Class 10 Maths MCQs for Chapter 11 (Constructions) are available online here with answers. All these multiple choice questions, chapter-wise, are prepared as per the latest CBSE syllabus and NCERT guidelines. Solving these objective type questions will help students to score good marks in the board exam, which they can verify with the help of detailed explanations presented here.

## Class 10 Maths MCQs for Constructions

Practice the questions below and choose the correct answer. Verify your answers with the solutions provided here. Also, find important questions for class 10 Maths here.

**1. To divide a line segment PQ in the ratio 3:4, first a ray OP is drawn so that âˆ POQ is an acute angle and then at equal distances points are marked on the ray OP such that the minimum number of these points is:**

(a)5

(b)7

(c)9

(d)11

Answer: b

Explanation: We know that to divide a line segment in the ratio m : n, first draw a ray AX which makes an acute angle BAX, then marked m+n points at equal distances from each other.

Here m = 3, n = 4

So minimum number of these point = m + n = 3 + 4 = 7

**2. To divide a line segment AB of length 7.6cm in the ratio 5:8, a ray AX is drawn first such that âˆ 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

Explanation: The minimum points located in the ray AX is 5+8 = 13. Hence, point B will join point A13.

**3. To construct a triangle similar to a given Î”PQR with its sides 5/8 of the similar sides of Î”PQR, draw a ray QX such that âˆ 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)

Explanation: Here we locate points Q1, Q2, Q3, Q4, Q5, Q6, Q7 and Q8 on QX at equal distances and in next step join the last point Q8 to R.

**4. To construct a triangle similar to a given Î”PQR with its sides 9/5 of the corresponding sides of Î”PQR draw a ray QX such that âˆ 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)

Explanation: To draw a triangle similar to a given triangle with its sides m/n of the similar sides of given triangle, the minimum number of points to be located at an equal distance is equal to m or n, whichever is greater.

Here, m/n = 9/5

9>5, therefore the minimum number of points to be located is 9.

**5. To construct a pair of tangents to a circle at an angle of 60Â° 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)

Explanation: The angle between the two radii should be 120^{0} because the figure produced by the intersection point of pair of tangents and the two endpoints of those two radii and the centre of the circle, is a quadrilateral. Hence, the sum of the opposite angles should be 180^{o}.

**6. 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 âˆ 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

**7. To draw a pair of tangents to a circle which are inclined to each other at an angle of 45Â°, 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

**8. A pair of tangents can be constructed from a point P to a circle of radius 4 cm situated at a distance of ___________ from the centre.**

(a)3.5

(b)2.5

(c)5.5

(d)2

Answer: c

Explanation: The pair of tangents can be drawn from an external point only, so its distance from the centre must be greater than the radius. Since only 5cm is greater than radius of 3.5cm. So the tangents can be drawn from the point situated at a distance of 5cm from the centre.

**9. 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

Explanation: The greater of 2 or 3 will be the maximum number of points. Hence, the last point will A3.

**10. To construct a triangle similar to a given Î”PQR with its sides 7/2 of the similar sides of Î”PQR, draw a ray QX such that âˆ 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

Explanation: Here we locate points Q1, Q2, Q3, Q4, Q5, Q6 and Q7 and QX at equal distances and in next step join the last point Q8 to R.