Welcome to your Constructions MCQs Mock Test of 10th Class Mathematics

1.
Q 1. 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

2.
Q2. To divide a line segment AB in the ratio 3:4, 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:

3.
Q 3. 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

4.
Q4. To divide a line segment AB of length 7.6 cm in the ratio 5 : 8, a ray AX is drawn first such that ∠BAX forms 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:

5.
Q 5. To divide a line segment AB in the ratio 4 : 7, 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

6.
Q6. To construct a triangle similar to a given ΔPQR with its sides 5/8 of the similar sides of ΔPQR, draw a ray QX such that ∠QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q1, Q2, Q3, … on QX at equal distances, and the next step is to join:

7.
Q 7. 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 B4 parallel to AX and the points A1, A2, A3, …….. and B1, B2, B3,………. are located at equal distances on ray AX and B4, respectively. Then the points joined are

8.
Q8. To construct a triangle similar to a given ΔPQR with its sides, 9/5 of the corresponding sides of ΔPQR draw a ray QX such that ∠QRX is an acute angle and X is on the opposite side of P with respect to QR. The minimum number of points to be located at equal distances on ray QX is:

9.
Q 9. To construct a triangle similar to a given ΔABC with its sides 37 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

10.
Q10. To construct a pair of tangents to a circle at an angle of 60° to each other, it is needed to draw tangents at endpoints of those two radii of the circle, the angle between them should be:

11.
Q 11. To construct a triangle similar to a given ΔABC with its sides 85 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. Then minimum number of points to be located at equal distances on ray BX is

12.
Q12. To divide a line segment PQ in the ratio m : n, where m and n are two positive integers, draw a ray PX so that ∠PQX is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is:

13.
Q 13. 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

14.
Q14. 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 endpoints of those two radii of the circle, the angle between which is:

15.
Q15. 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.

16.
Q16. To construct a triangle ABC and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. A ray AX is drawn where multiple points at equal distances are located. The last point to which point B will meet the ray AX will be:

17.
Q17. To construct a triangle similar to a given ΔPQR with its sides 3/7 of the similar sides of ΔPQR, draw a ray QX such that ∠QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q1, Q2, Q3, … on QX at equal distances, and the next step is to join:

18.
Q18. If the scale factor is 3/5, then the new triangle constructed is _____ the given triangle.

19.
Q19. 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

20.
Q20. By geometrical construction, which one of the following ratios is not possible to divide a line segment?

21.
Q21. By geometrical construction, is it possible to divide a line segment in the ratio 1/√3 : √3?

22.
Q22. In constructions, the scale factor is used to construct ______ triangles.

23.
Q23. In the division of a line segment AB, any ray AX making angle with AB is _______.

24.
Q24. A point P is at a distance of 8 cm from the centre of a circle of radius 5 cm. How many tangents can be drawn from point P to the circle?

25.
Q25. To divide a line segment AB in the ratio p : q, 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 9. Here, the possible ratio of p : q is

26.
Q26. A line segment drawn perpendicular from the vertex of a triangle to the opposite side is known as

27.
Q27. If the line segment is divided in the ratio 3 : 7, then how many parts does it contain while constructing the point of division?

28.
Q28. Which theorem criterion we are using in giving the just the justification of the division of a line segment by usual method ?

29.
Q29. In division of a line segment AB, any ray AX making angle with AB is

30.
Q30. To divide a line segment AB in the ratio 4 : 7, 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

31.
Q31. 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

32.
Q32. A line segment drawn perpendicular from the vertex of a triangle to the opposite side is called the

33.
Q33. 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?

34.
Q34. To divide a line segment AB in the ration 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 :

35.
Q35. To draw a pair of tangents to a circle which are inclined to each other at angle x°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is

36.
Q36. To construct a triangle similar to given ?ABC with its sides 8585 of the corresponding sides of ?ABC, draw a ray BX such that ?CBX is an acute angle and X is one the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is :

37.
Q37. 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??

38.
Q38. 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:

39.
Q39. If two tangents are drawn at the end points of two radii of a circle which are inclined at 120° to each other, then the pair of tangents will be inclined to each other at an angle of

40.
Q40. To draw a pair of tangents to circle which are inclined to each other at 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 :

41.
Q41. 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 A_(1 ,) A_(2 ,) A_(3 ,) … and B_(1 ,) B_(2 ,) B_(3 ,)… are located a equal distances on ray AX and BY, respectively, Then the points joined are :

42.
Q42. 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?

43.
Q43. To divide line segment AB in the ratio A : b ( a, b 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

44.
Q44. PT and PS are tangents drawn to a circle, with centre C, from a point P. If ?TPS = 50°, then the measure of ?TCS is ?

45.
Q45. To divide a line segment AB in the ratio p : q ( p, q are positive integers), draw a ray AX so that ?BAX s an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is :

46.
Q46. 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

47.
Q47. 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