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Constructions Practice Questions

Class 10 · Mathematics · 1621 free MCQs with instant results and detailed explanations.

1621
Total
724
Easy
702
Medium
195
Hard

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Topics in Constructions

Division of a Line Segment 748
Construction of Tangents 873

Sample Questions from Constructions

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
How many times can a line segment be divided into equal parts using a compass and straightedge?
A. Any number of times
B. Only twice
C. Three times
D. Only once
Show Answer & Explanation
Correct Answer: A
A line segment can be divided into equal parts an unlimited number of times using a compass and straightedge.
Q2
Easy
If a line segment AB is divided into 5 equal parts, what is the length of each part if AB measures 20 cm?
A. 4 cm
B. 5 cm
C. 3 cm
D. 2 cm
Show Answer & Explanation
Correct Answer: A
To find the length of each part, divide the total length (20 cm) by the number of parts (5): 20 cm / 5 = 4 cm.
Q3
Easy
Which of the following tools is essential for dividing a line segment accurately?
A. Protractor
B. Compass
C. Ruler
D. Set squares
Show Answer & Explanation
Correct Answer: B
A compass is essential for marking equal distances along a line segment when dividing it.
Q4
Medium
In a construction, if you are asked to divide a line segment of 10 cm in the ratio 3:2, what is the length of the longer segment?
A. 6 cm
B. 4 cm
C. 3 cm
D. 2 cm
Show Answer & Explanation
Correct Answer: A
The total parts of the ratio are 3 + 2 = 5. The length of the longer segment is (3/5) * 10 cm.
Q5
Medium
You need to divide a line segment of length 15 cm in the ratio 1:2 using a compass and straightedge. What is the first step?
A. Draw a line segment of 15 cm.
B. Mark a point at 5 cm.
C. Draw a circle with radius 1 cm.
D. Use the divider to measure 1 cm.
Show Answer & Explanation
Correct Answer: A
The first step in any construction is to create the line segment of the given length before dividing it.
Q6
Medium
When dividing a line segment into two equal parts, which construction tool is essential?
A. Ruler
B. Compass
C. Protractor
D. Graph paper
Show Answer & Explanation
Correct Answer: B
A compass is crucial for marking arcs and finding the midpoint of the segment accurately.
Q7
Medium
Which of the following ratios will divide a line segment into three equal parts?
A. 1:2
B. 1:1:1
C. 2:3
D. 1:3
Show Answer & Explanation
Correct Answer: B
The ratio 1:1:1 means each part is equal, thus dividing the segment into three equal sections.
Q8
Hard
Given a line segment of length 15 cm, how would you construct a point that divides it in the ratio 3:5 using a compass and straightedge?
A. Construct a line perpendicular to the segment.
B. Use a protractor to measure angles.
C. Mark 3 parts and 5 parts along a straight line.
D. Draw a circle with radius 15 cm.
Show Answer & Explanation
Correct Answer: C
To divide a segment in the given ratio, marking equal parts along a straight line is essential.
Q9
Hard
How can you verify that point D divides line segment EF in the ratio 3:7 if E(0, 0) and F(10, 20)?
A. Calculate the distance from E to D and from D to F.
B. Check if D is the midpoint of EF.
C. Use the section formula to find D's coordinates.
D. Draw line segments to scale.
Show Answer & Explanation
Correct Answer: C
The section formula will confirm the coordinates of point D relative to E and F with the given ratio.
Q10
Hard
A hexagon is inscribed in a circle. If a line segment AB divides it into two equal areas, what is the significance of point C on AB?
A. C is the midpoint of AB.
B. C is the centroid of the hexagon.
C. C is the orthocenter of the triangle formed.
D. C determines the angle bisector.
Show Answer & Explanation
Correct Answer: A
To divide the hexagon into equal areas, point C must be the midpoint of line segment AB.

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Constructions — Class 10 Mathematics Practice Questions Online

This page contains 1621 practice MCQs for the chapter Constructions in Class 10 Mathematics. The questions are organized by difficulty — 724 easy, 702 medium, 195 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 2 topics, giving you comprehensive coverage of the entire chapter.