Below you will find MCQ Questions of Chapter 11 Constructions Class 10 Maths that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 10 MCQ Questions with answers will widen your skills and understand concepts in a better manner.
MCQ Questions for Class 10 Maths Chapter 11 Constructions with answers
1. To construct a triangle similar to given ΔABC with its sides 8585 of the corresponding sides of ΔABC, 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 :
(a) 3
(b) 5
(c) 8
(d) 13
► (c) 8
2. To divide a line segment AB in the ration 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 at equal distances on ray AX and BY, respectively. Then, the points joined are
(a) A_{5} and B_{6}
(b) A_{4} and B_{5}
(c) A_{5} and B_{4}
(d) A_{6} and B_{5}
► (d) A_{6} and B_{5}
3. To divide a line segment AB in the ration 2 : 5, first a ray AX is drawn, so 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) 2
(b) 4
(c) 5
(d) 7
► (d) 7
4. To construct a triangle similar to given ΔPQR with its sides 5/8 of the corresponding sides of ΔPQR, first a ray PX is drawn such that ∠QPX is an acute angle and X lies on the opposite side of R with respect to PQ. Then locate points P_{1}, P_{2}, P_{3}…. OnPX at equal distances and next step is to join :
(a) P_{5} to Q
(b) P_{8} to Q
(c) P_{3} to Q
(d) P_{6} to Q
► (b) P_{8} to Q
5. To draw tangents to each of the circle with radii 3 cm and 2 cm from the centre of the other circle, such that the distance between their centres A and B is 6 cm, a perpendicular bisector of AB is drawn intersecting AB at M. The next step is to draw
(a) a circle with AB as diameter
(b) a circle with MB as diameter
(c) a circle with AM as diameter
(d) extend AB to P such that BP = MB and draw a circle with MP as diameter
► (a) a circle with AB as diameter
6. 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 points of the two radii of the circle, which are inclined at an angle of
(a) 105°
(b) 115°
(c) 125°
(d) 135°
► (d) 135°
7. 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) 70°
(b) 105°
(c) 140°
(d) 145°
► (d) 145°
8. 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
(a) 150°
(b) 130°
(c) 120°
(d) 100°
► (b) 130°
9. 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)
► (c) (a + b)
10. 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
► (d) 12
11. To divide a line segment LM in the ratio a : b, where a and b are positive integers, draw a ray LX so that ∠MLX is an acute angle and then mark points on the ray LX at equal distances such that the minimum number of these points is :
(a) greater of a and b
(b) a + b
(c) ab
(d) a + b – 1
► (b) a + b
12. 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°
► (a) 60°
13. 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 A_{1},A_{2},A_{3},…. are located at equal distances on the ray AX and the point B is joined to
(a) A_{11}
(b) A_{10}
(c) A_{12}
(d) A_{9}
► (a) A_{11}
14. To divide a line segment AB in the ration 2 : 3, 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 tha the minimum number of these points is
(a) 2
(b) 3
(c) 5
(d) 6
► (c) 5
15. 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
(v) 11
(d) 12
► (d) 12
16. Which theorem criterion we are using in giving the just the justification of the division of a line segment by usual method ?
(a) SSS criterion
(b) Area theorem
(c) BPT
(d) Pythagoras theorem
► (c) BPT
17. A pair of tangents can be constructed to a circle inclined at an angle of :
(a) 165°
(b) 185°
(c) 195°
(d) 175°
► (d) 175°
18. To divide a line segment AB in the ratio 3 : 7 , 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 at equal distances on ray AX and BY respectively. Then the points joined are :
(a) A_{4} and B_{3}
(b) A_{7} and B_{3}
(c) A_{5} and B_{5}
(d) A_{3} and B_{7}
► (a) A_{3} and B_{7}
19. 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
► (c) 10 cm
20. To divide line segment AB in the ration m : n (m, n 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) greater of m and n
(b) mn
(c) m + n
(d) m + n - 1
► (c) m + n
21. To construct a triangle similar to given ΔABC with its sides 3/7 of the corresponding sides of ΔABC draw a ray BX such that ΔCBX 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) 3
(b) 4
(c) 7
(d) 10
► (c) 7
22. 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°
► (b) 90°
Hope the given MCQ Questions will help you in cracking exams with good marks. These Constructions MCQ Questions will help you in practising more and more questions in less time.