Please refer to MCQ Questions Chapter 10 Construction Class 10 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 10 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 10 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 10 Construction in Class 10 Mathematics provided below to get more marks in exams.

**Chapter 10 Construction MCQ Questions**

Please refer to the following **Chapter 10 Construction MCQ Questions Class 10 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 10 Construction Class 10 Mathematics**

**Question. To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at the end points of those two radii of the circle. The angle between them should be **

(a) 135º

(b) 90º

(c) 60º

(d) 120º

**Answer**

D

**Question. A line segment AB is divided in the ratio 5:6, draw a ray 5:6 such that ∠BAX is an acute angle. A ray BY parallel to AX and the points A _{1}, A_{2}, A_{3},… and B_{1}, B_{2}, B_{3},… are located at equal distances on ray AX and BY, respectively. Then, the points joined are: **

(a) A

_{5}and B

_{6}

(b) A

_{6}and B

_{5}

(c) A

_{4}and B

_{5}

(d) A

_{5}and B

_{ 4}

**Answer**

A

**Question. To divide a line segment AB in the ratio 2:5, first a ray AX is drawn, so that ∠BAX is an acute angle and then at equal distance points are marked on the ray AX such that the minimum number of these point is: **

(a) 2

(b) 5

(c) 4

(d) 7

**Answer**

D

**Question. To divide a line segment AB in the ratio 5:7, first a ray AX is drawn, so that ∠BAX is an acute angle. Then at equal distances, points are marked on the ray AX such that the minimum number of these points is: **

(a) 8

(b) 10

(c) 11

(d) 12

**Answer**

D

**Question. Dividing a line segment AB in the ratio 4:7, a ray 4:7 is drawn first such that ∠BAX is an acute angle and then points A _{1}, A_{2}, A_{3}, … are located at equal distances on the ray AX and the point B is joined to: **

(a) A

_{12}

(b) A

_{11}

(c) A

_{10}

(d) A

_{9}

**Answer**

B

**Question. To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn such that ∠BAX is an acute angle and then at equal distances points are marked on the ray such that the minimum number of these points is **

(a) 8

(b) 10

(c) 11

(d) 12

**Answer**

D

**Question. To divide line segment AB in the ratio m : n, draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distance such that the minimum number of these points is **

(a) m + n

(b) m – n

(c) m × n

(d) m ÷ n

**Answer**

A

**Question. To divide a line segment AB in the ratio 5 : 6, we draw a ray such that ∠BAX is an acute angle, locate points A1, A2, A3, … at equal distances on the ray AX and join point B to **

(a) A_{12}

(b) A_{11}

(c) A_{10}

(d) A_{9}

**Answer**

B

**Question. The ratio of the sides of the triangle to be constructed with the corresponding sides of the given triangle is known as **

(a) scale factor

(b) length factor

(c) side factor

(d) K-factor

**Answer**

A

**Question. To draw a pair of tangents to a circle which are inclined to each other at an angle of 30°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be **

(a) 150°

(b) 90°

(c) 60°

(d) 120°

**Answer**

A

**Question. If you draw a pair of tangents to a circle C(O, r) from point P such that OP = 2r, then the angle between the two tangents is **

(a) 90°

(b) 30°

(c) 60°

(d) 45°

**Answer**

C

**In the following question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:****(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).****(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).****(c) Assertion (A) is true but reason (R) is false.****(d) Assertion (A) is false but reason (R) is true.**

**Question. Assertion (A): If two tangents AB and AC are drawn from a common point A to a circle of radius 4 cm, then AB = AC. ****Reason (R): Tangents drawn from an external point to a circle are equal.**

**Answer**

A

**In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:****(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).****(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).****(c) Assertion (A) is true but reason (R) is false.****(d) Assertion (A) is false but reason (R) is true.**

**Question. Assertion (A): By geometrical construction, it is possible to divide a line segment in the ratio √3 : 1/√3 ****Reason (R): To divide a line segment in the ratio p : q, p and q must be positive integers.**

**Answer**

A

**Question. Assertion (A): When a line segment is divided in the ratio 2 : 3, the number of parts in which the line is divided is 5. ****Reason (R): To divide a line segment in the ratio p : q, we divide it into (p + q) parts.**

**Answer**

A

**Fill in the Blanks :**

**Question. The number of tangents can be constructed to a given circle from a point which lies inside the circle is/are ……………………………. . **

**Answer**

**0**

**Question. If a line segment AB of length 6 cm is divided internally by a point C in the ratio of 3 : 2, then the length of AC is ……………………………. . **

**Answer**

**3.6 cm**

**Question. In the given figure, P divides the line segment AB in the ratio ………………… **

**Answer**

**3:1**

**True or False :**

**Question. A pair of tangents can be constructed to a circle inclined at an angle of 170°.**

**Answer**

**True**

**Question. By geometrical construction, it is possible to divide a line segment in the ratio : √3:(1/√3) . **

**Answer**

**True**

**One Word Questions :**

**Question. For dividing a line LM in ratio 5 : 3 into how many parts the arm of acute angle be divided.**

**Answer**

8

**Question. For dividing line PQ in ratio 4 : 7 in how many minimum points will the parallel lines at P and Q be divided into.**

**Answer**

11

**Question. A PQ’R’ ∼ PQR is to be constructed to get PQ’/PQ = 5/2 . If PQ = 6cm, What will be PQ′ ?**

**Answer**

15cm

**Question. ABC ∼ A B C such that AB/A B = 2/7 2/7 , if BC = 9cm what will be B C .**

**Answer**

31.5cm

**Question. PQR ∼ PQ R with PQ/PQ = 3/5 if QR = 15cm, what will be QR ?**

**Answer**

25cm

**Question. In constructing A’BC’ ∼ ABC such that BC 5/2 BC , into how many equal parts is BC divided?**

**Answer**

2

**Question. If a point is to be located on a line AB such that AP = 4.5cm and AP : PB = 3 : 2. ****What is the length of AB ? **

**Answer**

7.5cm

**Question. In a ΔPQR ∼ΔP′QR′ such that P ‘Q/PQ = 1/2 . If QR=6cm, what is QR′ ?**

**Answer**

3cm

**Question. If a point L is to be located on line YZ such that LY : LZ = 2 : 3. If YZ = 15cm, what is LZ?**

**Answer**

9cm

**Question. ABC ∼ AB C such that B C 4/5 BC . Into how many equal parts does the side BC be divided?**

**Answer**

five

**Question. If a line AB = 7cm is divided in ratio 3 : 4 by a point P, find BP.**

**Answer**

4cm

**Question. A LM’N’ ∼ LMN is to be made such that LM’/LM = 4/3. If LM’ = 4.8cm. find LM.**

**Answer**

3.6cm

**Question. If a tangent 8cm long is drawn to a circle of radius 6cm. What will be the distance of the point from the centre?**

**Answer**

10cm

**Question. If a line AB = 24cm is divided in the ratio 5 : 3 by the point P. What is AP equal to?**

**Answer**

15cm

**Question. If for a circle of radius 7cm, a tangent is to be made at a point 25cm away from the centre of the circle, without measuring. What will be the length of the tangent?**

**Answer**

24cm

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