MULTIPLE CHOICE QUESTIONS: (MCQ’s)
1. 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
2. To divide a line segment AB of length 7.6 cm 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
3. 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
4. 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
5. 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
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 endpoints of those two radii of the circle, the angle between which is:
(a) 135
(b) 155
(c) 160
(d) 120
7. 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) 3.5
(b) 2.5
(c) 5
(d) 2
8. 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
9. 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
10. We can construct only ___ tangents at a given time from a point outside it
(a) one
(b) two
(c) zero
(d) three
Answers. + Clues.
1: (b) ⇒ First draw a ray AX which makes an acute angle BAX, then mark m + n points at equal distances from each other. Here m = 3, n = 4 .
2 : (d) ⇒ The minimum points located in the ray AX is 5 + 8 = 13.
3 : (c) ⇒ 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 : (b) ⇒ To draw it take the minimum number of points to be located at an equal distance is equal to m or n, whichever is greater.Here 9 > 5.
5 : (d)⇒ The figure produced by the intersection point of pair of tangents and the two end points of those two radii and the centre of the circle, is a quadrilateral.
6 : (a) ⇒ 45° + x = 180°
7: (a) ⇒ Tangents are constructed at the end of a radius
8 : (c) ⇒ The greater of 2 or 3 will be the maximum number of points.
9 : (c) ⇒ We locate points Q1, Q2, Q3, Q4, Q5, Q6 and Q7 and QX at equal distances and in next step join the last point Q7 to R.
10 : (b) ⇒ textbook 11.3