# MCQ Questions for Class 10 Maths Chapter 11 Constructions with Answers

Students are advised to solve the Constructions Multiple Choice Questions of Class 10 Maths to know different concepts. Practicing the MCQ Questions on Constructions Class 10 with answers will boost your confidence thereby helping you score well in the exam.

Explore numerous MCQ Questions of Constructions Class 10 with answers provided with detailed solutions by looking below.

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 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

Answer: (d) B_{7} 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 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_{9}

## Answer

Answer: (b) A_{11}

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) A_{4} and B_{5}

(b) A_{5} and B_{4}

(c) A_{5} and B_{6}

(d) A_{6} and B_{5}

## Answer

Answer: (c) A_{5} and B_{6}

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 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

Answer: (b) A_{11}

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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