We provide constructions practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on constructions skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of constructions Questions

Question No | Questions | Class |
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1 | Choose the correct statement: A. Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest. B. The difference of two sides of a triangle is equal to the third side. C. The sum of the three sides of a triangle is less than the sum of its three medians. D. If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it. | 9 |

2 | In the fig. ( A P ) and ( B P ) are the tangents draw from an external point P. Prove that ( angle A O B ) and ( angle A P B ) are supplementary | 10 |

3 | Draw a square of ( 4 mathrm{cm} . ) Constuct angle bisectors of 4 angles.Let all meet at 0 measure ( A O ) and ( 0 C . ) Then ( A O^{2}+O C^{2}= ) ( mathbf{A} cdot mathbf{8} ) B. 4 c. 16 D. 32 | 9 |

4 | Construct a triangle ( A B C ) in which ( B C=8 c m, angle B=45^{circ} ) and ( A B ) ( boldsymbol{A C}=mathbf{3 . 5} boldsymbol{c m} ) | 9 |

5 | Construct a tangent to a circle of radius ( 4 c m ) from a point on the concentric circle of radius ( 6 mathrm{cm} ) and measure its length. Also verify the measurement by actual calculation. | 10 |

6 | Draw a circle of radius ( 5 mathrm{cm} . ) From a point ( 8 mathrm{cm} ) away from the centre, construct two tangents to the circle. Measure them. (Write the steps of construction). | 10 |

7 | In the figure, PQ and PR are the tangents to a circle with centre 0. If ( angle P=frac{4}{5} angle O . ) Find ( angle O ) and ( angle P ) | 10 |

8 | In a circle, let ( A B ) be diameter. Let ( P ) is point on circle. Then measure of angle APB is A ( .30^{circ} ) B . ( 40^{circ} ) ( c .90^{circ} ) D. ( 60^{circ} ) | 9 |

9 | Construct a pair of tangents to a circle of radius ( 4 mathrm{cm} ) such that the acute angle between the tangents is ( 45^{circ} ) | 10 |

10 | In an equilateral triangle ( Delta A B C ) with sides ( 5 mathrm{cm} . ) Angle bisectors of ( angle A, angle B, angle C ) meet at point ( 0 . ) Measures of OA approximately is A . 2.5 B. 4 ( c .3 .2 ) D. 2.8 | 9 |

11 | Construct tangents to a circle of radius ( 4 mathrm{cm} ) at ( Q ) and ( R, ) from a point ( P ) on the concentric circle of radius ( 6 mathrm{cm} ) | 10 |

12 | The point (4,0) lie on the line A. ( y-x=0 ) В. ( y=0 ) c. ( x=0 ) D. ( y+x=0 ) | 10 |

13 | Construct a triangle with sides ( 5 mathrm{cm}, 6 mathrm{cm} ) and ( 7 mathrm{cm} ) and then another triangle whose sides are ( frac{7}{5} ) times of the corresponding sides of the first triangle. Write down the steps of construction. | 10 |

14 | Write down the co-ordinates of the points ( A ) to ( J ) marked in the following diagram: | 10 |

15 | In what ratio does (-4,6) divides the line segment joining the point ( boldsymbol{A}(-mathbf{6}, mathbf{4}) ) and ( B(3,-8) ) | 10 |

16 | nd D are any two points on the same side of a line L. now how to find a point P on the line L such that PC and PD are equally inclined to the line L. Justify your steps. (1980) | 9 |

17 | If the point ( P(2,2) ) is equidistant from the points ( A(-2, k) ) and ( B(-2 k,-3) ) find ( k ) | 10 |

18 | ( mathbf{A} triangle boldsymbol{A} boldsymbol{B} boldsymbol{C} ) in which ( boldsymbol{A} boldsymbol{B}= ) ( mathbf{5 . 4} mathbf{c m}, angle boldsymbol{C} boldsymbol{A} boldsymbol{B}=mathbf{4 5}^{circ} ) and ( boldsymbol{A} boldsymbol{C}+boldsymbol{B} boldsymbol{C}= ) ( mathbf{9} mathrm{cm} . ) Then, perimeter of ( Delta boldsymbol{A B C} ) is A. ( 14.4 mathrm{cm} ) B. ( 11.4 mathrm{cm} ) ( c .12 .4 mathrm{cm} ) D. ( 15.4 mathrm{cm} ) | 9 |

19 | The lengths of the tangents (in ( c m ) ) measured by a ruler are: ( mathbf{A} cdot mathbf{6} ) B. 7 c. 8 D. 9 | 10 |

20 | n the figure, ( C ) is the centre of the circle. ( X ) and ( Y ) axes are tangents to the circle at the points ( A ) and ( B ) respectively. If the coordinates of ( A ) are ( (4,0), ) find the coordinates of ( B ) and ( C ) | 10 |

21 | ( Delta A M T sim Delta A H E cdot ln Delta A M T, M A= ) ( 6.3 c m, angle M A T=120^{circ}, A T=4.9 mathrm{cm} ) ( frac{M A}{H A}=frac{7}{5} ) Construct ( Delta A H E ) | 10 |

22 | Point (0,-9) lies A. on the ( X ) -axis B. In the II quadrant c. on the Y-axis D. In the ( I V ) quadrant | 10 |

23 | Find the equation for the graph above. ( mathbf{A} cdot x=3 ) ( mathbf{B} cdot y=3 ) C. ( y=-5 ) D. ( x=-5 ) | 10 |

24 | Construct a triangle similar to a given triangle ( A B C ) with its side equal to ( frac{5}{3} ) of corresponding side of triangle ( boldsymbol{A B C} ) (i.e., of scale factor ( frac{5}{3} ) ). | 10 |

25 | Draw ( angle A B C ) of measure ( 110^{circ} ) and bisect it. | 9 |

26 | Using a ruler and compass only. (i) Construct a ( triangle A B C ) with the following data. ( A B=3.5 mathrm{cm}, B C=6 mathrm{cm} ) and ( angle A B C=120^{circ} ) (ii) In the same diagram, draw a circle with ( B C ) as diameter. Find a point ( P ) on the circumference of the circle which is equidistant from ( A B ) and ( B C ) (iii) Measure ( angle B C P ) | 9 |

27 | If tangents are drawn from the end points of 2 radii that are inclined at an angle ( 125^{circ}, ) what is the angle between the tangents? A . 55 B. ( 110^{circ} ) c. ( 125^{circ} ) D. ( 90^{circ} ) | 10 |

28 | The areas of two similar triangles are 45 sq. ( mathrm{cm} ) and 80 sq.cm. The sum of their perimeters is ( 35 mathrm{cm} . ) Find the perimeter of each triangle in cm. ( mathbf{A} cdot 15,20 ) B. 13,22 c. 17,18 D. None of these | 10 |

29 | Construct a ( triangle A B C ) in which ( A B= ) ( mathbf{5} c boldsymbol{m} cdot angle boldsymbol{B}=mathbf{6 0}^{circ} ) altitude ( boldsymbol{C} boldsymbol{D}=mathbf{3} boldsymbol{c m} ) Construct a ( triangle A Q R ) similar to ( triangle A B C ) such that side of ( triangle A Q R ) is 1.5 times that of the corresponding sides of ( triangle boldsymbol{A} boldsymbol{C} boldsymbol{B} ) | 10 |

30 | Construct a triangle ( A B C ) whose perimeter is ( 12.5 mathrm{cm} ) and whose base angles are ( 60^{circ} ) and ( 75^{circ} ) | 9 |

31 | If ( P(x, y) ) is any point on the line joining the points ( (a, 0) ) and ( (0, b) ) then the value of ( frac{x}{a}+frac{y}{b} ) ( A ) B. 2 ( c cdot 3 ) D. | 10 |

32 | The construction of a ( Delta A B C ) in which ( B C=6 mathrm{cm} ) and ( angle B=50^{circ}, ) is not possible when ( (A B-A C) ) is equal to: A ( .5 .6 mathrm{cm} ) в. ( 5 mathrm{cm} ) ( c cdot 6 c m ) D. ( 4.8 mathrm{cm} ) | 9 |

33 | Find the co-ordinate of a points on ( x ) axis which is equidistant from the points (-2,5) and (2,-3) | 10 |

34 | If ( 2^{2 x-y}=32 ) and ( 2^{x+y}=16 ) then ( x^{2}+ ) ( y^{2} ) is equal to A . 9 B. 10 ( c cdot 11 ) D. 13 | 10 |

35 | To find a point ( boldsymbol{P} ) on the line segment ( A B=6 mathrm{cm}, ) such that ( A P: A B=2: 5 ) in which ratio does the line segment ( A B ) is divided by ( P ? ) | 10 |

36 | The co-ordinates of the point of trisection of the line segment joining the points (-4,3) and (2,-1) are A ( .(2,1) ) в. (3,1) ( ^{mathbf{c}} cdotleft(-2, frac{5}{3}right) ) D. None of these | 10 |

37 | ( A B C ) is a triangle. ( D ) is a point on ( A B ) such that ( A D=frac{1}{4} A B ) and ( E ) is a point on ( A C ) such that ( A E=frac{1}{4} A C . ) Prove that ( D E=frac{1}{4} B C ) | 9 |

38 | Construct a triangle ( P Q R ) in which ( angle Q=30^{circ}, angle R=90^{circ} ) and ( P Q+Q R+ ) ( boldsymbol{P R}=11 mathrm{cm} ) | 9 |

39 | Construct a triangle XYZ in which ( angle Y= ) ( 30^{0}, angle Z=90^{0} ) and ( X Y+Y Z+Z X=11 mathrm{cm} ) | 9 |

40 | If tangents are drawn from the endpoints of two radii that are inclined at an angle of ( 165^{circ}, ) what is the angle between the tangents? A ( cdot 5^{circ} ) B. 35 ( c cdot 15^{circ} ) D. None of these | 10 |

41 | If the mid-point of the line segment joining the points ( A(6, x-2) ) and ( B(-2,4) ) is (2,-3) find the value of ( x ) | 10 |

42 | Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2,-1) (1,0),(4,3) and (1,2) meet. A . (5,1) в. (1,1) c. (1,5) (年. (1,5) D. ( (1,1-) ) | 10 |

43 | From (1,4) you travel ( 5 sqrt{2} ) units by making ( 135^{0} ) angles with positive ( x ) axis (anticlockwise) and then 4 units by making ( 120^{0} ) angle with positive ( x ) -axis (clockwise) to reach Q. Find co- ordinates of point ( Q ) A ( cdot(+6,9-2 sqrt{3}) ) в. ( (-6,9-2 sqrt{3}) ) c. ( (-6,9+2 sqrt{3}) ) D. ( (+6,9+2 sqrt{3}) ) | 10 |

44 | ( 1 D= ) | 10 |

45 | Construct a triangle ( A B C ) in which ( B C=7 c m, angle B=75^{circ} ) and ( A B+ ) ( A D=13 mathrm{cm} ) | 9 |

46 | Draw a circle of radius ( 3 mathrm{cm} ) and construct two tangents to it from an external point ( 8 c m ) away from its centre | 10 |

47 | Construct a rectangle ( A B C D ) of lengh 6 ( mathrm{cm} ) and breadth ( 4 mathrm{cm} . ) Construct angle bisectors of ( angle A ) and ( angle B . ) Let them meet at 0.The distance of 0 from length ( A B ) is: A . 3 B. 10 c. 2 D. 8 | 9 |

48 | Draw a circle with centre 0 and radius 3.5 ( mathrm{cm} . ) Take point ( mathrm{P} ) at a distance ( 5.7 mathrm{cm} ) from the centre. Draw tangents to the circle from point ( P ) | 10 |

49 | In triangle ( A B C ; ) angle ( A=90^{circ}, ) side ( A B=x c m, A C=(x+5) c m ) and area ( =150 mathrm{cm}^{2} ). Find the sides of the triangle. | 9 |

50 | Construct a ( triangle P Q R, ) such that ( angle Q=70^{circ} ) ( angle R=70^{circ} ) and ( P Q+Q R+R P=10 ) ( mathrm{cm} ) | 9 |

51 | Draw ( angle P O Q ) of measure ( 75^{circ} ) and find its line of symmetry. | 9 |

52 | Construct a scalene triangle ( boldsymbol{A B C} ) given base ( A B=3 c m, ) base angle ( = ) ( 90^{circ} ) and sum of the lengths ( B C+ ) ( boldsymbol{A C}=mathbf{9} boldsymbol{c m} ) | 9 |

53 | Draw the tangents to the circle from the point ( L ) with radius ( 2.9 mathrm{cm} . ) Point ( ^{prime} L^{prime} ) is at a distance ( 7.5 mathrm{cm} ) from the centre ( boldsymbol{M}^{prime} ) | 10 |

54 | ( triangle L T R sim triangle H Y D, triangle H Y D ) is such that ( boldsymbol{H} boldsymbol{Y}=mathbf{7 . 2} boldsymbol{c m}, boldsymbol{Y} boldsymbol{D}=boldsymbol{6} boldsymbol{c m}, angle boldsymbol{Y}= ) ( 40^{circ} ) and ( frac{L R}{H D}=frac{5}{6} ) and construct ( triangle boldsymbol{L} boldsymbol{T} boldsymbol{R} ) | 10 |

55 | Measure the length of ( A B ) with a ruler. Then ( A B=? ) A ( .7 .5 mathrm{cm} ) B. ( 9.6 mathrm{cm} ) ( c .10 mathrm{cm} ) D. ( 8.4 mathrm{cm} ) | 10 |

56 | Show that the mid-point of the line segment joining the points (5,7) and (3,9) is also the mid-point of the line segment joining the points (8,6) and (0,10) | 10 |

57 | What is an angle bisector? | 9 |

58 | In Figure ( 1, ) the ratio of ( A B ) to ( B C ) is 7: 5. If ( A C=1, ) calculate the distance from ( A ) to the midpoint of ( B C ) A ( cdot frac{5}{8} ) B. ( frac{2}{3} ) c. ( frac{19}{24} ) D. ( frac{3}{4} ) | 10 |

59 | Construct a triangle ( A B C ) whose perimeter ( 12 mathrm{cm} ) and who base angles ( operatorname{are} 50^{circ} ) and ( 80^{circ} ) | 9 |

60 | Construct a triangle ( A B C ) in which ( B C=5.6 mathrm{cm}, angle B=45^{circ} ) and ( A B+ ) ( boldsymbol{A C}=boldsymbol{8} boldsymbol{c m} ) | 9 |

61 | Find the ratio in which the line joining ( A(1,-5) ) and ( B(-4,5) ) is divided by the ( x-a x ) is. Also find the co-ordinates of the point of division. | 10 |

62 | Construct a triangle ( A B C ) in which ( B C=7 c m, angle B=75^{circ} ) and ( A B+ ) ( boldsymbol{A C}=mathbf{1 3} boldsymbol{c m} ) | 9 |

63 | Any point on the ( x ) -axis is of the form ( mathbf{A} cdot(x, y) ) в. ( (0, y) ) c. ( (x, 0) ) D. ( (x, x) ) | 10 |

64 | Find the length ( E C ) ( s ) D | 10 |

65 | The construction of ( triangle A B C ) in which ( A B=6 mathrm{cm}, angle A=30^{circ}, ) is not possible when ( boldsymbol{A C}+boldsymbol{B C}= ) ( mathbf{A} cdot 6.3 mathrm{cm} ) B. ( 7.2 mathrm{cm} ) ( c .5 .6 mathrm{cm} ) D. ( 6.9 mathrm{cm} ) | 9 |

66 | ( triangle R H P sim triangle N E D ) in ( triangle N E D, N E= ) ( 7 mathrm{cm}, angle E=30^{circ}, angle N=20^{circ} ) and ( frac{H P}{E D}=frac{4}{5} ) Construct ( triangle R H P ) | 10 |

67 | Draw a line segment of length ( 6.3 mathrm{cm} ) & divide it in the ratio ( 3: 4 . ) Measure the two parts. | 10 |

68 | Perimeter of ( triangle A B C ) is ( 14 mathrm{cm}, mathrm{AB}=4.5 mathrm{cm} ) and ( angle A=80^{circ} . ) Construct ( triangle A B C ) | 9 |

69 | The line joining the points (1,-2) and (-3,4) is trisected; find the coordinates of the points of trisection. | 10 |

70 | Write the steps to construct ( triangle A B C, ) in which ( B C=5.2 c m, angle A C B=45^{circ} ) and perimeter of ( triangle boldsymbol{A B C} ) is ( 10 mathrm{cm} ) | 9 |

71 | In the figure 0 is the centre of the circle. The tangents at ( mathrm{B} ) and ( mathrm{D} ) intersect each other at point P. If AB is parallel to CD and ( angle A B C=55^{circ} ) Find (i) ( angle B O D ) (ii) ( angle B P D ) | 10 |

72 | Construct a ( triangle A B C ) in which ( A B= ) ( 4 mathrm{cm}, B C=5 mathrm{cm} ) and ( A C=6 mathrm{cm} ) Now, construct a triangle similar to ( triangle A B C ) such that each of its sides is two-third of the corresponding sides of ( triangle A B C . ) Also, prove your assertion. | 10 |

73 | If ( 4 x+3 y=120, ) find how many non- negative integer solutions are possible? ( mathbf{A} cdot mathbf{1} ) B. 11 c. Infinite D. None of these | 10 |

74 | What is the equation for the graph shown above? ( mathbf{A} cdot y=2 ) B. ( y=-4 ) c. ( x=2 ) D. ( x=-4 ) | 10 |

75 | Draw the line joining the following points. ( P(-4,5) ) and ( Q(3,-4) ) | 10 |

76 | Write the following based on the graph. The ordinate of Lis ( 4 .-7 ) B ( c_{1}-5 ) None of these | 10 |

77 | What should be the angle between corresponding radii such that the tangents don’t intersect? A . ( 0^{circ} ) B. ( 90^{circ} ) ( c cdot 180^{circ} ) D. ( 45^{circ} ) | 10 |

78 | Construct a pair of tangents to a cricle of radius ( 3.5 mathrm{cm} ) from a point ( 3.5 mathrm{cm} ) away from the circle. | 10 |

79 | Draw ( angle A B C ) of measure ( 115^{circ} ) and bisect it. | 9 |

80 | Plot the point (5,0) on a graph paper. | 10 |

81 | If the roots of the equation ( x^{3}-11 x^{2}+ ) ( 36 x-36=0 ) are in ( H . P . ) then the middle root is A. an even number B. a perfect square of an integer c. a prime number D. a composite number | 9 |

82 | Divide the line segment ( A B=12 mathrm{cm} ) in 6 equal parts. | 10 |

83 | Construct a triangle of sides ( 5 mathrm{cm}, 6 mathrm{cm} ) and ( 7 mathrm{cm}, ) then construct a triangle similar to it, whose sides are ( frac{2}{3} ) of corresponding sides of the first triangle. | 10 |

84 | Construct triangle ( boldsymbol{A B C} ) in which ( B C=3.4 c m, A B-A C=1.5 c m ) and ( angle B=45^{circ} ) | 9 |

85 | Construct a ( triangle A B C ) in which ( A B= ) ( 4 mathrm{cm}, angle B=60^{circ} ) and altitude ( C L= ) ( 3 mathrm{cm} . ) Construct a ( triangle A D E ) similar to ( triangle A B C ) such that each side of ( triangle A D E ) is ( frac{3}{2} ) times that of the corresponding side of ( triangle A B C ) | 10 |

86 | ( triangle L M N sim triangle X Y Z . ln triangle L M N, L M= ) ( 6 mathrm{cm}, M N=6.8 mathrm{cm}, L N=7.6 mathrm{cm} ) and ( frac{L M}{X Y}=frac{4}{5} ; ) Construct ( triangle X Y Z ) | 10 |

87 | 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 two radii which are inclined at an angle of ( mathbf{A} cdot 60^{circ} ) B. ( 90^{circ} ) ( c cdot 120^{circ} ) D. ( 45^{circ} ) | 10 |

88 | ( Delta A B C sim Delta L M N cdot ln Delta A B C, A B= ) ( 5.1 mathrm{cm}, angle B=55^{circ}, angle C=65^{circ} ) and ( frac{A C}{L N}=frac{3}{5}, ) then construct ( Delta L M N ) | 10 |

89 | The coordinates of a point, which lies on ( y ) -axis and is at a distance of 4 units above ( x ) -axis is A ( .(0,4) ) в. (4,4) c. (4,0) D. (0,-4) | 10 |

90 | Draw ( triangle A B C, ) where ( m angle A B C= ) ( 90^{circ} ; B C=4 c m ) and ( A C=5 c m ) and then construct ( triangle B X Y ) with ( 4 / 3 ) scale factor. Write points of construction | 10 |

91 | Construct a ( triangle A B C ) in which ( A B= ) ( 6 mathrm{cm}, angle A=30^{circ} ) and ( angle B=60^{circ} ) Construct another ( triangle A B^{prime} C^{prime} ) similar to ( triangle A B C ) with base ( A B^{prime}=8 mathrm{cm} ) | 10 |

92 | Draw ( angle L M N=165^{circ} ) and divide in into four equal parts. | 9 |

93 | The point (0,6) lies on: A. X-axis B. Y-axis c. origin D. None | 10 |

94 | The line ( A B ) divides the line segment OP in the ratio A . 1: 1 B. 3: 4 c. 1: 2 ( mathbf{D} cdot 9: 16 ) | 10 |

95 | Draw an equilateral triangle. Draw angle bisector of angle A .Let it meet the side ( B C ) at ( D ) Measure the Length BD and CD. Then: | 9 |

96 | Find the ratio in which the ( y ) -axis divides the line segment joining the points ( boldsymbol{A}(boldsymbol{3}, boldsymbol{4}) ) and ( boldsymbol{B}(-boldsymbol{2}, mathbf{1}) . ) Also, find the point of intersection. A ( cdot 3: 2,left(0, frac{11}{5}right) ) в. ( _{1: 2,left(0, frac{13}{5}right)} ) c. ( _{1: 2,left(0, frac{3}{5}right)} ) D. ( 3: 4,left(0, frac{13}{5}right) ) | 10 |

97 | Construct a right angled triangle whose perimeter is equal to ( 10 mathrm{cm} ) and one acute angle equal to ( 60^{circ} ) | 9 |

98 | ( mathbf{P} ) is the midpoint of the part of the line ( 3 x+y-2=0 ) intercepted between the axes. Then the image of ( mathbf{P} ) in origin is ( mathbf{A} cdotleft(-1,-frac{1}{3}right) ) B ( cdotleft(-frac{1}{3},-4right) ) ( ^{c} cdotleft(-frac{1}{3},-1right) ) D. (-2,-3) | 10 |

99 | Plot the given points on a graph paper and join them with straight lines. Give a special name to the figure obtained: (3,2),(3,-4),(-2,2) and (-2,-4) | 10 |

100 | The perimeters of two similar triangles is in the ratio ( 3: 4 . ) The sum of their areas is 75 sq. cm. Find the area of each triangle in sq. cm. A . 30,45 B. 27,48 c. 25,50 D. None of these | 10 |

101 | To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{4}{5} ) of that of ( Delta A B C . ) Locate points ( X_{1}, X_{2}, X_{3}, dots ) on ray ( B X ) at equal distances such that ( angle A B X ) is acute. The minimum number of points to be located on ( B X ) is: A . 14 B. 5 ( c .9 ) D . 20 | 10 |

102 | Draw a circle of radius ( 3 mathrm{cm} ). Take a point outside the circle at a distance of ( 6 mathrm{cm} ) from the centre of the circle. Construct tangents from this point to the circle. Measure the angle between the tangents and select the correct value from below. ( mathbf{A} cdot 60 ) B. 30 ( c cdot 45 ) D. ( 90^{circ} ) | 10 |

103 | PQ and PR are the tangents to a circle with centre ( O . ) If ( angle P=frac{4}{5} angle O . ) Find ( angle Q P R ) A ( cdot 100^{circ} ) B. ( 180^{circ} ) ( c .80^{circ} ) D. None of these | 10 |

104 | Draw a ( triangle A B C ) with side ( B C=7 mathrm{cm} ) ( angle B=45^{circ}, angle A=105^{circ} . ) Then, construct a triangle whose sides are ( frac{4}{3} ) times the corresponding sides of ( triangle boldsymbol{A B C} ) | 10 |

105 | f the sides of a parallelogram touch a circle. Prove that the parallelogram is a rhombus. | 10 |

106 | The length of ( D E= ) 1 B ( c cdot 13 ) D | 10 |

107 | Draw a right triangle which the sides (other than hypotenuse) are of lengths ( 4 mathrm{cm} ) and ( 3 mathrm{cm} . ) Then construct another ( mathbf{5} ) triangle whose sides are ( frac{-operatorname{times}}{3} ) the corresponding sides of the given triangle. | 10 |

108 | Draw a circle with center ( boldsymbol{O} ) and radius ( 6 mathrm{cm} . ) Take a point ( P ) outside the circle at a distance of ( 10 mathrm{cm} ) from ( O . ) Draw tangents to the circle from point ( P . ) Let the tangents intersect the circle in points ( A ) and ( B . ) Find the approximate value of ( angle O P B ) A ( .37^{circ} ) B. ( 53^{circ} ) ( c cdot 45^{circ} ) D. None of these | 10 |

109 | Draw a line ( P Q=12.5 mathrm{cm} . ) Divide it 7 equal parts. | 10 |

110 | Draw a circle. Let AB be diameter. Let P is point on circle. Construct angle bisector of ( angle P . ) The bisector A. cuts diameter between B and centre B. cuts diameter between A and centre c. cuts diameter A and B at centre D. none | 9 |

111 | Draw a circle with centre ( C ) and radius ( 3 mathrm{cm} . ) Take a point ( boldsymbol{P} ) outside the circle such that ( C P=6 mathrm{cm} . ) Construct tangents ( boldsymbol{P} boldsymbol{A} ) and ( boldsymbol{P} boldsymbol{B} ) from this point to the circle, where ( A ) and ( B ) are the intersection points of the tangents. Then ( boldsymbol{m} angle boldsymbol{A} boldsymbol{C B}=? ) ( mathbf{A} cdot 60 ) B. ( 120^{circ} ) ( c cdot 30^{circ} ) D. ( 90^{circ} ) | 10 |

112 | To construct a triangle similar to a given ABC with its sides ( frac{3}{7} ) of the corresponding sides of ( Delta A B C, ) first draw a ray BX such that ( angle C B X ) is 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}, dots ) on BX at equal distances and next step is to join A. ( B_{10} ) to ( c ) B. ( B_{3} ) to ( c ) ( c cdot B_{7} operatorname{toc} ) D. ( B_{4} ) to ( c ) | 10 |

113 | The co-ordinates of the vertices of ロPQRS are ( P(-1,2), Q(-4,-2), R(-4,-3) ) and ( boldsymbol{S}(-1,-mathbf{5}) ) respectively. Draw ( square boldsymbol{P} Q boldsymbol{R} boldsymbol{S} ) and state it is which type of quadrilateral. | 10 |

114 | To construct a triangle similar to a ( operatorname{given} A B C ) with its sides ( frac{7}{3} ) of the corresponding sides of ( Delta A B C, ) draw a ray ( B X ) making acute angle with ( B C ) and ( X ) lies on the opposite side of ( A ) with respect to ( B C . ) The points ( B_{1}, B_{2}, dots, B_{7} ) are located at equal distances on ( B X, B_{3} ) is joined to ( C ) A. True B. False | 10 |

115 | Draw a circle with centre ( O ) and radius ( 6 mathrm{cm} . ) Take a point ( P ) outside the circle at a distance of ( 10 mathrm{cm} ) from ( 0 . ) Draw tangents to the circle from point ( P . ) Let the tangents intersect the circle in points ( A ) and ( B . ) Find ( B P ) A ( .6 mathrm{cm} ) B. ( 8 mathrm{cm} ) c. ( 8.5 mathrm{cm} ) D. None of these | 10 |

116 | ( A(-a, 0) ; B(a, 0) ) are fixed points. ( C ) is a point which divides internally ( A B ) in a constantly ration ( tan alpha . ) If ( A C & C B ) subtend equal angles at ( P, ) that the equation of the locus of ( boldsymbol{P} ) is ( boldsymbol{x}^{2}+boldsymbol{y}^{2}+ ) ( 2 a x sec 2 alpha+a^{2}=0 ) | 10 |

117 | Find the ratio in which the straight line segment joining (-2,-3) and (5,6) is divided by (i) x-axis (ii) y-axis. Also, find the coordinates of the point of division in each case. | 10 |

118 | Points ( (mathbf{6}, mathbf{8}),(mathbf{3}, mathbf{7}),(-mathbf{2},-mathbf{2}) ) and (1,-1) are joined to form a quadrilateral. What will be the structure of the quadrilateral? A. Rhombus B. Parallelogram c. square D. Rectangle | 10 |

119 | To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{3}{5} ) of that of ( Delta A B C, ) a ray ( B X ) is drawn at acute angle with ( B C ). How many minimum no of points should be marked on ( B X ? ) ( A cdot 2 ) B. 3 ( c cdot 4 ) D. 5 | 10 |

120 | The area of ( square O A P B ) is: A ( .24 mathrm{cm}^{2} ) B. ( 36 mathrm{cm}^{2} ) c. ( 48 mathrm{cm}^{2} ) D. ( 60 mathrm{cm}^{2} ) | 10 |

121 | Draw an angle of measure ( 147^{circ} ) and construct its bisector. | 9 |

122 | The length of ( D C= ) B ( c .30 ) D | 10 |

123 | The intercepts made by the line ( x+ ) ( 5 y=3 ) on the ( X ) -axis is a.Find ( a ) | 10 |

124 | Construct a ( triangle A B C, ) when ( A B= ) ( mathbf{5} . mathbf{2} mathbf{c m}, angle mathbf{A}=mathbf{3 0}^{circ} ) and ( angle mathbf{B}=mathbf{7 5}^{circ} ) | 9 |

125 | Construct a tangent to a circle of radius ( 4 mathrm{cm} ) from a point on the concentric circle of radius ( 6 mathrm{cm} ) and measure its length. Also verify the measurement by actual calculation. | 10 |

126 | In ( Delta A B C, A B=5, B C=6, A C=7 ) ( Delta P Q R-Delta A B C . ) Perimeter of ( Delta P Q R ) is ( 360 . ) Find ( mathrm{PQ}, ) QR and PR. | 10 |

127 | The coordinates of a point whose abscissa is 5 and which lies on the ( x ) axis is A . (5,0) B. (0,5) D. (5,5) | 10 |

128 | On the Cartesian plane, ( Q ) is the midpoint of the straight line ( boldsymbol{P} boldsymbol{R} ) Find the values of ( x ) and ( y ) A ( . x=3, y=2 ) B. ( x=4, y=2 ) c. ( x=4, y=3 frac{1}{2} ) D. ( x=8, y=3 ) | 10 |

129 | Construct a triangle of sides ( 4 mathrm{cm}, 5 mathrm{cm} ) and ( 6 mathrm{cm} ) and then a triangle similar to it whose sides are ( frac{2}{3} ) of the corresponding sides of the first triangle. The length of side ( A^{prime} C^{prime} ) (in ( c m ) is: | 10 |

130 | In the figure, show that perimeter of ( triangle A B C=2(A P+B Q+C R) ) | 10 |

131 | What are the coordinates of ( boldsymbol{S} ) ? ( A cdot(3,2) ) B. (3,-2) ( c cdot(-2,3) ) D. (-3,-2) | 10 |

132 | Draw a line segment of 6cm and divide it in the ratio 3: 2 | 10 |

133 | Draw a circle with the help of a bangle. Take a point ( boldsymbol{P} ) outside the circle. Construct the pair of tangents from this point ( boldsymbol{P} ) to the circle. | 10 |

134 | Draw ( angle A B C ) of measure ( 120^{circ} ) and bisect it. | 9 |

135 | Which equation represents the line that passes through the point (-1,4) and is parallel to the ( y ) -axis? A. ( y=-1 ) B . ( x=-1 ) c. ( x=4 ) D. ( y=4 ) | 10 |

136 | Transform ( 2 x-3 y+5=0 ) to the parallel axes through the point (2,-3) | 10 |

137 | In which quadrant or on which axis each of the following points lies. Write abscissa and ordinate each of the following: (i) (3,-4) (ii) (-3,5) (iii) (-10,0) (iv) (-2,-7) | 10 |

138 | Construct a triangle of sides ( 4 mathrm{cm}, 5 mathrm{cm} ) and ( 6 mathrm{cm} ) and then a triangle similar to it whose sides are ( frac{2}{3} ) of the corresponding sides of the first triangle. | 10 |

139 | Which equation represents the line that passes through the point (-5,-4) and is parallel to the ( y ) -axis? A . ( x=-5 ) B . ( x=-4 ) c. ( y=-5 ) D. ( y=-4 ) | 10 |

140 | Which equation represents the line that passes through the point (2,3) and is parallel to the ( y ) -axis? ( mathbf{A} cdot x=2 ) B. ( y=3 ) c. ( x=3 ) D. ( y=2 ) | 10 |

141 | See figure and complete the following statements. The ( x ) -coordinate and ( y ) -coordinate of the | 10 |

142 | Construct a triangle ( A B C ) in which ( A B=5.8 c m, B C+C A=8.4 mathrm{cm} ) and ( angle B=60^{circ} ) | 9 |

143 | Triangle ( A B C ) is inscribed in the parabola described by the equation ( y^{2}-6 x-4 y+10=0 ) so that ( A ) is the vertex of the parabola and ( B ) and ( C ) are the end points of the latus rectum of the parabola. The area of triangle ( A B C ) is A . 18 B. 9 ( c .4 .5 ) D. 2.25 | 10 |

144 | Construct a triangle ( A B C ) whose perimeter ( 12 mathrm{cm} ) and whose base angles are ( 65^{circ} ) and ( 85^{circ} ) | 9 |

145 | 5. e diameter PQ of a semicircle is 6 cm. Construct a square BCD with points A, B on the circumference, and the side on the diameter PQ. Describe briefly the method of construction. (1980) side of a line L. | 10 |

146 | Construct an angle of ( 45^{circ} ) from a horizontal line and justify the construction. | 9 |

147 | Draw a circle with centre ( O ) and radius ( 4 mathrm{cm} . ) Take point ( boldsymbol{A} ) such that ( boldsymbol{d}(boldsymbol{O}, boldsymbol{A})= ) ( 9 mathrm{cm} . ) Draw tangents from point ( boldsymbol{A} ) | 10 |

148 | To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{3}{5} ) of that of ( Delta A B C, ) a ray ( B X ) is drawn at acute angle with ( B C . ) If we mark points ( B_{1}, B_{2}, B_{3}, dots . ) at equal distances from ( B ) along ( B X, ) then point to be joined in next step is? A. ( B_{3} ) в. ( B_{4} ) ( c cdot B_{5} ) D. ( B_{6} ) | 10 |

149 | A triangle ( A B C ) can be constructed in which ( angle B=60^{circ}, angle C=45^{circ} ) and ( A B+B C ) ( +A C=11 mathrm{cm} . ) Is this Statement true? A . True B. False | 9 |

150 | Find the area of the triangle formed by the line ( y=2 x+4 ) and coordinate axes | 10 |

151 | Construct a triangle ( boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) whose perimeter ( 15 mathrm{cm} ) and whose base angles are ( 60^{circ} ) and ( 70^{circ} ) | 9 |

152 | Construct a triangle ( A B C ) whose perimeter ( 12 mathrm{cm} ) and whose base angles are ( 50^{circ} ) and ( 80^{circ} ) | 9 |

153 | Find the sum of ‘x’ co-ordinates of the vertices of a triangle if the mid-points of its sides be the points (6,-1),(-1,-2) and (1,-4) | 10 |

154 | Rearrange the following steps of constructing a triangle when the base angle say ( angle B ) and ( angle C ) and its perimeter ( boldsymbol{B C}+boldsymbol{C A}+boldsymbol{A B} ) is given: 1. Draw perpendicular bisectors ( boldsymbol{P Q} ) of ( A X ) and ( R S ) of ( A Y ) 2. Draw a line segment, say ( X Y ) equal to ( B C+C A+A B ) 3. Let ( P Q ) intersect ( X Y ) at ( B ) and ( R S ) intersect ( X Y ) at ( C . ) Join ( A-B ) and ( A-C ) 4. Make ( angle L X Y ) equal to ( angle B ) and ( angle M Y X ) equal to ( angle C ) 5. Bisect ( angle L X Y ) and ( angle M Y X ). Let these bisectors intersect at a point ( boldsymbol{A} ) ( mathbf{A} cdot 1 rightarrow 3 rightarrow 5 rightarrow 4 rightarrow 2 ) В. ( 2 rightarrow 4 rightarrow 5 rightarrow 1 rightarrow 3 ) c. ( 5 rightarrow 4 rightarrow 3 rightarrow 2 rightarrow 1 ) D. ( 2 rightarrow 3 rightarrow 5 rightarrow 4 rightarrow 1 ) | 9 |

155 | Construct a bisector of an angle. | 9 |

156 | Construct ( triangle L M N ) in which base ( M N=7 mathrm{cm}, angle L M N=75^{circ} ) and ( boldsymbol{L} boldsymbol{M}+boldsymbol{L} boldsymbol{N}=mathbf{9} boldsymbol{c m} ) | 9 |

157 | If two tangents are drawn at the end points of two radii that are inclined at an angle of ( 110^{circ} . ) Find the angle between the tangents. ( mathbf{A} cdot 110^{circ} ) B. 55 ( c cdot 70^{circ} ) D. ( 20^{circ} ) | 10 |

158 | In a triangle ( E D C ), what is the angle ( C ) ? 3.19 ( c cdot 7 ) D | 10 |

159 | ( triangle A B C sim triangle D E F . triangle A B C ) is such that ( A B=5.2 mathrm{cm}, B C=4.6 mathrm{cm}, angle B=45^{circ} ) and ( frac{B C}{E F}=frac{2}{3} ; ) Construct ( triangle D E F ) | 10 |

160 | Which equation represents the line that passes through the point (5,-3) and is parallel to the ( y ) -axis? A. ( x=-3 ) В. ( y=-3 ) c. ( x=5 ) D. ( y=5 ) | 10 |

161 | Draw the following angles using ruler and compasses. Also label them. ( mathbf{1 8 0}^{circ} ) | 9 |

162 | Construct a ( triangle A B C ) in which ( A C= ) ( mathbf{5} c m, ) and ( angle B A C=60^{circ} ) and ( A B- ) ( B C=1.2 mathrm{cm} ) | 9 |

163 | If the axes are transformed from origin to the point ( (-2,1), ) then new coordinates of (4,-5) are A. (2,6) (年) (2,6) в. (6,4) c. (6,-6) D. (2,-4) | 10 |

164 | Construct a ( triangle A B C ) in which ( B C= ) ( mathbf{5 . 6} c boldsymbol{m}, angle boldsymbol{B}=mathbf{3 0}^{circ} ) and the difference between the other sides is ( 3 mathrm{cm} ). | 9 |

165 | Construct the bisector of an angle ( 75^{circ} ) | 9 |

166 | ( 4 x-3=0 ) is a line parallel to A . ( y ) axis B. ( x ) axis ( mathbf{c} cdot y=x ) D. ( y=2 x ) | 10 |

167 | A pair of perpendicular tangents are drawn to a circle from an external point. Prove that length of each tangent is equal to the radius of the circle. | 10 |

168 | Quadrilaterals ABCD and PQRS are similar.What is the length of PQ? A . 2.67 B. 3.75 ( c ) ( D .5 ) | 10 |

169 | To construct a triangle similar to given ( Delta A B C ) with sides equal to ( frac{7}{5} ) of the sides of ( Delta A B C, ) a ray ( B X ) is drawn such that ( angle C B X ) is acute angle and ( B_{1}, B_{2}, B_{3}, dots ) are marked at equal distances on ( B X ). The points to be joined in the next step are: в. ( B_{5}, C ) ( mathbf{c} cdot B_{7}, C ) D. ( B_{2}, C ) | 10 |

170 | Draw the graph for the linear equation ( 3 y+5=0 ) and select the correct option: A. The line is parallel to the ( x ) -axis and passes through ( left(0,-frac{5}{3}right) ) B. The line is parallel to the ( y ) -axis and passes through ( left(0,-frac{5}{3}right) ) c. The line is parallel to the ( x ) -axis and passes through ( left(0, frac{5}{3}right) ) D. The line is parallel to the ( y ) -axis and passes through ( left(0, frac{5}{3}right) ) | 10 |

171 | Construct ( triangle M N O ) where base ( N O= ) ( 6.7 mathrm{cm}, angle M N O=45^{circ} ) and ( M O ) ( M N=2.8 mathrm{cm} ) | 9 |

172 | The angles is to be bisected to obtain an angle of ( 90^{0} ) is A ( cdot 60^{0} ) and ( 45^{0} ) B. ( 60^{0} ) and ( 120^{circ} ) ( mathrm{c} cdot 120^{0} ) and ( 180^{circ} ) D. ( 30^{circ} ) and ( 60^{circ} ) | 9 |

173 | What will be the absolute value of ( a ), for which point ( Pleft(frac{a}{2}, 2right) ) is the mid-point of the line segment joining the point ( Q(-5,4) ) and ( R(-1,0) ) | 10 |

174 | topp Q туре your question which of the following construction is/are possible? 4 | 10 |

175 | The distance between ( Pleft(x_{1}, y_{1}right) ) and ( Qleft(x_{2}, y_{2}right) ) is ( P Q=left|x_{2}-x_{1}right|, ) when PQ is parallel to the ( x ) -axis. If True enter 1 else 0 | 10 |

176 | If tangents are drawn from the endpoints of two radii that are inclined at an angle ( 105^{circ}, ) what is the angle between the tangents? A ( cdot 5^{circ} ) B. 35 ( c cdot 75 ) D. None of these | 10 |

177 | Construct ( Delta A B C, ) such that ( B C= ) ( 6 c m, angle A B C=100^{0} ) and ( A C-A B= ) ( 2.5 c m ) | 9 |

178 | ( Delta mathrm{ABC} sim Delta mathrm{LBN}, ln Delta mathrm{ABC}, mathrm{AB}=6.1 mathrm{cm} angle mathrm{B} ) ( =45^{circ}, mathrm{BC}=5.4 mathrm{cm} ; frac{A C}{L N}=frac{4}{7} . ) Construct ( Delta A B C ) and ( Delta L B N ) | 10 |

179 | Draw the tangents to the circle from the point ( L ) with radius 3 cm. Point ( L ) is at a distance of ( 8 mathrm{cm} ) from the centre ( M ) | 10 |

180 | In the diagram Write the sum of coordinates of ( boldsymbol{U} ) | 10 |

181 | Coordinates of point ( boldsymbol{R} ) are ( mathbf{A} cdot(1,1) ) B. (-1,-1) ( mathbf{C} cdot(-1,1) ) D. (1,-1) | 10 |

182 | Construct a triangle ( A B C ) in which ( A B=5.6 c m, B C=5.4 c m ) and ( angle B= ) ( 40^{circ} ) | 9 |

183 | A straight line parallel to the ( x ) -axis has equation A. ( x=a ) B . ( y=a ) ( mathbf{c} cdot y=x ) D. ( y=-x ) | 10 |

184 | Draw a right triangle ( A B C ) in which ( B C=12 mathrm{cm}, A B=5 mathrm{cm} ) and ( angle B= ) ( 90^{0} . ) Construct a triangle similar to it and of scale factor ( frac{2}{3} . ) Is the new triangle also a right triangle? A. Yes B. No c. can’t say D. Data insufficient | 10 |

185 | Construct a triangle ( A B C, ) given: ( B C=7 ) ( mathrm{cm}, mathrm{AB}-mathrm{AC}=1 mathrm{cm} ) and ( angle A B C=45^{circ} ) Measure the lengths of ( A B ) and ( A C ). ( A cdot A B=8.6 mathrm{cm}: A C=7.6 mathrm{cm} ) B. AB = 2.7 cm: AC = 1.7 cm ( mathrm{C} cdot mathrm{AB}=6.1 mathrm{cm}: mathrm{AC}=5.1 mathrm{cm} ) D. Data insufficient | 9 |

186 | ( Delta S H R sim Delta S V U . ln Delta S H R, S H= ) ( 4.5 mathrm{cm}, H R=5.2 mathrm{cm}, S R=5.8 mathrm{cm} ) and ( frac{S H}{S V}=frac{3}{5} ) Construct ( Delta S V U ) | 10 |

187 | Which of the following points lie above X-axis ( boldsymbol{a}) boldsymbol{A}(-boldsymbol{3}, boldsymbol{5}) ) ( boldsymbol{b}) boldsymbol{B}(boldsymbol{5},-1) ) ( c) C(0,2) ) ( boldsymbol{d}) boldsymbol{D}(boldsymbol{0}, boldsymbol{2}) ) ( e) E(5,1) ) ( boldsymbol{f}) boldsymbol{F}(boldsymbol{3}, mathbf{1}) ) | 10 |

188 | Construct a triangle ( A B C ) in which ( B C=8 c m, angle B=45^{circ} ) and ( A B- ) ( A D=3.5 mathrm{cm} ) | 9 |

189 | To divide a line segment in the ratio ( p ) ( boldsymbol{q}(boldsymbol{p}, boldsymbol{q} text { are integers }) ) a ray ( boldsymbol{A} boldsymbol{X} ) is drawn so that ( angle B A X ) is an acute angle and then mark points on ray ( A X ) at equal distances such that the minimum number of points is: ( mathbf{A} cdot p q ) В. ( p+q-1 ) c. ( p+q ) D. Greater of ( p ) and ( q ) | 10 |

190 | (5,0) is a point that lies on A. ( y ) -axis B. ( x ) -axis ( mathbf{c} cdot y=x ) D. ( y=5 x ) | 10 |

191 | These two quadrilaterals are similar What is the value of ( x ) (the length of B’C’) A ( cdot 2 frac{2}{3} ) B. 5 ( c cdot 6 ) D. ( 6 frac{2}{3} ) | 10 |

192 | In the given quadrilateral ( A B C D, B C=38 ) ( mathrm{cm}, mathrm{QB}=27 mathrm{cm}, mathrm{DC}=25 mathrm{cm} ) and ( mathrm{AD} perp ) DC find the radius of the circle. | 10 |

193 | In abscissa of a point ( P ) is negative and ordiante of ( P ) is positive, then ( P ) lies in : A. I Quadrant B. II Quadrant c. III Quadrant D. IV Quadrant | 10 |

194 | Draw a triangle ( P Q R ), right angled at ( Q ) such that ( P Q=3 mathrm{cm}, Q R=4 mathrm{cm} . ) Now construct ( triangle A Q B ) similar to ( triangle P Q R ) each of whose sides is ( frac{7}{5} ) times the corresponding side of ( triangle boldsymbol{P} Q boldsymbol{R} ) | 10 |

195 | Construct the triangle with the following measurements and locate the centroid: ( triangle boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) with ( boldsymbol{X} boldsymbol{Y}=mathbf{6 . 5 c m}, boldsymbol{Y} boldsymbol{Z}= ) ( 5.6 c m ) and ( X Z=7.2 c m ) | 10 |

196 | In a class test (+3) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores (-5) marks in this test, though she has got 7 correct answers How many questions has she attempted incorrectly. | 10 |

197 | ( A B ) is divided into maximum equal parts 4 3 ( c ) D. 10 | 10 |

198 | To construct a triangle similar to given ( Delta A B C ) with its sides ( frac{4}{5} ) of that of ( Delta A B C, ) locate points ( X_{1}, X_{2}, X_{3}, dots . . ) on ray ( B X ) at equal distances such that ( angle A B X ) is acute. The points to be joined in the next step are: A. ( X_{4}, C ) в. ( X_{5}, C ) c. ( x_{4}, A ) D. ( X_{5}, A ) | 10 |

199 | Draw a circle with center ( boldsymbol{O} ) and radius 6cm. Take a point ( boldsymbol{P} ) outside the circle at a distance of ( 10 mathrm{cm} ) from ( O . ) Draw tangents to the circle from point ( P . ) Let the tangents intersect the circle in points ( A ) and ( B . ) Find the approximate value of ( angle B O P ) in degrees. A ( .37^{circ} ) B. ( 53^{circ} ) ( c cdot 45^{circ} ) D. None of these | 10 |

200 | ( odot(P, 4 c m) ) is given. Draw a pair of tangents through ( A ), which is in the exterior is ( 60^{circ} . ) Write the construction steps. | 10 |

201 | Construct ( triangle boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) in which ( angle boldsymbol{Y}= ) ( mathbf{3 0}^{o}, angle Z=mathbf{6 0}^{circ} ) and ( boldsymbol{X} boldsymbol{Y}+boldsymbol{Y} boldsymbol{Z}+boldsymbol{Z} boldsymbol{X}= ) ( mathbf{1 0} c boldsymbol{m} ) | 9 |

202 | Construct an equilateral triangle. ( Delta A B C . ) Construct an angle bisector of ( angle A ) Let it meet side ( B C ) at ( D ). Find measures of ( A B, A C, B D, D C ) Find the relation between ( frac{A B}{A C} ) and ( frac{B D}{D C} ) ( mathbf{A} cdot frac{A B}{A C}frac{B D}{D C} ) C ( cdot frac{A B}{A C}=frac{B D}{D C} ) D. None | 9 |

203 | Construct ( Delta P Q R, ) such that ( Q R= ) ( 6.5 c m, angle P Q R=60^{0} ) and ( P Q-P R= ) ( 2.5 c m ) | 9 |

204 | To construct a triangle similar to given ( triangle A B C ) with its sides ( frac{2}{3} ) of that of ( Delta A B C, ) locate points on ray ( B X ) at equal distances as ( B_{1}, B_{2}, B_{3}, ldots ) such that ( angle C B X ) is acute. The points to be joined in the next step are: A. ( B_{4}, C ) в. ( B_{3}, C ) c. ( B_{1}, C ) D. ( B_{2}, C ) | 10 |

205 | Construct an equilateral triangle of side ( mathbf{5 . 5} mathrm{cm} ) | 10 |

206 | The construction of ( Delta E F G ) when ( F G=3 c m ) and ( m angle G=60^{circ} ) is possible when difference of ( E F ) and ( E G ) is equal to: A . ( 3.2 mathrm{cm} ) B. ( 3.1 mathrm{cm} ) ( mathrm{c} .3 mathrm{cm} ) D. 2.8 ( c m ) | 9 |

207 | Solve: ( frac{2}{x}+frac{3}{y}=13, frac{5}{x}+frac{7}{y}=31 ) | 10 |

208 | Find the coordinates of the point of trisection of the line segment joining (1,-2) and (-3,4) | 10 |

209 | Construct ( triangle boldsymbol{A B C} ) with ( boldsymbol{B C}=mathbf{6 . 5} mathrm{cm} ) ( boldsymbol{A C}=mathbf{5} mathrm{cm} ) and ( angle boldsymbol{C}=mathbf{6 0}^{circ} . ) | 10 |

210 | If the perpendicular distance of a point ( P ) from the ( X ) -axis is 5 units and the foot of the perpendicular lies on the negative direction of ( X ) -axis, then the point ( boldsymbol{P} ) has A. ( X ) -coordinate ( =-5 ) B. Y-coordinate = – 5 c. ( Y ) -coordinate ( =-5 ) only D. ( Y ) -coordinate ( =5 ) or -5 | 10 |

211 | ( ln ) a ( triangle A B C ) in which ( A C=5 mathrm{cm} ) and ( angle B A C=60^{circ} ) and ( B C-A B=1.2 mathrm{cm} ) The, ( A B ) is A . 3.18 в. 4.32 ( c .5 .12 ) D. None of these | 9 |

212 | State which quadrants or on which axis do the following points line? 1. ( boldsymbol{A}(-mathbf{3}, mathbf{2}) ) 2. ( B(5,3) ) 3. ( C(0,4) ) 4. ( boldsymbol{D}(-mathbf{3}, mathbf{0}) ) | 10 |

213 | In the figure, a circle is inscribed in a quadrilateral ABCD in which ( angle B=90^{circ} ) If ( A D=23 c m, A B=29 c m ) and ( D S= ) ( 5 c m ) find the radius of the circle | 10 |

214 | Which is ( 2^{n d} ) step? ( a ) ( (b) ) ( e cdot(c) ) ). | 10 |

215 | ( A(-3,2) ) and ( B(5,4) ) are the end points of a line segment, find the sum of coordinates of the mid points of the line segment. | 10 |

216 | The construction of ( Delta L M N ) when ( M N=6 mathrm{cm} ) and ( m angle M=45^{circ} ) is not possible when difference between ( L M ) and ( L N ) is equal to: ( mathbf{A} cdot 6.9 mathrm{cm} ) B. ( 5.2 mathrm{cm} ) ( c .5 mathrm{cm} ) D. 4 ст | 9 |

217 | The coordinates of ( B ) is ( (3,-2) . ) If true enter 1 or else. | 10 |

218 | Draw a circle with centre 0 and radius ( 3.5 mathrm{cm} . ) Draw two tangents PA and PB from an external point ( P ) such that ( < ) ( A P B=45^{0} . ) What is the value of ( < ) ( boldsymbol{A O B}+<boldsymbol{A P B} ) | 10 |

219 | Which of the following points lie on the negative side of ( x- ) axis ? This question has multiple correct options A. (-4,0) в. (-3,2) c. (0,-4) D. (5,-7) | 10 |

220 | The construction of ( Delta P Q R ) given that ( Q R=5.2 mathrm{cm} ) angle ( Q=50 . ) Is it possible when the difference of ( P Q ) and PR is ( 3.5 mathrm{cm} ) ? justify. | 9 |

221 | Construct a triangle similar to a given ( triangle A B C ) such that each of its sides is ( (3 / 4)^{t h} ) of the corresponding sides of ( triangle A B C . ) It is given that ( B C= ) ( 6 c m, angle B=50^{circ} ) and ( angle C=60^{circ} ) | 10 |

222 | Which equation represents the line that passes through the point (1,3) and is parallel to the ( x ) -axis? ( mathbf{A} cdot y=3 ) B. ( y=1 ) ( mathbf{c} cdot x=1 ) D. ( x=3 ) | 10 |

223 | In the figure ( P Q, P R ) and ( B C ) are the tangents to the circle. BC touches the circle at ( X . ) If ( P Q=7 mathrm{cm}, ) find the perimeter of ( triangle boldsymbol{P B C} ) | 10 |

224 | The graph of ( x=8 ) represents: A. line parallel to ( y ) -axis and at a distance of 8 units B. line parallel to ( x ) -axis and at a distance of 8 units c. line parallel to ( y ) -axis and at a distance of 0 units D. None of these | 10 |

225 | Construct two tangent to a circle of radius ( 3.5 mathrm{cm} ) from a point ( 4.5 mathrm{cm} ) away from the circle. | 10 |

226 | Which of the following could be the value of ( A C-B C ) in the construction of a triangle ( A B C ) in which base ( A B= ) ( mathbf{5} c m, angle A=30^{circ} ? ) A . 5.5 B. 5 c. 2.5 D. None of these | 9 |

227 | Draw a right angle and construct its bisector. | 9 |

228 | Plot the following points on a graph paper and find out in which quadrant do they lie? (i) ( A(3,5) ) (ii) B (-2, 7) (iii) ( C(-3,-5) ) ( D(2,-7)(v) 0(0,0) ) | 10 |

229 | Construct a triangle of sides ( 4.2 c m, 5.1 c m ) and ( 6 c m . ) Then construct a triangle similar to it, whose sides are ( frac{2}{3} ) of corresponding sides of the first triangle. | 10 |

230 | Triangles ( A B C ) and ( P Q R ) are similar What is the length of PQ? ( A ) B. 10.5 ( c cdot 13 ) D. 15 | 10 |

231 | Find the ratio in which (2,1) divides the line segment joining ( (mathbf{1}, mathbf{4}),(mathbf{4},-mathbf{5}) ) | 10 |

232 | Every point is located in one of the four quadrants. | 10 |

233 | Draw a circle with centre ( O ) and radius ( 6 mathrm{cm} . ) Take a point ( P ) outside the circle at a distance of ( 10 mathrm{cm} ) from ( 0 . ) Draw tangents to the circle from point ( P . ) Let the tangents intersect the circle in points ( A ) and ( B ). Find the area of triangle OBPin sq.cm. A .24 B . 26 c. 25 D. None of these | 10 |

234 | Construct a perpendicular line from point ( p ) to any line ( A B ) | 9 |

235 | Draw a parallelogram ( A B C D ) in which ( B C=5 mathrm{cm}, A B=3 mathrm{cm} ) and ( angle A B C= ) ( 60^{0} . ) divide it into triangles ( B C D ) and ( A B D ) by the diagonal ( B D . ) Construct the triangle ( B D^{prime} C^{prime} ) similar to ( B D C ) with scale factor ( frac{4}{3} . ) Draw the line ( operatorname{segment} D^{prime} A^{prime} ) parallel to ( D A, ) where ( A^{prime} ) lies on extended side ( B A ). Is ( A^{prime} B C^{prime} D^{prime} ) a parallelogram? A. Yes B. No c. Data insufficient D. Ambiguous | 10 |

236 | Construct a bisector of an angle of ( 60^{circ} ) | 9 |

237 | The point (0,3) lies on A. ( + ) ve ( x ) -axis B. + -ve y-axis c. – ve ( x ) -axis D. – ve y-axis | 10 |

238 | Construct ( triangle M N O ) such that ( N O= ) ( mathbf{6 . 2} mathrm{cm}, angle boldsymbol{N}=mathbf{5 0}^{circ} ) and ( boldsymbol{M} boldsymbol{O}-boldsymbol{M} boldsymbol{N}= ) ( 2.4 mathrm{cm} ) | 9 |

239 | Determine a point which divides a line segment of length ( 12 mathrm{cm} ) internally in the ratio ( 2: 3 . ) Also, justify you construction. | 10 |

240 | Construct a triangle ( A B C, ) whose perimeter is ( 12 mathrm{cm} ) and whose sides are in the ratio 2: 3: 4 | 9 |

241 | The angle subtended at the point (1,2,3) by the points ( P(2,4,5) ) and ( Q(3,3,1) ) is A ( cdot 90^{circ} ) B. ( 60^{circ} ) ( c cdot 30^{circ} ) D. ( 0^{circ} ) ( E cdot 45^{circ} ) | 10 |

242 | Which is last step? 4. ( (a) ) 3. ( (b) ) ( (c) ) 2 | 10 |

243 | Draw a ( triangle A B C, ) right – angled at ( B ) such that ( A B=3 c m, B C=4 ) cm. Now construct a ( triangle P B Q ) similar to ( Delta A B C ) each of whose side is ( frac{7}{5} ) times the corresponding side of ( Delta A B C ) | 10 |

244 | Draw the graph of the equation ( 2 x+ ) ( mathbf{3} boldsymbol{y}+boldsymbol{6}=mathbf{0} ) | 10 |

245 | Bisecting means dividing into two parts. A. Unequal B. Equal c. Triangular D. None of these | 9 |

246 | If ( 3 cos theta=1, ) find the value of ( frac{6 sin ^{2} theta+tan ^{2} theta}{4 cos theta} ) | 10 |

247 | Find the midpoint between the coordinates ( (mathbf{9}, mathbf{3}) ) and ( (mathbf{1}, mathbf{1}) ) ( mathbf{A} cdot(5,2) ) B ( cdot(3,2) ) ( mathbf{c} cdot(5,1) ) D ( cdot(3,1) ) | 10 |

248 | Take a circle with centre ( C ) and construct a tangent to a circle from an external point ( boldsymbol{P} ) | 10 |

249 | Identify the true statement. A. The ( X ) -axis is a vertical line B. The ( Y ) -axis is a horizontal line C. The scale on both the axes must be the same in a Cartesian plane D. The point of intersection between the ( X ) -axis and ( Y ) axis is called the origin | 10 |

250 | ( Delta A M T sim Delta A H E . ln Delta A M T, A M= ) ( 6.3 mathrm{cm}, angle M A T=120^{circ}, A T=4.9 mathrm{cm} ) and ( frac{M A}{H A}=frac{7}{5} . ) Construct both the triangles. | 10 |

251 | Construct a triangle ( M N P, ) whose perimeter is ( 15 mathrm{cm} ) and whose sides are in the ratio 2: 3: 4 | 9 |

252 | If ( boldsymbol{A}left(boldsymbol{a}^{2}, boldsymbol{2} boldsymbol{a}right) boldsymbol{B}=left(frac{mathbf{1}}{boldsymbol{a}^{2}}, frac{boldsymbol{-} boldsymbol{2}}{boldsymbol{a}}right), boldsymbol{P}=(boldsymbol{1}, boldsymbol{0}) ) then ( frac{boldsymbol{1}}{boldsymbol{P} boldsymbol{A}}+frac{boldsymbol{1}}{boldsymbol{P} boldsymbol{B}}= ) | 10 |

253 | Construct a triangle with sides ( 4 mathrm{cm}, 5 ) ( mathrm{cm} ) and ( 7 mathrm{cm} ) and then another triangle whose sides are ( frac{3}{4} ) of the corresponding sides of the first triangle. | 10 |

254 | The graph of the equation ( y=a ) is a straight line parallel to A . ( x ) -axis B. ( y ) -axis c. cannot be determined D. Not Paralle | 10 |

255 | For constructing a triangle whose perimeter and both base angles are given, the first step is to: A. Draw a base of any length B. Draw the base of length = perimeter c. Draw the base angles from a random line. D. Draw a base of length ( =frac{1}{3} times ) perimeter. | 9 |

256 | The graph of ( y=6 ) is a line: A. parallel to ( x ) -axis & at a distance of 6 units from the ( x- ) axis B. parallel to ( y ) -axis at a distance of 6 units from the origin c. making an intercept 6 on the ( x ) -axis D. making an intercept 6 on both the axes. | 10 |

257 | If the midpoints of the line segment joining the points ( P(6, b-2) ) and (-2,4) is ( (2,-3), ) find the value of ( b ) | 10 |

258 | If the mid point of the line joining the points ( P(6, b-2) ) and ( Q(-2,4) ) is (2,-3) Find the value of ‘b’ | 10 |

259 | Construct a ( Delta A B C ) in which ( A B=5 c m . ) ( mathrm{B}=60^{circ} ) altitude ( mathrm{CD}=3 mathrm{cm} . ) Construct ( Delta mathrm{AQR} ) similar to ( Delta mathrm{ABC} ) such that side of ( Delta A Q R ) is 1.5 times that of the corresponding sides of ( Delta A C B ) | 10 |

260 | Draw ( overline{P Q}, ) where ( P Q=10 c m . ) Draw ( operatorname{circle} odot(P, 4) ) and ( odot(Q, 3) . ) Draw tangents to each circle from the centre of the other circle. Write points of construction. | 10 |

261 | State to which quadrant does the following points belong: ( U(-6.2,4.3) ) | 10 |

262 | n the figure, if ( A B=A C ) prove that ( B Q= ) ( mathrm{QC} ) | 10 |

263 | Find the ratio in which the point ( P(5,4,-6) ) divides the line segment joining the points ( A(3,2,-4) ) and ( B(9,8,-10) . ) Also, find the harmonic conjugate of ( boldsymbol{P} ) | 10 |

264 | Construct a triangle with sides ( 5 mathrm{cm}, 6 mathrm{cm} ) and ( 7 mathrm{cm} ) and then another triangle whose sides are ( frac{7}{5} ) of the corresponding sides of the first triangle. | 10 |

265 | Draw a circle of radius ( 6 mathrm{cm} ) and construct tangents to it from an external point ( 10 mathrm{cm} ) away from the centre. Measure and verify the length of the tangents. | 10 |

266 | Construct a triangle ( A B C ) in which base ( A B=5 c m, angle A=30^{circ} ) and ( A C- ) ( B C=2.5 mathrm{cm} ) | 9 |

267 | Construct a triangle ( P Q R ), whose perimeter is ( 14 mathrm{cm} ) and whose sides are in the ratio 2: 4: 5 | 9 |

268 | Construct a triangle of sides ( 4 mathrm{cm}, 5 mathrm{cm} ) and ( 6 mathrm{cm} ) and then a triangle similar to it whose sides are ( frac{3}{5} ) time of the corresponding sides of the given triangle. | 10 |

269 | Draw the graph of the equation ( y=3 x ) | 10 |

270 | The intercepts made by the line ( x- ) ( 2 y=6 ) on the ( Y ) -axis is b.Find ( b ) | 10 |

271 | Draw a circle of radius ( 3.2 mathrm{cm} . ) At a point on it, draw a tangent to the circle using the tangent-chord theorem. | 10 |

272 | The construction of ( Delta L M N ) when ( M N=7 mathrm{cm} ) and ( m angle M=45^{circ} ) is not possible when difference of ( L M ) and ( boldsymbol{L} boldsymbol{N} ) is equal to: A . 4.5 B. 5.5 ( c .6 .5 ) D. 7.5 | 9 |

273 | Draw a triangle ( A B C ) with side ( B C= ) ( mathbf{6} c boldsymbol{m}, boldsymbol{A} boldsymbol{B}=mathbf{5} boldsymbol{c m} ) and ( angle boldsymbol{A} boldsymbol{B} boldsymbol{C}=mathbf{6 0}^{boldsymbol{o}} ) Then construct a triangle whose sides ( operatorname{are} frac{3}{4} ) of the corresponding sides of the triangle ( boldsymbol{A B C} ) | 10 |

274 | If ( y ) -coordinate of a point is zero then the point will always lie A . in ( I ) quadrant B. in ( I I ) quadrant c. on ( X ) -axis D. on ( Y ) -axis | 10 |

275 | Let ( A B C ) be a right triangle in which ( A B=3 c m, B C=4 c m ) and ( angle B= ) ( 90^{circ} . B D ) is the perpendicular from ( B ) on ( A C . ) The circle through ( B, C, D ) is drawn. Construct the tangents from ( boldsymbol{A} ) to this circle. | 10 |

276 | Construct a triangle ( A B C ) in which ( A B+A C=5.6 c m, B C=4.5 c m ) and ( angle B=45^{circ} ) | 9 |

277 | Which shape has the verties (3,2),(0,5),(-3,2) and (0,-1)( ? ) A. Rectangle B. Square c. Trapezium D. Rhombus | 10 |

278 | Construct triangle ( boldsymbol{A B C} ) in which ( B C=6 c m, A B-A C=3.1 c m ) and ( angle B=30^{circ} ) | 9 |

279 | Divide a line segment of length ( 9 mathrm{cm} ) internally in the ratio 4: 3 | 10 |

280 | Construct three tangents ( from a point outside to the circle ( ) ) to the circle of radius ( 5 mathrm{cm} ) | 10 |

281 | The point which lies in the perpendicular bisector of the line segment joining the points ( A(-2,-5) ) and ( B(2,5) ) is ( A cdot(0,0) ) B. (0, 2) c. (2, 0) ( D cdot(-2,0) ) | 10 |

282 | Construct an isosceles triangle whose base is ( 8 mathrm{cm} ) and altitude ( 4 mathrm{cm} ) and then another triangle whose sides are ( 1 frac{1}{2} ) times the corresponding sides of the isosceles triangle. | 10 |

283 | Lay down the positions of the points whose polar coordinates are ( left(-1,-180^{circ}right) ) | 10 |

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