MCQ Class 10 Constructions Set I

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1. There will be total 30  MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

 

1. 3 

In the construction given, what is the ratio in which the point C divides the line segment AB?

Question 1 of 30

2. The figure given below has been constructed by following the steps given below.
I : Draw a ray AX making an acute angle with a given side AB of ΔABC on the opposite side of vertex C.
II : Locate 3 points A1, A2, A3 on the line AX such that AA1 = A1A2 = A2A3 . Join BA3 .
III : Draw a line through A2 parallel ti BA3 to intersect AB at point b' . Draw a line through B' parallel to the line BC to intersect AC at C'.

1 

Then , ΔAB'C' and ΔABC are

Question 2 of 30

3. PQ is a tangent to a circle with centre O at the point P. If triangle OPQ is an isosceles triangle, then angle OQP is equal to

2

Question 3 of 30

4. In the given figure, PQ is the tangent to the circle at A. DB is the diameter and O is the centre of the circle. If angle ADB = 30° then angle QAB is

1

Question 4 of 30

5. AB is divided into 3 equal parts at P and Q. If AB = x AQ, then x =

Question 5 of 30

6. In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is

2

Question 6 of 30

7. If TP and TQ are two tangents to a circle with centre O so that angle POQ = 110° then angle PTQ is equal to

3

Question 7 of 30

8. Following the given steps the given below has benen constructed.
I : Draw a line segment PQ of length of 12.5 cm. Draw a ray PX making an angle of 90° with PQ.
II : With P as centre, draw an arc of radius 19 cm to intersect the ray PX at point S.
III : Join SQ and make an angle SQY equal to ∠PSQ.
IV : Let QY intersect PX at R.

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Question 8 of 30

9. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at appoint Q such that OQ = 12 cm. Length PQ is

1

Question 9 of 30

10. A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?

Question 10 of 30

11. A line segment AB can be divided into ratio 1 by locating a point C which divides AB in the ratio.

Question 11 of 30

12. To draw a pair of tangents to a circle which are inclined to each other at an angle of 45° it is required to draw tangents at the end point of those two radii of the circle, the angle between which is :

Question 12 of 30

13. D and E are the mid points of sides AB and AC respectively of a triangle ABC such that DE is parallel to BC. If AD = x cm, DB = (x - 2) cm, AE = (x + 2) cm and EC = (x-1) cm, then the value of x is

1

Question 13 of 30

14. In the figure QA and PB are perpendiculars on AB. If AO = 10 cm, BO = 6 cm and PB = 9cm, then AQ is

2

Question 14 of 30

15. In which of the following ratios a line segment cannot be divided using ruler and compass?

Question 15 of 30

16. ABCD is a quadrilateral with BC = 8 cm. Quadrilateral AB'C'D' is constructed with a scale factor 3/4 . What will be the length of B'C'?

Question 16 of 30

17. In the given figure, triangles ABC and DEF are similar. The area of triangle ABC is 9 sq. cm and the area of triangle DEF is 16 sq. cm. If BC = 2.1 cm find the length of EF.

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Question 17 of 30

18. If four sides of a quadrilateral ABCD are tangential to a circle, then

23

Question 18 of 30

19. In the given figure, AB and DE are perpendiculars to BC. If AB = 9cm, DE = 3cm and AC = 24cm then AD is equal to

12

Question 19 of 30

20. Identify the incorrect statement.

Question 20 of 30

21. AB is divided into 3 equal parts at P and Q. If AB = x AQ, then x =

Question 21 of 30

22. 1 

From the given figure, find out what is AC : AB.

Question 22 of 30

23. In the given figure, triangle ABC has been constructed similar to triangle A'BC'. What is the scale factor?

2

Question 23 of 30

24. Length of the tangent to a circle from a point 26 cm away from the centre is 24 cm. What is the radius of the circle?

Question 24 of 30

25. Given a triangle with side AB = 8 cm. To get a line segment AB' = 3/4 of AB, it is required to divide the line segment AB in the ratio:

Question 25 of 30

26. Which of the following relation would hold true for the sides of the similar triangles in the given diagram?

1231

Question 26 of 30

27. Sides of two similar triangles are in the ratio 3:8. Areas of these triangles are in the ratio

0

Question 27 of 30

28. In the triangles PQR and NLM, angle M will be

Question 28 of 30

29. In the given figure, AC: CB is

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Question 29 of 30

30. PT and PS are tangents drawn to a circle, with cantre C, from a point P. If ∠TPS = 50° , then the measure of ΔTCS is

Question 30 of 30

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