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Constructions Class 10 MCQs Questions with Answers
What are you waiting for? Get all the answers to Class 10 Maths Chapter 11 MCQs! It’s time that students power up and start practicing these MCQ Questions of Constructions Class 10 with answers. The best way of doing so would be solving them yourself in order not only to know which answer is correct but also to understand why each solution works as well.
Question 1.
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
Answer: (d) 115°
Question 2.
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
Answer: (c) 10 cm
Question 3.
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
Answer: (d) Altitude
Question 4.
To construct a triangle similar to given ΔABC with its sides \(\frac { 3 }{ 7 }\) 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 equal distance and next step is to join :
(a) B4 to C
(b) B10 to C
(c) B6 to C
(d) B7 to C
Answer
Answer: (d) B7 to C
Question 5.
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) A10
(b) A11
(c) A12
(d) A9
Answer
Answer: (b) A11
Question 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 point of those two radii of the circle, the angle between which is :
(a) 105°
(b) 135°
(c) 145°
(d) 70°
Answer
Answer: (b) 135°
Question 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 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) A4 and B5
(b) A5 and B4
(c) A5 and B6
(d) A6 and B5
Answer
Answer: (c) A5 and B6
Question 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°
Answer
Answer: (b) 130°
Question 9.
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
Answer: (c) 8
Question 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
Answer
Answer: (d) 12
Question 11.
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 A1, A2, A3, … are located at equal distances on the ray AX and the point B is joined to
(a) A4
(b) A11
(c) A10
(d) A7
Answer
Answer: (b) A11
Question 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°
Answer
Answer: (a) 60°
Question 13.
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
Answer: (a) 180°−x°
Question 14.
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°
Answer
Answer: (c) 120°
Question 15.
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
Answer: (d) 2
Question 16.
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
Answer: (a) 2
Question 17.
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
Answer: (c) ( a + b)
Question 18.
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
Answer: (d) acute angle
Question 19.
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
Answer: (c) BPT
Question 20.
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
Answer: (a) p + q
Question 21.
When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?
(a) \(\frac { 2 }{ 3 }\)
(b) 2
(c) 3
(d) 5
Answer
Answer: (d) 5
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