CBSE Class 10 Mathematics Constructions VBQs

Multiple Choice Questions

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 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 AX is drawn first such that ÐBAX 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
Answer : B

Question. A line segment AB is divided in the ratio 5:6, draw a ray AX such that ∠BAX is an acute angle. 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 B 6
(b) A6 and B 5
(c) A4 and B 5
(d) A5 and B 4
Answer : A

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. 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. 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

Fill in the Blanks

Fill in the blanks/tables with suitable information:

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. The number of tangents can be constructed to a given circle from a point which lies inside the circle is/are .................................. .
Answer : 0

Write True or False

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

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

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) A₁₂
(b) A₁₁
(c) A₁₀
(d) A₉
Answer : B

Assertion-Reason Type Questions

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

Case Study Based Questions

I. The management of a school decided to arouse interest of their students in Mathematics. So they want to construct some geometrical shapes in one corner of the school premises. They showed a rough sketch of a right triangular structure on a plane sheet of paper with sides AB = 6 m, BC = 8 m and ∠B = 90°. The diagram shows a perpendicular from the vertex B to the front side AC. They want to build a circular wall through B, C and D but they had certain problems in doing so.
So they called on some students of class X to solve this problem. They made some suggestions.

Question. To find centre of the circle, the students made some suggestions which are as follows:
(a) Draw perpendicular BD on AC
(b) Draw perpendicular bisectors of BC and CD.
(c) The intersecting point of perpendiculars of BC and CD are the centre of the circle.
(d) All of the above
Answer : D

Question. Referring to the above, what will be the length of AD?
(a) 3.6 m
(b) 3.8 m
(c) 4.8 m
(d) 5.6 m
Answer : A

Question. Referring to the above, what is the length of perpendicular drawn on side AC from vertex B?
(a) 2.6 m
(b) 3.0 m
(c) 4.8 m
(d) 4.0 m
Answer : C

Question. Referring to the above, the length of tangent AE is
(a) 10 m
(b) 8 m
(c) 12 m
(d) 6 m
Answer : D

Question. Referring to the above, sum of angles ∠BAE and ∠BOE is
(a) 120°
(b) 180°
(c) 90°
(d) 60°
Answer : B

II. The construction of a road is in progress. A road already exists through a forest that goes over a circular lake. The engineer wants to build another road through the forest that connects this road, but does not go through the lake.

As it turns out, the road the engineer will be building and the road it will connect to both represent characteristics of a circle that have their own name. The road/bridge that already exists is called a secant of the circular lake, and the road the engineer is going to build is called the tangent of the circular lake.

Question. Refer to the above, if PT = 12 km and PA = 9 km, then the length of existing bridge is
(a) 7 km
(b) 9 km
(c) 12 km
(d) 16 km
Answer : A

Question. Refer to the above if the length of existing bridge is 5 km and the length of the existing road outside the lake is 4 km, then the length of the road under construction is
(a) 4 km
(b) 6 km
(c) 10 km
(d) 14 km
Answer : B

Question. Refer to the question (2) if the road under construction, PT is 6 km and it is inclined at an angle of 30° to the line joining the centre, the radius of the lake is
(a) 3√3 km
(b) 4√3 km
(c) 2√3 km
(d) 5√3 km
Answer : C

Question. Refer to the question (3) above, the circumference of the lake is
(a) 2√3 π km
(b) 3√3 π km
(c) 4√3 π km
(d) 5√3 π km
Answer : C

Question. Refer to the question (3) above, the area of the lake is
(a) 12π km₂
(b) 16π km₂
(c) 18π km₂
(d) 9π km₂
Answer : A

Question. Construct a triangle similar to a given ∆ABC, where AB = 4cm , BC = 6 cm and ∟ABC = 600 , such that each of its sides is 5/7 th of the corresponding sides of the ∆ABC. 

Value based Question: 

i. What qualities of Gandhiji would you like to construct within you.

Key Points:

* Simplicity

* Truthfulness

* Non-violence

Question. Draw a line segment of length 8cm divided it in the ratio 3:4 

Value based Question: 

Dividing Joint families into nuclear families is good or bad.

Key Points:

* Unity

* Adjustability

* Equality

Question. Draw a circle of radius 5cm. Draw tangents from end points of its diameter. What do you observe? 

Value based question: 

If each tangent represents the quality of a human being, find out the qualities that should be adopted for a better human being.

Key Points:

* Kindness, generosity

* zealous, nobleness