## 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 ∠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

_{4}
(b) A

_{11}
(c) A

_{10}
(d) A

► (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

► (d) 5

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:

(a) 8

(b) 10

(c) 11

(d) 12

► (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 ∠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 – 1

(d) greater of p and q

► (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 ∠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

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

► (c) BPT

7. 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°

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

► (d) acute angle

9. To divide a line segment AB in the ratio 5 : 6 draw a ray AX such that ∠BAX is an acute angel, 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 :

(a) A

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

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

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

_{6}and B_{5}
► (c) A

10. 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)

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

► (d) 2

_{5}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 ∠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)

11. 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°

► (b) 135°

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

► (a) 2

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

_{10}
(b) A

_{11}
(c) A

_{12}
(d) A

► (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

► (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 ∠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

► (d) B

_{7}to C► (d) B

_{7}to C
16. 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 :

(a) 60°

(b) 90°

(c) 120°

(d) 130°

► (c) 120°

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

► (d) Altitude

18. 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°

► (a) 180°−x°

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. 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°

21. 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°

► (d) 115°

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

(a) 20°

(b) 70°

(c) 90°

(d) 110°