: 8, draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is
(a) 14
(b) 15
(c) 16
(d) 17
Answer
Answer: (b) 15
Explanation: To divide a line segment AB in the ratio m: n, draw a ray AX so that ∠BAX is an acute angle and then mark m + n points at equal distances from each other.
So, the minimum number of these points is
m + n = 7 + 8 = 15
7. If a point lies inside the circle, then number of tangents is
(a) 0
(b) 1
(c) 2
(d) Countably infinite
Answer
Answer: (a) 0
Explanation: If a point lies inside a circle, there cannot be a tangent to the circle through this point.
Constructions Class 10 MCQ with Answers
8. How many tangents can be drawn from a point which lies outside the circle.
(a) 1
(b) 2
(c) 3
(d) 4
Answer
Answer: (b) 2
9. A point M is at a distance of 4 cm from the centre of the circle of radius 4 cm. How many tangents can be drawn from M
(a) 0
(b) 1
(c) 2
(d) 3
Answer
Answer: (b) 1
Explanation: As the distance of M from centre and radius of the circle is same, this means that M lies on the circle.
We know that only a single tangent can be drawn from a point which lies on the circle.
10. By geometrical construction, is it possible to divide a line segment in the ratio 1/√5 : √5 ?
(a) Yes
(b) No
Answer
Answer: (a) Yes
Explanation: 1/√5 : √5
Multiplying by √5
1: 5
Thus, we can simplify the ratio in integers and it is possible to divide a line segment in this ratio.
11. AB and AC are two tangents drawn from a point A on a circle of centre at point D. If ∠CAB = 75°. Then ∠BDC is
(a) 125°
(b) 115°
(c) 110°
(d) 105°
Answer
Answer: (d) 105°
Explanation: ∠BDC= 105°
the figure produced by the intersection point of pair of tangents and the two endpoints of those two radii and the centre of the circle, is a quadrilateral.
We know that the sum of the opposite angles should be 180°.
75° + 105° = 180°
12. A point X is at a distance of 10 cm from the centre of the circle of radius 7.5 cm. How many tangents can be drawn from M
(a) 1
(b) 0
(c) 2
(d) Infinite
Answer
Answer: (c) 2
Explanation: As distance of point is 10 cm and radius of circle is 7.5 cm which is less than the distance of X.
This means that X lies outside the circle and we know that 2 tangents can be drawn from an exterior point.
13. A point A is at a distance of 4 cm from the centre of the circle of radius 4.5 cm. Then A lies
(a) Outside the circle
(b) Inside the circle
(c) On the circle
(d) None of these
Answer
Answer: (b) Inside the circle
Explanation: Distance of A from the centre < radius of circle.
4cm <4.5 cm
14. If centre of a circle is not given, then can we construct a circle?
(a) Yes
(b) No
(c) Can’t say
(d) None
Answer
Answer: (a) Yes
Explanation: If centre of the circle is not given, we may locate its centre first by taking any two non-parallel chords and then finding the point of intersection of their perpendicular bisectors and then proceeding as we proceed for circle whose centre is known.
Constructions Class 10 MCQ with Answers
15. To divide a line segment AB of length 5 cm in the ratio 2 : 3, a ray AX is drawn first such that ∠BAX forms an acute angle and then points A1, A2, A3, ….are located at equal distances on the ray AX and the point B is joined to
(a) A1
(b) A2
(c) A4
(d) A5
Answer
Answer: (d) A5
Explanation: The minimum points located at the ray AX is 2 + 3 = 5.
So, point B is joined to A5.
16. PB and PC are two tangents drawn from a point P on a circle of centre at point D. If ∠CPB = (x+ y) °. Then ∠BDC is
(a) x°
(b) y°
(c) 180° – (x+ y) °
(d) 180° + (x+ y) °
Answer
Answer: (c) 180° – (x+ y) °
17. If the line segment is divided in the ratio 4:5, then number of parts it contain while constructing is
(a) 4
(b) 5
(c) 9
(d) 1
Answer
Answer: (c) 9
Explanation: The line segment is divided in the ratio 4: 5 this means that it has 4 parts on one side and 5 parts on the other side of the point of division.
total parts is = 4 + 5 i.e. 9 parts.
MCQ Questions for Class 10 Maths
- Real Numbers Class 10 MCQ with Answers
- Polynomials Class 10 MCQ with Answers
- Pair of Linear Equations in Two Variables
- MCQ Questions on Quadratic Equations for Class 10
- Arithmetic Progressions
- Triangles Class 10 MCQ with Answers
- Coordinate Geometry
- Introduction to Trignometry
- Some Applications of Trigonometry Class 10 MCQ with Answers
- Circles Class 10 MCQ with Answers
- Constructions Class 10 MCQ with Answers
- Areas Related to Circles
- Surface Areas and Volumes
- Statistics Class 10 MCQ with Answers
- Probability Class 10 MCQ
Frequently Asked Questions on Constructions Class 10 MCQ with Answers
1. Are these MCQ on Constructions Class 10 are based on 2021-22 CBSE Syllabus?
Yes . There are 17 MCQ’s on this Chapter in this blog.
2. Are you giving all the chapters of Maths Class 10 MCQs with Answers which are given in CBSE syllabus for 2021-22 ?
Yes, we are providing all the chapters of Maths Class 10 MCQs with Answers.