# CBSE 10th Maths Exam 2021: Important MCQs from Chapter 11 Constructions with Answers in Detail

Check here important MCQ questions with answers from Class 10 Maths Chapter 11- Constructions. PDF of all the questions is also provided here to download.

Created On: Mar 17, 2021 17:36 IST
CBSE 10th Maths Exam 2020: Important MCQs from Chapter 11 Constructions with Answers in Detail

Get here MCQs on Class 10 Maths Chapter 11 - Constructions. All these questions are not only provided with the correct answers but also their detailed solutions. Students can also download all these solved MCQs in PDF format to practice whenever they get time. These questions are really useful to identify and revise the important topics and concepts for the upcoming CBSE Class 10 Maths Board Exam 2021.

Note - Students must note that 'Construction of a triangle similar to a given triangle. has been excluded from the revised CBSE syllabus of Class10 Maths. So, students should prepare according to the new syllabus only.

Check below the solved MCQs from Class 10 Maths Chapter 11 Constructions:

1. To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle and 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

Explanation: We know that to divide a line segment in the ratio m : n, first draw a ray AX which makes an acute angle BAX , then marked m+n points at equal distances from each other.

Here m = 5, n = 7

So minimum number of these point = m + n = 5 + 7 = 12

2. To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is 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) A12

(B) A11

(C) A10

(D) A9

Explanation: Here minimum 4+7=11 points are located at equal distances on the ray AX and then B is joined to last point, i.e., A11.

3. To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, ... and B1, B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are

(A) A5 and B6

(B) A6 and B5

(C) A4 and B5

(D) A5 and B4

Explanation:   Observe the following figure:

4. To construct a triangle similar to a given ΔABC with its sides 3/7 of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3, ... on BX at equal distances and next step is to join:

(A) B10 to C

(B) B3 to C

(C) B7 to C

(D) B4 to C

Explanation: Here we locate points B1,B2,B3,B4,B5,B6 and B7 on BX at equal distances and in next step join the last point B7 to C

5. To construct a triangle similar to a given ΔABC with its sides 8/5 of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is:

(A) 5

(B) 8

(C) 13

(D) 3

Explanation: To construct a triangle similar to a given triangle with its sides m/n of the corresponding sides of given triangle ,the minimum number of points to be located at equal distance is equal to the greater of m and n in m/n.

Here, m/n = 8/5

So the minimum number of points to be located at equal distance on ray BX is 8.

6. 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 end points of those two radii of the circle, the angle between them should be:

(A) 135°

(B) 90°

(C) 60°

(D) 1200

Explanation: The angle between them should be 1200 because the figure formed by the intersection point of pair of tangents, the two end points of those two radii (at which tangents are drawn) and the centre of circle, is a quadrilateral. Thus the sum of the opposite angles in this quadrilateral must be 180o.

7. To divide a line segment AB in the ratio p : q (p, q are 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) greater of p and q

(B) p + q

(C) p + q – 1

(D) pq

Explanation: We know that to divide a line segment in the ratio m : n, first draw a ray AX which makes an acute angle BAX , then mark m + n points at equal distances from each other.

Here m = p, n = q

So minimum number of these points = m + n = p + q

8. To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is:

(A) 105°

(B) 70°

(C) 140°

(D) 145°

Explanation: The angle between them should be 1450 because the figure formed by the intersection point of pair of tangents, the two end points of those two radii (at which tangents are drawn) and the centre of circle, is a quadrilateral. Thus the sum of the opposite angles in this quadrilateral must be 180o.

9. By geometrical construction, it is possible to divide a line segment in the ratio:

Explanation:

10. A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of ___________ from the centre.

(A) 5cm

(B) 2cm

(C) 3cm

(D) 3.5cm

Explanation: The pair of tangents can be drawn from an external point only, so its distance from the centre must be greater than radius. Since only 5cm is greater than radius of 3.5cm. So the tangents can be drawn from the point situated at a distance of 5cm from the centre.

11. To divide a line segment AB in the ratio 5:6, draw a ray AX such that ∠BAX is an acute angle, then drawa ray BY parallel to AX and the points A1, A2, A3,…. and B1, B2, B3,…. are located to equal distances on ray AX and BY, respectively. Then, the points joined are

(A) A5 and B6

(B) A6 and B5

(C) A4 and B5

(D) A5 and B4

Explanation:

To divide line segment AB in the ratio 5:6.

Steps of construction

1. Draw a ray AX making an acute ∠BAX.

2. Draw a ray BY parallel to AX by taking ∠ABY equal to ∠BAX.

3. Divide AX into five (m = 5) equal parts AA1, A1A2, A2A3, A3A4 and A4A5

4. Divide BY into six (n = 6) equal parts and BB1, B1B2, B2B3, B3B4, B4B5 and B5B6.

5. Join B6 A5. Let it intersect AB at a point C.

Then, AC : BC = 5 : 6

12. A rhombus ABCD in which AB = 4cm and ABC = 60o, divides it into two triangles say, ABC and ADC. Construct the triangle AB’C’ similar to triangle ABC with scale factor 2/3. Select the correct figure.

13. A triangle ABC is such that BC = 6 cm, AB = 4 cm and AC = 5 cm. For the triangle similar to this triangle with its sides equal to (3/4)th of the corresponding sides of ΔABC, correct figure is:

14. For ∆ABC in which BC = 7.5 cm, ∠B =450 and AB – AC = 4, select the correct figure.

(D) None of these

15. Draw the line segment AB = 5 cm. From the point A draw a line segment AD = 6cm making an angle of 600 with AB. Draw a perpendicular bisector of AD. Select the correct figure.

(D) None of these