# MCQs for Class 10 Maths Chapter 11 Constructions

MCQs for **Class 10 Maths Chapter 11 Constructions**: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# Class 10 Maths Chapter 11 Constructions MCQ

1. 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

Answer: (d) 12

2. 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:

(a)5

(b)7

(c)9

(d)11

Answer: (b)7

3. 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

Answer: (c) 8

4. 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

(a) greater of p and q

(b) p + q

(c) p + q – 1

(d) pq

Answer: (b) p + q

5. 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_{7}

Answer: (b) A_{11}

6. To divide a line segment PQ in the ratio 5 : 7, first a ray PX is drawn so that ∠QPX is an acute angle and then at equal distances points are marked on the ray PX such that the minimum number of these points is

(a) 5

(b) 7

(c) 12

(d) 10

Answer: (c) 12

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 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

(a) A5 and B6

(b) A6 and B5

(c) A4 and B5

(d) A5 and B4

Answer: (a) A5 and B6

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8. To divide a line segment AB of length 7.6cm 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:

(a)A5

(b)A6

(c)A10

(d)A13

Answer: (d)A13

9. 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

Answer: (d) 7

10. 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) 105°

(b) 70°

(c) 140°

(d) 145°

Answer: (d) 145°

11. 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

Answer: (d) 5

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

(a) 23

(b) 2

(c) 3

(d) 5

Answer: (d) 5

13. To construct a triangle similar to a given ΔABC with its sides 3/7 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:

(a) B10 to C

(b) B3 to C

(c) B7 to C

(d) B4 to C

Answer: (c) B7 to C

14. 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:

(a)Q10 to C

(b)Q3 to C

(c)Q8 to C

(d)Q4 to C

Answer: (c)Q8 to C

15. 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 P1, P2, P3…. OnPX at equal distances and next step is to join :

(a) P5 to Q

(b) P8 to Q

(c) P3 to Q

(d) P6 to Q

Answer: (b) P8 to Q

16. 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

Answer: (d) 12

17. 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

Answer: (a) p + q

18. To construct a triangle similar to a given ΔABC with its sides 8/5 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) 5

(b) 8

(c) 13

(d) 3

Answer: (b) 8

19. 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:

(a)5

(b)9

(c)10

(d)14

Answer: (b)9

20. 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

Answer: (a) a circle with AB as diameter

21. To construct a triangle similar to a given ΔABC with its sides 3/7 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

(a) B10 to C

(b) B3 to C

(c) B7 to C

(d) B4 to C

Answer: (c) B7 to C

22. 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

Answer: (c) 8

23. 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:

(a) 135°

(b) 90°

(c) 60°

(d) 120^{o}

Answer: (d) 120^{o}

24. 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:

(a)100

(b)90

(c)180

(d)120

Answer: (d)120

25. 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°

Answer: (d) 135°

26. 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

(a) 5

(b) 8

(c) 13

(d) 3

Answer: (b) 8

27. 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

Answer: (c) BPT

28. 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

(a) greater of p and q

(b) p + q

(c) p + q – 1

(d) pq

Answer: (b) p + q

29. 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:

(a)M+n

(b)M-n

(c)M+n-1

(d)Greater of m and n

Answer: (a)M+n

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30. 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°

Answer: (d) 145°

31. 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

(a) 135°

(b) 90°

(c) 60°

(d) 120°

Answer: (d) 120°

32. 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°

Answer: (b) 130°

33. Construction Class 10 MCQ Question 1. To divide a line segment PQ in the ratio 5 : 7, first a ray PX is drawn so that âˆ QPX is an acute angle and then at equal distances points are marked on the ray PX such that the minimum number of these points is

(a) 5

(b) 7

(c) 12

(d) 10

Answer: (c) 12

34. 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) 105°

(b) 70°

(c) 140°

(d) 145°

Answer: (d) 145°

35. 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:

(a)135

(b)155

(c)160

(d)120

Answer: (a)135

36. 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)

Answer: (c) (a + b)

37. 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

Answer: (d) acute angle

38. 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.

(a) 5cm

(b) 2cm

(c) 3cm

(d) 3.5cm

Answer: (a) 5cm

39. 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:

(a)A1

(b)A2

(c)A3

(d)A4

Answer: A3

40. 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

Answer: (d) 12

41. 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)

Answer: (c) ( a + b)

42. To divide a line segment AB in the ratio 5:6, draw a ray AX such that ∠BAX is an acute angle, then drawa ray BY parallel to AX and the points A1, A2, A3,…. and B1, B2, B3,…. are located to equal distances on ray AX and BY, respectively. Then, the points joined are

(a) A5 and B6

(b) A6 and B5

(c) A4 and B5

(d) A5 and B4

Answer: (a) A5 and B6

43. 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:

(a)Q10 to C

(b)Q3 to C

(c)Q7 to C

(d)Q4 to C

Answer: (c)Q7 to C

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44. 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°

Answer: (a) 60°

45. 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°

Answer: (b) 135°

46. A rhombus ABCD in which AB = 4cm and ABC = 60o, divides it into two triangles say, ABC and ADC. Construct the triangle AB’C’ similar to triangle ABC with scale factor 2/3. Select the correct figure.

Answer: (a)

47. 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

(a) A11

(b) A10

(c) A12

(d) A9

Answer: (a) A11

48. 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

Answer: (a) 2

49. A triangle ABC is such that BC = 6 cm, AB = 4 cm and AC = 5 cm. For the triangle similar to this triangle with its sides equal to (3/4)th of the corresponding sides of ΔABC, correct figure is:

Answer: (d)

50. 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

Answer: (c) 5

51. 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

Answer: (d) 2

52. 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

Answer: (d) 12

53. To construct a triangle similar to given ΔABC with its sides 3/7 of the corresponding sides of ΔABC, 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_{7} to C

Answer: (d) B_{7} to C

54. A pair of tangents can be constructed to a circle inclined at an angle of :

(a) 165°

(b) 185°

(c) 195°

(d) 175°

Answer: (d) 175°

55. A pair of tangents can be constructed to a circle inclined at an angle of :

(a) 165°

(b) 185°

(c) 195°

(d) 175°

Answer: (d) 175°

56. 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 A1,A2,A3, … and B1,B2,B3,… are located at equal distances on ray AX and BY respectively. Then the points joined are :

(a) A4 and B3

(b) A7 and B3

(c) A5 and B5

(d) A3 and B7

Answer: (a) A3 and B7

57. 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

Answer: (d) Altitude

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58. 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

Answer: (c) 10 cm

59. 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°

Answer: (a) 180°−x°

60. 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

Answer: (c) m + n

61. 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

Answer: (c) 10 cm

62. 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

Answer: (c) 7

63. 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°

Answer: (b) 90°

64. 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°

Answer: (a) 60

65. 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°

Answer: (d) 115°

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