# MCQ Questions for Class 10 Maths Chapter 11 Constructions with Answers

Below you will find NCERT MCQ Questions for Class 10 Maths Chapter 11 Constructions with Answers which is very helpful during the preparation of examinations. These MCQ Online Test are one marks questions which will give you overview of the chapter in no time. One should try to understand Class 10 MCQ Questions as it is based on latest exam pattern released by CBSE.

Also, students can check NCERT Solutions for Class 10 Maths Chapter 11 for improving their marks and have good understanding of the chapter. ## Chapter 11 Constructions MCQ Questions for Class 10 Maths with Answers

1. 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
(a) ab
(b) Greater of a and b
(c) (a + b)
(d) (a + b – 1)
Solution (c) (a + b)

2. 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) 90°
(b) 135°
(c) 130°
(d) 145°
Solution (d) 145°

3. If the construction of a triangle ABC in which AB = 6 cm, ∠A = 70° and ∠B = 40° is possible then find the measure of ∠C.
(a) 50°
(b) 70°
(c) 90°
(d) none of these
Solution (b) 70°

4. A pair of tangents can be constructed to a circle inclined at an angle of :
(a) 155°
(b) 165°
(c) 175°
(d) 185°
Solution (c) 175°

5. 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?
(a) 11 cm
(b) 13 cm
(c) 10 cm
(d) 12 cm
Solution (c) 10 cm

6. To divide a line segment AP in the ration 2 : 9, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1,A2,A3... are located of equal distances on the ray AX and the points P is joined to
(a) A3
(b) A8
(c) A11
(d) A12
Solution (c) A11

7. To construct a triangle similar to a given triangle ABC with its sides 2/3 of the corresponding sides side of A with respect to BC. Then locate points X1,X2,X3… at equal distance on BX. The points to be joined in the next step are
(a) X4 and C
(b) X3 and C
(c) cand C
(d) X1 and C
Solution (c) X3 and C

8. 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
Solution (d) 12

9. To construct a triangle similar to given ΔABC with its sides 7/4 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) 2
(b) 3
(c) 4
(d) 7
Solution (d) 7

10. 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
(a) 180°−x°
(b) 90°+x°
(c) 90°−x°
(d) 180°+x°
Solution (a) 180°−x°

11. Two distinct tangents can be constructed from a point P to a circle of radius 2r situated at a distance:
(a) r from the centre
(b) 2r from the centre
(c) more than 2r from the centre
(d) less than 2r from the centre
Solution (c) more than 2r from the centre

12. 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?
(a) 1
(b) 2
(c) Infinite
(d) 0
Solution (b) 2

13. To divide a line segment LM in the ratio 4 : 3, a ray LX is drawn firs such that ∠MLX is an acute angle and then points L1, L2, L3, … are located at equal distances on the ray LX and the points M is joined to :
(a) L4
(b) L2
(c) L3
(d) L7
Solution (d) L7

14. 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
(a) 60°
(b) 90°
(c) 100°
(d) 120°
Solution (a) 60°

15. 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 (a) 5
(b) 2
(c) -4
(d) 4
Solution (d) 4

16. To draw a pair of tangents to a circle which are at right angles to each other, it is required to draw tangents at end points of the two radii of the circle, which are inclined at an angle of
(a) 60°
(b) 90°
(c) 45°
(d) 120°
Solution (b) 90°

17. 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 :​
(a) 105°
(b) 135°
(c) 145°
(d) 70°
Solution (b) 135°

18. A draw a pair of tangents to a circle which are inclined to each other at an angle of 65°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is :
(a) 95°
(b) 105°
(c) 110°
(d) 115°
Solution (d) 115°

19. To divide a line segment AB internally in the ratio 4 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on ray AX such that the minimum number of these points is
(a) 9
(b) 10
(c) 11
(d) 12
Solution (c) 11

20. A line segment drawn perpendicular from the vertex of a triangle to the opposite side is called the
(a) Bisector
(b) Median
(c) Perpendicular
(d) Altitude
Solution (d) Altitude

21. 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 to those two radii of the side, the angle between which is​
(a) 90°
(b) 30°
(c) 120°
(d) 45°
Solution (c) 120°

22. To draw tangents to a circle of radius ‘p’ from a point on the concentric circle of radius ‘q’, the first step is to find
(a) midpoint of p
(b) midpoint of q
(c) midpoint of q – r
(d) midpoint of p + q
Solution (b) midpoint of q
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