## MCQ Questions for Class 10 Maths: Ch 11 Constructions

1. To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that âˆ BAX is an acute angle and then points A

_{1}A_{2}A_{3}, â€¦ are located at equal distances on the ray AX and the point B is joined to
(a) A

_{4}
(b) A

_{11}
(c) A

_{10}
(d) A

â–º (b) A_{7}_{11}

2. When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?

(a) 2/3

(b) 2

(c) 3

(d) 5

â–º (d) 5

3. To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that âˆ 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

â–º (d) 12

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

(a) p + q

(b) pq

(c) p + q â€“ 1

(d) greater of p and q

â–º (a) p + q

5. To construct a triangle similar to given Î”ABC with its sides 8585 of the corresponding sides of Î”ABC, draw a ray BX such that âˆ 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

â–º (c) 8

6. 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

â–º (c) BPT

7. PT and PS are tangents drawn to a circle, with centre C, from a point P. If âˆ TPS = 50Â°, then the measure of âˆ TCS isÂ â€‹

(a) 150Â°

(b) 130Â°

(c) 120Â°

(d) 100Â°

â–º (b) 130Â°

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

(a) right angle

(b) obtuse angle

(c) any arbitrary angle

(d) acute angle

â–º (d) acute angle

9. To divide a line segment AB in the ratio 5 : 6 draw a ray AX such that âˆ BAX is an acute angel, then draw a ray BY parallel to AX and the points A_(1 ,) A_(2 ,) A_(3 ,) â€¦ and B_(1 ,) B_(2 ,) B_(3 ,)â€¦ are located a equal distances on ray AX and BY, respectively, Then the points joined are :

(a) A

_{4}and B_{5}
(b) A

_{5}and B_{4}
(c) A

_{5}and B_{6}
(d) A

_{6}and B_{5}
â–º (c) A

10. To divide line segment AB in the ratio A : b ( a, b are positive integers), draw a ray AX so that âˆ 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 â€“ 1)

â–º (c) ( a + b)

14. 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) 3

(c) Infinite

(d) 2

â–º (d) 2

_{5}Â and B_{6}10. To divide line segment AB in the ratio A : b ( a, b are positive integers), draw a ray AX so that âˆ 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 â€“ 1)

â–º (c) ( a + b)

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

(a) 105Â°

(b) 135Â°

(c) 145Â°

(d) 70Â°

â–º (b) 135Â°

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) 2

(b) 1

(c) Infinite

(d) 0

â–º (a) 2

13. To divide a line segment AB in the ration 4 : 7, a ray AX is drawn first such that âˆ BAX is an acute angle and then points A

_{1},A_{2},A_{3},â€¦are located at equal distances on the ray AX and the point B is joined to :
(a) A

_{10}
(b) A

_{11}
(c) A

_{12}
(d) A

â–º (b) A_{9}_{11}14. 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) 3

(c) Infinite

(d) 2

â–º (d) 2

15. To construct a triangle similar to given Î”ABC with its sides 3/7 of the corresponding sides of Î”ABC, first draw a ray BX such that âˆ CBXis an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B

_{1},B_{2},B_{3}, on BX equal distance and next step is to join :
(a) B

_{4}to C
(b) B

_{10}to C
(c) B

_{6}to C
(d) B

â–º (d) B

_{7}to Câ–º (d) B

_{7}Â to C
16. To draw a pair of tangents to circle which are inclined to each other at angle of 60Â°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be :

(a) 60Â°

(b) 90Â°

(c) 120Â°

(d) 130Â°

â–º (c) 120Â°

17. 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

â–º (d) Altitude

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

(a) 180Â°âˆ’xÂ°

(b) 90Â°+xÂ°

(c) 90Â°âˆ’xÂ°

(d) 180Â°+xÂ°

â–º (a) 180Â°âˆ’xÂ°

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?â€‹

(a) 11 cm

(b) 13 cm

(c) 10 cm

(d) 12 cm

â–º (c) 10 cm

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

(a) 60Â°

(b) 90Â°

(c) 100Â°

(d) 120Â°

â–º (a) 60Â°

21. A draw a pair of tangents to a circle which are inclined to each other at an angle of 65Â°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is:

(a) 95Â°

(b) 105Â°

(c) 110Â°

(d) 115Â°

â–º (d) 115Â°

22. To draw a pair tangents to a circle which are inclined to each other at an angle of 70Â°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should beÂ

(a) 20Â°

(b) 70Â°

(c) 90Â°

(d) 110Â°