Engineering Drawing Questions and Answers – Representative Factor – 1
1. Representative fraction is the ____________________
a) ratio of the length in drawing to the actual length
b) ratio of the actual length to the length in drawing
c) reciprocal of actual length
d) square of the length in drawing
View Answer
Answer: a
Explanation: Representative fraction is the ratio of the length of the object represented on drawing to the actual length of the object represented.
2. The scale of a drawing is given as 1:20. What is the representative fraction?
a) 20
b) 1/20
c) 0.5
d) 0.02
Answer: b
Explanation: The scale of the drawing is given as 1:20 that is a reducing scale, this means dimensions are made to 1/20th of full size. So the representative factor is that dimension in drawing to actual dimension. R.F. = (1/20)/1 = 1/20.
3. The scale of a drawing is given as 15:1. What is the representative fraction?
a) 15
b) 0.15
c) 1.5
d) 1/15
View Answer
Answer: a
Explanation: The scale of the drawing is given as 15:1 that is an enlarging scale, this means dimensions are increased to 15 times of actual ones. So the representative factor is that dimension in drawing to actual dimension. R.F. = 15/1 = 15.
4. The length of the drawing is 50 mm, the scale is given as 1:5. Find the actual length.
a) 50 cm
b) 10 cm
c) 25 cm
d) 10 mm
View Answer
Answer: c
Explanation: The scale given is 1:5 (reducing scale) that is the drawing is made with 1/5th of actual dimensions. So we have to multiply the drawing length with 5. 50 mm x 5 =250 mm and 1 cm =10 mm. The actual length in cm is 25.
5. The actual length is 1m. The length of the drawing is 5cm. Find the representative factor.
a) 1/5
b) 20
c) 1/20
d) 5
View Answer
Answer: c
Explanation: Representative factor is the ratio of the length represented in drawing to the actual length. Here given actual length is 1 m =100cm and length of drawing is 5 cm. R.F. =5 cm/100 cm = 0.05 (or) = 1/20.
6. The representative factor is 4. The actual length is 20 mm. Find the length of the drawing.
a) 5 cm
b) 5 mm
c) 0.2 mm
d) 8 cm
View Answer
Answer: d
Explanation: The representative factor given is 4 (more than one), shows the scale is enlarging. Representative factor = ratio of the length in drawing to actual length. R.F. = (length in drawing)/20 mm = 4.
Length in drawing = 20 mm x 4 = 80 mm = 8 cm.
7. A machine part is drawn two times with different scales. The ratio of 1st drawing’s R.F. to 2nd drawing R.F. with respect to the actual object is found to be 2. The length of the second drawing is 10 mm. Find the 1st drawing length.
a) 5 mm
b) 200 mm
c) 5 cm
d) 2 cm
Answer: d
Explanation: 2 = 1st drawing R.F/2nd drawing R.F. = (length of 1st drawing/actual length)/(length of 2nd drawing/ actual length) = length of first drawing/length of second drawing = length of first drawing/ 10 mm. 2 x 10 mm = 20 mm. So therefore the length of first drawing is 20 mm = 2 cm.
8. The length of the drawing is 20 cm, the scale is given as 2:1. Find the actual length.
a) 50 cm
b) 10 cm
c) 25 cm
d) 10 mm
View Answer
Answer: b
Explanation: The scale given is 2:1 (enlarging scale) that is the drawing is made 2 times of actual dimensions. So we have to divide the drawing length with 2. 20 mm / 2 =100 mm and 1 cm =10 mm. The actual length in cm is 10 cm.
9. The actual length is 1cm. The length of the drawing is 30 cm. Find the representative factor.
a) 1/30
b) 30
c) 0.03
d) 15
View Answer
Answer: b
Explanation: Representative factor is the ratio of the length represented in drawing to the actual length. Here given actual length is 1 cm and length of drawing is 30 cm. R.F. = 30 cm/1 cm = 30.
10. The representative factor is 0.02. The actual length is 50 cm. Find the length of drawing.
a) 10 cm
b) 5 cm
c) 0.25 cm
d) 10 mm
View Answer
Answer: d
Explanation: The representative factor given is 0.02 (less than one), shows the reducing scale. Representative factor = ratio of length in drawing to actual length. R.F. = (length in drawing)/50 cm = 0.02. Length in drawing = 0.02 x 50 cm = 1 cm = 10 mm.
11. The ratio of a length of an actual object to the length of drawing is given as 5. Find the scale and R.F. (Representative factor).
a) 1:5, 1/5
b) 5:1, 1/5
c) 1:5, 5
d) 5:1, 5
View Answer
Answer: a
Explanation: Given that the ratio of actual length to length of drawing which is reciprocal of R.F. So the R.F. for given values is 1/5. From the given information it can be understood that the actual object is 5 times larger than the drawing, so the scale is reducing scale i.e. 1:5.
12. The representative factor is 2, the drawing length is 100 mm. Find the actual length.
a) 20 cm
b) 50 mm
c) 20 mm
d) 50 cm
View Answer
Answer: b
Explanation: The scale is enlarging scale. The ratio of length of drawing to actual length gives the representative factor. 100 mm / actual length = 2, actual length = 100 mm/2 = actual length = 50 mm (or) 5 cm.
13. The representative factor is 0.5, the drawing length is 10 cm. Find the actual length.
a) 20 cm
b) 50 mm
c) 20 mm
d) 50 cm
View Answer
Answer: a
Explanation: The scale is reducing scale. The ratio of length of drawing to actual length gives the representative factor. 10 cm / actual length = 0.5, actual length = 10 cm/0.5 = actual length = 20 cm (or) 200 mm.
14. Representative factor is defined as the ratio of the length of the drawing to the actual length of the object.
a) True
b) False
View Answer
Answer: a
Explanation: The representative factor is defined as the ratio of the length of the drawing to the actual length of the object. The value of representative factor can give information on whether the scale is enlarging or reducing.
15. What is the representative factor of a line, whose length is 24cm on the drawing sheet, representing an actual length of 6m?
a) 1:50
b) 1:25
c) 1:24
d) 1:60
View Answer
Answer: b
Explanation: Representative factor is calculated as the ratio of the length of the drawing to the actual length of the object. Both the quantities should be taken in the same unit. In this example, R.F. equals to 24 ÷ (600) i.e. 1:25.
16. A 20mm line, drawn on the drawing sheet represents an actual length of 5m. What is the representative factor?
a) 1:2.5
b) 1:25
c) 25:1
d) 1:250
View Answer
Answer: d
Explanation: The formula for calculating the representative factor is the length of the drawing divided by the actual length of the object. Hence for this example, R.F = 20 ÷ 5000 i.e. 1:250. The units of the quantities in the formula must be the same.
17. A line of 10cm is drawn on a drawing sheet. It represents an actual length of 25mm. What is the representative factor?
a) 1:4
b) 1:40
c) 4:1
d) 40:1
View Answer
Answer: c
Explanation: Representative factor is calculated as the ratio of the length of the drawing to the actual length of the drawing it represents. From this formula we get, R.F. = 100 ÷ 25. Hence the representative factor is 4:1.
18. Which of the following representative factor will have an enlarging scale?
a) 1:24
b) 1:5
c) 1:3
d) 1:0.5
View Answer
Answer: d
Explanation: The representative factor 1:0.5 can be written as 2:1. Since the actual length of the drawing is less than the representative length, the scale is enlarging. If the actual length of the object is greater than the representative value, R.F. will be less than unity.
19. Which of the following representative factors depict that the actual length of the object is greater than the length of the drawing?
a) 2:5
b) 4:1
c) 3:2
d) 5:3
View Answer
Answer: a
Explanation: Considering that a 2cm line drawn on the drawing sheet represents an actual length of 5cm. Hence in the case of representative factor 2:5 i.e. 1:2.5, the actual length is greater than the length of the drawing.
20. What is the representative factor if the length of the drawing is 15mm and the actual length of the object is 3m?
a) 1:2
b) 1:0.2
c) 1:200
d) 1:20
View Answer
Answer: c
Explanation: The representative factor is the ratio of a length of the drawing to the actual length of an object. Hence for the line of length 15mm and the actual length 3m, R.F. = 15 ÷ 3000 = 1:200. The units of both the quantities should be same.
21. Which of the following is not a valid representative factor?
a) 1:2
b) 1:3
c) 2:5
d) 0:4
View Answer
Answer: d
Explanation: The representative factor cannot be zero. As the length of the drawing cannot be zero, having a value zero means that there is no drawing made. Representative factors are used to scale down or up the drawing from the actual object.
22. A line of length 4mm is represented by a line of 4cm. What is the representative factor?
a) 1:1
b) 10:1
c) 1:10
d) 1:100
View Answer
Answer: b
Explanation: The actual length of the object is 4mm and the length of the drawing is 4cm. From the formula for calculating the representative factor we get, R.F. = 4 ÷ 0.4 = 10. Hence the representative factor is 10:1.
23. What is the representative factor if sides of a square measuring 4cm in the drawing sheet while the actual length of the side of the square is 3m?
a) 1:0.75
b) 4:3
c) 1:75
d) 3:4
View Answer
Answer: c
Explanation: The length of the drawing is 4cm and the actual length of the drawing is 3m. By using the formula for calculating the representative factor we get the value of R.F. as 1:75. R.F. = 4 ÷ 300. The units of both the quantities should be the same.
24. What is the type of scale in which the representative fraction is 1:1?
a) Enlarged scale
b) Reduced scale
c) Full size scale
d) Graphical scale
View Answer
Answer: c
Explanation: A full size scale is a type of scale in which the length of the drawing and the actual length of the object is of the ratio 1:1. Hence by definition, its representative fraction is 1:1. In full size scale, the drawing is drawn with the actual measurements.
25. Which of the following representative fraction depicts an enlarging scale?
a) 1:0.2
b) 1:2
c) 1:3
d) 1:1
View Answer
Answer: a
Explanation: Enlarging scale means that the drawing is drawn with the bigger dimensions in comparison to the actual dimensions of the object. A representative fraction of 1:0.2 means 5:1, i.e. the drawing is five times bigger than the actual object. Hence the scale is enlarging scale.
26. Which of the following scales is a reducing scale?
a) 3:2
b) 1:3
c) 1:1
d) 1:0.4
View Answer
Answer: b
Explanation: The representative fraction 1:3 indicates that the dimension of the drawing is one-third of the actual object. Since the drawing is smaller than the actual object, this type of scale is called a reducing scale.
27. Which of the following is not an enlarging scale?
a) 2:1
b) 4:3
c) 3:5
d) 6:1
View Answer
Answer: c
Explanation: Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.
28. Which of the following scales is neither an enlarging nor a reducing scale?
a) 3:2
b) 1:4
c) 1:0.5
d) 1:1
View Answer
Answer: d
Explanation: A scale which is neither enlarging nor reducing is called as full size scale. The representative fraction of a full size scale is 1:1. In full size scale, the drawing is made just as the actual dimensions of the object.
29. A scale which is numerically represented on the drawing sheet is called as _____
a) Graphical scale
b) Engineer’s scale
c) Reducing scale
d) Full size scale
View Answer
Answer: b
Explanation: An engineer’s scale is the representation of the scale used in drawing on the drawing sheet numerically. For example, if the length of the drawing is 5 cm and the actual length is 10m, then it is numerically represented as 5cm = 10m.
30. Which of the following scale is used in survey maps?
a) Engineer’s scale
b) Diagonal scale
c) Graphical scale
d) Vernier scale
View Answer
Answer: c
Explanation: Graphical scales are used in survey maps. The graphical scale is drawn on the drawing. When the drawing ages, the engineer’s scale shrinks and may not give accurate results. Hence graphical scale is used as the drawing shrinks, the scale will also shrink.
31. What is the formula for calculating the length of the scale?
a) Minimum length to be measured x R.F.
b) Minimum length to be measured ÷ R.F.
c) Maximum length to be measured ÷ R.F.
d) Maximum length to be measured x R.F.
View Answer
Answer: d
Explanation: The length of the scale is calculated by using the following formula,
Length of the scale = R.F. x Maximum length to be measured.
32. Units of the measurements must be shown in the scale drawn.
a) True
b) False
View Answer
Answer: a
Explanation: Units of the scale must be clearly indicated on the drawing. This helps in clearing any misunderstanding concerning the different units used in the scale. The representative fraction should be mentioned in the drawing as well.
33. The minimum length to be shown must be known for drawing an unusual scale.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum length of the scale must be known to draw unusual scales on the drawing sheet. The representative fraction of the scale is also essential information. The units of the scale must be mentioned on the drawing.
34. What is the length of the scale, the representative fraction is 1:50000 and the scale must measure up to 25 km?
a) 5 x 10-4 cm
b) 50 cm
c) 5 cm
d) 0.5 cm
View Answer
Answer: b
Explanation: The formula for calculating the length of the scale is given by, Length of the scale = R.F. x maximum length to be measured; Hence length of the scale = 1 ÷ 50000 x 25 x 1000 x 100 = 50 cm. It is very important to note the units while calculating.
35. In a map, 30 miles is represented by 20 cm. What is the length of the kilometer scale if the maximum length to be measured is 10 km? (1 mile = 1.609 km)
a) 4.14 cm
b) 10.73 cm
c) 9.32 cm
d) 24.14 cm
View Answer
Answer: a
Explanation: The formula for calculating the length of the scale is given by; Length of the scale = R.F. x maximum length to be measured. Hence from the formula, length of the scale = 20 ÷ (30 x 1.609 x 1000 x 100) x 10 x 1000 x 100 = 4.14 cm.
36. What is the representative fraction of the kilometer scale if 20 miles is represented as 5 cm and maximum length to be measured is 5 km? (1 mile = 1.609 km)
a) 1:4
b) 1:643600
c) 1:1.287
d) 0.7768:1
View Answer
Answer: b
Explanation: The representative fraction is calculated by the formula, R.F. = length of the drawing ÷ actual length of the object. Here the length of the drawing is 5 cm and the actual length is 20 miles. In R.F. both quantities should be in the same unit. R.F. = 5 ÷ (20 x 1.609 x1000 x 100) = 1:643600.
37. What is not essential information to construct a scale from the following?
a) The R.F. of the scale
b) The units to represent
c) Length of scale
d) Maximum length
View Answer
Answer: c
Explanation: The length of the scale can be found using ’length of the scale = Representative fraction x Maximum length’. To draw drawing R.F (representative fraction), Units to represent (example: meters and centimeter or another if needed) and maximum length required is essential.
38. Which scale represents only two units or a unit and its sub-division?
a) Diagonal scale
b) Plane scale
c) Scale of chords
d) Vernier scale
View Answer
Answer: b
Explanation: A plain scale is constructed by dividing a line into the suitable number of equal parts or units, the first of which is sub-divided into smaller parts. Plain scales represent either two units or a unit and its sub-division.
39. Which scale is employed when we need to measure in three units?
a) Plane scale
b) Scale of chords
c) Vernier Scale
d) Diagonal scale
View Answer
Answer: d
Explanation: A diagonal scale is used when very small distances are to be accurately measured or when measurements are required in three units. Small divisions of short lines are obtained by the principle of diagonal scales.
40. We need a scale which has to show dm, cm and mm. Which scale do you prefer?
a) Diagonal scale
b) Plain scale
c) Vernier scale
d) Comparative scale
Answer: a
Explanation: Diagonal scale is meant for drawing scales which represents 3 units. A diagonal scale is used when very minute distances to be measured. Small divisions of short lines are obtained by the principle of the diagonal scale.
41. Which of the following statement is incorrect with regard to plain scales?
a) Plain scales represent two units
b) Zero should be placed between the units and its subdivisions
c) The representative factor should be mentioned below the scale
d) It can read up to three decimal places
View Answer
Answer: d
Explanation: Plane scales measure a unit and its subunits so it can represent only the first decimal place of measurement. In the construction of plain scales, all units are placed to the right side of the zero, which is called as the main scale and to the left of zero, sub-divisions of units are placed.
42. Diagonal scales can only measure the first decimal place of measurement.
a) False
b) True
View Answer
Answer: a
Explanation: Diagonal scales can measure even minute distances accurately to three decimal places. This is achieved through the principle of diagonal scale, using the principle of similar triangles, sub-divisions are again divided into the number of equal parts.
43. Put the statements in an order to divide the line AB into 10 parts using the principle of diagonal scales.
i. Number the division-points as 1, 2, 3, up to 9 starting from C and later join AC.
ii. Divide the line BC into 10 equal parts.
iii. Draw a perpendicular line BC TO the line AB.
iv. Hence 9’9 is 0.9AB and similarly, other 2’2 is 0.2AB.
v. Number the cutting points on AC as 1’, 2’, 3’ and so on up to 9’.
vi. Draw lines parallel to AB through the division-points.
a) i, iv, v, ii, vi, iii
b) i, v, vi, ii, iv, iii
c) iii, ii, i, vi, v, iv
d) i, ii, iii, iv, v, vi
View Answer
Answer: c
Explanation: In the principle of the diagonal scale we apply the concept of similar triangles. So, we need to draw a perpendicular to B, say BC and form a right angle triangle ABC. By dividing the line BC into 10 equal parts (required number of parts as mentioned in the question) and drawing lines parallel to AB through division points, all these lines give the measurement as 0.1AB, 0.2 AB, 0.3AB, 0.4AB and so on up to 0.9AB.
44. How can we decide the minimum length of a scale, when Representative factor (R.F) and the maximum length of measurement (L) are known?
a) Length of scale = R.F+L
b) Length of scale = R.F/L
c) Length of scale = R.F-L
d) Length of scale = R.F*L
View Answer
Answer: d
Explanation: We can draw the scale as long as possible but the minimum length of scale should be capable of measuring the maximum length of required measurement. We know R.F = (length of the drawing)/(Actual length of the object), Hence length of scale = R.F* maximum length of required measurement.
45. When the length of the line drawn is 2 mm, and the taken representative fraction is 1:2. Find the actual length of the line?
a) 1 mm
b) 0.5 mm
c) 4 mm
d) 3 mm
View Answer
Answer: c
Explanation: Representative fraction is the ratio of the length of the drawings to actual length, hence actual length = (length of the drawing)/R.F. Here R.F is 1:2 mm and length of the drawing is 2 mm, therefore the actual length of the line is 2*2 mm = 4 mm.
46. The maximum length is 50 m and length of scale is 10 cm. Find the Representative factor.
a) 1/50
b) 50
c) 500
d) 1/500
View Answer
Answer: d
Explanation: Length of the scale = Representative fraction x Maximum length, 10 cm = Representative fraction x 5000 cm, Representative factor = 1/500.
47. Given Representative factor as 4/50 and maximum length is 100 cm. Find the length of scale.
a) 8 cm
b) 10 cm
c) 9.7 cm
d) 12 cm
View Answer
Answer: b
Explanation: Length of the scale = Representative fraction x Maximum length, Length of scale = 4/50 x 100 cm, Length of scale= 8 cm.
48. Given, below are the steps related to constructing a scale of 1:50 to show meters and decimeters and the maximum length is 5 meters. Arrange the steps
i. Then divide the 1st part into 10 equal divisions
ii. Determining the length of scale 1/50 x 500 cm = 10 cm
iii. Determining R.F. here it is 1/50
iv. Draw a line 10 cm long and divide it to 5 equal parts
a) i, ii, iii, iv
b) iii, ii, iv, i
c) ii, iv, i, iii
d) iv, i, ii, iii
View Answer
Answer: b
Explanation: The general procedure involves finding R.F. at the 1st and next max length of scale and then dividing whole line into given number of units at last dividing the 1st part to number of sub-divisions that occur in the unit.
49. How many divisions a line has to be made if it is given to prepare plain scale up to 7 yards?
a) 8
b) 7
c) 6
d) It depends on R.F
View Answer
Answer: b
Explanation: Whatever the representative factor may given, we just require a number of units to divide the line in scale. Representative factor is only needed to find the length of the scale. Length of the scale = Representative fraction x Maximum length.
50. What is the length of the scale, representative fraction given is 3/40 and maximum length to be represented in scale is 100 cm?
a) 8.5 cm
b) 10 cm
c) 7.5 cm
d) 13.33
View Answer
Answer: c
Explanation: Length of the scale = Representative fraction x Maximum length. Length of the scale = 3/40 x 100 cm = 7.5 cm. That is to draw a scale for 100 cm with 3/40 R.F. We need to draw a 7.5 cm length line and divide to 10 decimeters.
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51. In preparing a plain scale of feet and yards, the first division is to be divided into how many sub-divisions?
a) 5
b) 3
c) 4
d) 10
View Answer
Answer: b
Explanation: Given that the plain scale is to be made with feet and yards. Generally, 1st part is divided into sub-divisions here is feet. We know 1 yard is equal to 3 feet, so 1st division should be divided into 3 sub-divisions.
52. In preparing a plain scale of feet and inches, how many sub-divisions do the first division is to be divided?
a) 10
b) 6
c) 12
d) 5
View Answer
Answer: c
Explanation: Given that the plain scale is to be made with feet and inches. Generally, 1st part is divided into sub-divisions here is inches. We know 1 feet is equal to 12 inches, so 1st division should be divided into 12 sub-divisions.
53. In preparing a plain scale of miles and furlongs, how many divisions do the first part is to be made?
a) 10
b) 12
c) 8
d) 6
View Answer
Answer: c
Explanation: Given that the plain scale is to be made with miles and furlongs. Generally, 1st part is divided into sub-divisions here is furlong. 1 mile is equal to 8 feet, so 1st division should be divided into 8 sub-divisions.
54. A plain scale is made to show 9 miles and sub division is furlong. To measure 3 miles and 6 furlongs how many divisions is to take on the right side of origin and how many division it is to take on the left side of origin?
a) 3, 6
b) 2, 4
c) 6, 3
d) 4, 2
View Answer
Answer: a
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side. Here it is asked to measure how many divisions do 3 miles takes. It is 3 and 6 furlongs take on left of the origin. It is 6.
55. A plain scale is made to show 7 yards and sub division is feet. To measure 2 feet, how many divisions it is to take on the left side of origin?
a) 1
b) 2
c) 3
d) 4
View Answer
Answer: b
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 2 feet takes. It is 2 from origin to left.
56. A plain scale is made to show 4 feet and sub division is inch. To measure 2 feet and 10 inches how many divisions is to take on the right side of origin?
a) 1
b) 2
c) 10
d) 9
View Answer
Answer: b
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 2 feet takes. It is 2 from origin to right.
57. A plain scale is made to show 8 meters and sub division is decimeters. To measure7 meters and 3 decimeters how many divisions is to take on the right side of origin and how many it is to take on the left side of origin?
a) 7, 3
b) 3, 7
c) 6, 4
d) 4, 6
View Answer
Answer: a
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 7 meters takes. It is 7 from origin to right. And 3 from origin to left.
58. A plain scale is made which shows 6 meters of maximum length and sub division is decimeter with a R.F. of 1 /60. How much length does the scale shows 4 m and 5 decimeters?
a) 4 m 5 dm
b) 4.5 m
c) 0.75 dm
d) 0.75 m
View Answer
Answer: b
Explanation: length of the scale = Representative fraction x Maximum length, length of scale =1/60 x 4.5 m = 0.075 m = 0.75 dm = 7.5 cm = 75 mm. (or) 1/60 x 4 m =0.0666 m + 1/60 x 5 dm = 0.083 dm, 0.666 dm + 0.08333 dm =0.7499 dm =7.5 cm = 75 mm.
59. A scale of 1:25 is to be constructed to show centimeters and it should be long enough to measure 10 meters. What is the length of the scale?
a) 4 cm
b) 0.4 cm
c) 40 cm
d) 400cm
View Answer
Answer: c
Explanation: The length of the scale is calculated as the product of the representative fraction and the maximum length to be measured. Hence, length of the scale = 1 ÷ 25 x 10 x 100 = 40 cm. While calculating it is very important to note the units of the dimensions.
60. From the following figure what is the maximum length that can be measured?
a) 11 dm
b) 10 dm
c) 13 dm
d) 12 dm
View Answer
Answer: d
Explanation: From the scale given in the figure it is clear that the maximum length that can be measured is 12 decimeters. It is clearly seen that we can measure 11 decimeters and then by adding 10 centimeters which is equal to one decimeter. Hence the maximum length is 12 dm.
61. What is the length of the scale? (R.F. = 1/5)
a) 2.4 cm
b) 24 cm
c) 240cm
d) 0.24cm
View Answer
Answer: b
Explanation: The length of the scale is calculated by the formula, length of the scale = R.F. x maximum length to be measured. Hence, length of centimeter scale = 1 ÷ 5 x 12 x 10 = 24 cm. Here, the representative factor is 1/5.
62. Using the given scale, we can measure 13.7 dm.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum length that can be measured is 12 dm. Any measurement beyond that using the given scale is not possible. As we can clearly see we can measure 11 dm and the rest 1 dm can be measured using 10 cm.
63. What is the least count of the given scale?
a) 1 cm
b) 0.1 cm
c) 1dm
d) 10 cm
View Answer
Answer: a
Explanation: The smallest value that can be measured is 1 cm or 0.1 dm. The maximum value that can be measured using the above scale is 12 dm. 10 cm equals to 1 dm. It is clear that 11 dm can be measured but in addition to it, we can measure 10 cm.
64. What is the maximum length that can be measured using the given scale?
a) 7 inches
b) 7 feet
c) 8 feet
d) 12 inches
View Answer
Answer: c
Explanation: It is clearly visible that the maximum length that can be measured using the given scale is 7 feet. The rest twelve inches can be measured. Since 12 inches = 1 foot, we can measure 1 foot in addition to the 7 feet. Hence we can measure 8 feet maximum using the above scale.
65. What is the scale in the following figure?
a) 1:2
b) 1:12
c) 1:4
d) 1:7
View Answer
Answer: b
Explanation: In the figure it is clearly shown that the representative factor is 1/12. Hence the scale is 1:12. The representative fraction is measured as the length of the drawing divided by the actual length of the object.
66. What is the length of the scale?
a) 7 feet
b) 7 inches
c) 8 feet
d) 8 inches
View Answer
Answer: d
Explanation: The length of the scale is calculated as, length of the scale = representative fraction x maximum length to be measured. Hence length of the scale = 1 ÷ 12 x 8 x 12 = 8 inches. While calculating, the units are to be noted.
67. What is the least count of the given scale?
a) 3“
b) 1“
c) 12”
d) 7”
View Answer
Answer: b
Explanation: The least count is the minimum amount of length that can be measured. Here in the given scale, the least count is 1 inch or one twelfth of a foot = 1/12th foot. The maximum length that can be measured is 8 feet.
68. From the given scale we can measure 3 feet 10”.
a) True
b) False
View Answer
Answer: a
Explanation: From the given scale we easily measure 3 feet. In addition to that we can measure 10 inches using the inches scale. In this type of plain scale we can measure using both feet and inches as 12 inches = 1 foot.
69. Which of the following scales is used when there are three units that need to be measured?
a) Plain scale
b) Comparative scale
c) Diagonal scale
d) Vernier scale
View Answer
Answer: c
Explanation: Diagonal scale is used when three different units of measurements are needed to be measured. With the help of this scale, we can get the reading in three different units. This scale also helps in accurate measurement of minute divisions.
70. Which of the following scales is used to accurately measure minute divisions?
a) Plain scale
b) Diagonal scale
c) Scale of chords
d) Comparative scale
View Answer
Answer: b
Explanation: Minute divisions are accurately measured by using diagonal scales. Diagonal scales are also when three different units of measurements are needed to be measured. With the help of these scales, we can get a relation between three different units.
71. What is the length of AB in the following scale?
a) 2.74 m
b) 3.74 m
c) 2.47 m
d) 3.47 m
View Answer
Answer: a
Explanation: Reading of the diagonal involves reading in three ways. The first measurement is taken in the meters scale, the second is from the decimeters scale and the third is from the centimeters scale. Hence in meters scale, the value is 2 m from 0; in decimeters scale, the value is 7 dm and in the centimeters scale, the value is 4 cm. Hence length of AB = 2.74 m.
72. What is the maximum length of the given scale?
a) 3 dm
b) 4 dm
c) 3 m
d) 4 m
View Answer
Answer: d
Explanation: The maximum length that can be measured using the given scale is 4 meters. It is clear that wee can measure 3 m from the meters scale. The rest 1 meter is measured as 10 decimeter. Hence 3 + 1 = 4 meters is the maximum length.
73. If the given scale is 1: 60, what is the length of the scale?
a) 6.67dm
b) 0.67 cm
c) 6.67 cm
d) 66.67 cm
View Answer
Answer: c
Explanation: The length of the scale is determined by the formula, length of the scale = representative fraction x maximum length to be measured, that is, length of the scale = 1 ÷ 60 x 4 x 100 = 6.67 cm. Hence the length of the scale is 6.67 cm.
74. From the given scale, we can measure 4.56 m.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum length that can be measured is 4 meters. Hence any value beyond 4.00 meters cannot be measured using the above scale. Measuring a value in diagonal scale, the line needs to coincide with one of the line in the scale and not go beyond it.
75. From the given scale below, what is the length of PQ?
a) 3 yd 2 ft 0”
b) 3 yd 1 ft 10”
c) 3 yd 0 ft 10”
d) 4 yd 2 ft 0”
View Answer
Answer: b
Explanation: The distance from the 0 on the horizontal to the point Q is 3 yards. In the feet scale, the point P lies on 1 feet and in the inches scale, the point P lies on 10 inches. Hence, the length of PQ is 3 yards 1 foot 10 inches.
76. What is the maximum length that can be measured using the given scale?
a) 6 yards
b) 5 yards
c) 6 feet
d) 15 feet
View Answer
Answer: a
Explanation: It is clear that we can measure up to 5 yards directly. But in addition to the five yards, we have 3 feet in the feet scale which equals to one yard. Hence the maximum length that can be measured is 6 yards.
77. What is the length of the scale, if the scale is 1:30?
a) 0.6 yard
b) 7.2 feet
c) 0.2 feet
d) 7.2 inches
View Answer
Answer: d
Explanation: The length of the scale is measured as; length of the scale = representative fraction x maximum length to be measured. Hence, length of the scale = 1 ÷ 30 x 6 x 3 x 12 = 7.2 inches. Representative fraction for the scale 1:30 is 1/30.
78. From the given scale, we can measure 5 yards 3 feet and 0 inches.
a) True
b) False
View Answer
Answer: a
Explanation: We can measure 5 yards and 3 feet using the given scale, as 5 yards are clearly indicated on the yards scale and 3 feet is also indicated on the feet scale. 3 feet equals 1 yard. Hence, 5 yard 3 feet is nothing but 6 yards and that is the maximum length that can be measured by the scale.
79. The diagonal scales are used when measurements are required in _____ units.
a) 1
b) 2
c) 3
d) 4
View Answer
Answer: c
Explanation: Using plain scale we can accommodate 2 units (example: yard, feet). But with the diagonal scale we can accommodate 3 units (example: yard, feet and inch). It is possible by the principle of diagonal division.
80. If a diagonal scale is to be made with a meter, decimeter and centimeter then, how many divisions it has to be made vertically?
a) 3
b) 5
c) 10
d) 9
View Answer
Answer: c
Explanation: Vertical divisions are related to how many centimeters take a decimeter. It is 10. Or anywhere in a diagonal scales vertical division are dependent of 2nd and 3rd unit which we use in drawing diagonal scale.
81. If a diagonal scale is to be made with a yard, feet and inch then, how many divisions it has to be made vertically?
a) 3
b) 12
c) 10
d) 6
View Answer
Answer: b
Explanation: Vertical divisions are related to how many inches take a foot. It is 12. Or anywhere in the diagonal scales vertical division are dependent of 2nd and 3rd unit which we use in drawing diagonal scale.
82. Arrange the steps involved in drawing the diagonal scale.
i) Dividing vertically and joining the points from subdivisions to successive next subdivisions on the last vertical line.
ii) Finding length of scale
iii) Finding R.F.
iv) Dividing horizontally and subdividing the 1st part.
a) i, ii, iii, iv
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, i, iv, iii
View Answer
Answer: b
Explanation: General procedure in preparing graphical scales includes finding representative fraction at first and then finding length of scale. Next dividing horizontally, sub-dividing the 1st division which is common in plain and diagonal scale. In diagonal scales the fourth step as said above places prominent role.
83. A plot of 35,000 sq m is drawn on map as plot of 14 cm and 5 cm. Find the R.F.
a) 1/35000
b) 1/50000
c) 1/34930
d) 1/2236
View Answer
Answer: d
Explanation: Area of plot in drawing is 14 x 5 = 70 sq cm (equivalent to 35000 sq m). So 1 sq cm =35000/70 = 500 sq m. 1 cm = square root of 500 m = 22.3 m (equivalent to 1 cm). Representative fraction = 1/ (22.36 m) =1/ (2236 cm).
84. Diagonal scale follows the principle of similar triangles.
a) True
b) False
View Answer
Answer: a
Explanation: Diagonal scale follows the principle of similar triangles where a short length is divided into a number of divisions in which sides are proportional which produces interpolated values in between the 1st least number in a unit to 0.
85. We can draw diagonal scale for meter, feet, inch.
a) True
b) False
View Answer
Answer: b
Explanation: There exists a particular order in selecting 1st, 2nd and 3rd unit while drawing diagonal scale that is 1st should have a higher quantity of all three, 3rd should have least quantity of all three and 2nd should be middle in them. And there exits at least appreciable multiples among themselves
86. Which of the following scales is used to accurately measure minute divisions?
a) Plain scale
b) Diagonal scale
c) Scale of chords
d) Comparative scale
View Answer
Answer: b
Explanation: Minute divisions are accurately measured by using diagonal scales. Diagonal scales are also when three different units of measurements are needed to be measured. With the help of these scales, we can get a relation between three different units.
a) ratio of the length in drawing to the actual length
b) ratio of the actual length to the length in drawing
c) reciprocal of actual length
d) square of the length in drawing
View Answer
Answer: a
Explanation: Representative fraction is the ratio of the length of the object represented on drawing to the actual length of the object represented.
2. The scale of a drawing is given as 1:20. What is the representative fraction?
a) 20
b) 1/20
c) 0.5
d) 0.02
Answer: b
Explanation: The scale of the drawing is given as 1:20 that is a reducing scale, this means dimensions are made to 1/20th of full size. So the representative factor is that dimension in drawing to actual dimension. R.F. = (1/20)/1 = 1/20.
3. The scale of a drawing is given as 15:1. What is the representative fraction?
a) 15
b) 0.15
c) 1.5
d) 1/15
View Answer
Answer: a
Explanation: The scale of the drawing is given as 15:1 that is an enlarging scale, this means dimensions are increased to 15 times of actual ones. So the representative factor is that dimension in drawing to actual dimension. R.F. = 15/1 = 15.
4. The length of the drawing is 50 mm, the scale is given as 1:5. Find the actual length.
a) 50 cm
b) 10 cm
c) 25 cm
d) 10 mm
View Answer
Answer: c
Explanation: The scale given is 1:5 (reducing scale) that is the drawing is made with 1/5th of actual dimensions. So we have to multiply the drawing length with 5. 50 mm x 5 =250 mm and 1 cm =10 mm. The actual length in cm is 25.
5. The actual length is 1m. The length of the drawing is 5cm. Find the representative factor.
a) 1/5
b) 20
c) 1/20
d) 5
View Answer
Answer: c
Explanation: Representative factor is the ratio of the length represented in drawing to the actual length. Here given actual length is 1 m =100cm and length of drawing is 5 cm. R.F. =5 cm/100 cm = 0.05 (or) = 1/20.
6. The representative factor is 4. The actual length is 20 mm. Find the length of the drawing.
a) 5 cm
b) 5 mm
c) 0.2 mm
d) 8 cm
View Answer
Answer: d
Explanation: The representative factor given is 4 (more than one), shows the scale is enlarging. Representative factor = ratio of the length in drawing to actual length. R.F. = (length in drawing)/20 mm = 4.
Length in drawing = 20 mm x 4 = 80 mm = 8 cm.
7. A machine part is drawn two times with different scales. The ratio of 1st drawing’s R.F. to 2nd drawing R.F. with respect to the actual object is found to be 2. The length of the second drawing is 10 mm. Find the 1st drawing length.
a) 5 mm
b) 200 mm
c) 5 cm
d) 2 cm
Answer: d
Explanation: 2 = 1st drawing R.F/2nd drawing R.F. = (length of 1st drawing/actual length)/(length of 2nd drawing/ actual length) = length of first drawing/length of second drawing = length of first drawing/ 10 mm. 2 x 10 mm = 20 mm. So therefore the length of first drawing is 20 mm = 2 cm.
8. The length of the drawing is 20 cm, the scale is given as 2:1. Find the actual length.
a) 50 cm
b) 10 cm
c) 25 cm
d) 10 mm
View Answer
Answer: b
Explanation: The scale given is 2:1 (enlarging scale) that is the drawing is made 2 times of actual dimensions. So we have to divide the drawing length with 2. 20 mm / 2 =100 mm and 1 cm =10 mm. The actual length in cm is 10 cm.
9. The actual length is 1cm. The length of the drawing is 30 cm. Find the representative factor.
a) 1/30
b) 30
c) 0.03
d) 15
View Answer
Answer: b
Explanation: Representative factor is the ratio of the length represented in drawing to the actual length. Here given actual length is 1 cm and length of drawing is 30 cm. R.F. = 30 cm/1 cm = 30.
10. The representative factor is 0.02. The actual length is 50 cm. Find the length of drawing.
a) 10 cm
b) 5 cm
c) 0.25 cm
d) 10 mm
View Answer
Answer: d
Explanation: The representative factor given is 0.02 (less than one), shows the reducing scale. Representative factor = ratio of length in drawing to actual length. R.F. = (length in drawing)/50 cm = 0.02. Length in drawing = 0.02 x 50 cm = 1 cm = 10 mm.
11. The ratio of a length of an actual object to the length of drawing is given as 5. Find the scale and R.F. (Representative factor).
a) 1:5, 1/5
b) 5:1, 1/5
c) 1:5, 5
d) 5:1, 5
View Answer
Answer: a
Explanation: Given that the ratio of actual length to length of drawing which is reciprocal of R.F. So the R.F. for given values is 1/5. From the given information it can be understood that the actual object is 5 times larger than the drawing, so the scale is reducing scale i.e. 1:5.
12. The representative factor is 2, the drawing length is 100 mm. Find the actual length.
a) 20 cm
b) 50 mm
c) 20 mm
d) 50 cm
View Answer
Answer: b
Explanation: The scale is enlarging scale. The ratio of length of drawing to actual length gives the representative factor. 100 mm / actual length = 2, actual length = 100 mm/2 = actual length = 50 mm (or) 5 cm.
13. The representative factor is 0.5, the drawing length is 10 cm. Find the actual length.
a) 20 cm
b) 50 mm
c) 20 mm
d) 50 cm
View Answer
Answer: a
Explanation: The scale is reducing scale. The ratio of length of drawing to actual length gives the representative factor. 10 cm / actual length = 0.5, actual length = 10 cm/0.5 = actual length = 20 cm (or) 200 mm.
14. Representative factor is defined as the ratio of the length of the drawing to the actual length of the object.
a) True
b) False
View Answer
Answer: a
Explanation: The representative factor is defined as the ratio of the length of the drawing to the actual length of the object. The value of representative factor can give information on whether the scale is enlarging or reducing.
15. What is the representative factor of a line, whose length is 24cm on the drawing sheet, representing an actual length of 6m?
a) 1:50
b) 1:25
c) 1:24
d) 1:60
View Answer
Answer: b
Explanation: Representative factor is calculated as the ratio of the length of the drawing to the actual length of the object. Both the quantities should be taken in the same unit. In this example, R.F. equals to 24 ÷ (600) i.e. 1:25.
16. A 20mm line, drawn on the drawing sheet represents an actual length of 5m. What is the representative factor?
a) 1:2.5
b) 1:25
c) 25:1
d) 1:250
View Answer
Answer: d
Explanation: The formula for calculating the representative factor is the length of the drawing divided by the actual length of the object. Hence for this example, R.F = 20 ÷ 5000 i.e. 1:250. The units of the quantities in the formula must be the same.
17. A line of 10cm is drawn on a drawing sheet. It represents an actual length of 25mm. What is the representative factor?
a) 1:4
b) 1:40
c) 4:1
d) 40:1
View Answer
Answer: c
Explanation: Representative factor is calculated as the ratio of the length of the drawing to the actual length of the drawing it represents. From this formula we get, R.F. = 100 ÷ 25. Hence the representative factor is 4:1.
18. Which of the following representative factor will have an enlarging scale?
a) 1:24
b) 1:5
c) 1:3
d) 1:0.5
View Answer
Answer: d
Explanation: The representative factor 1:0.5 can be written as 2:1. Since the actual length of the drawing is less than the representative length, the scale is enlarging. If the actual length of the object is greater than the representative value, R.F. will be less than unity.
19. Which of the following representative factors depict that the actual length of the object is greater than the length of the drawing?
a) 2:5
b) 4:1
c) 3:2
d) 5:3
View Answer
Answer: a
Explanation: Considering that a 2cm line drawn on the drawing sheet represents an actual length of 5cm. Hence in the case of representative factor 2:5 i.e. 1:2.5, the actual length is greater than the length of the drawing.
20. What is the representative factor if the length of the drawing is 15mm and the actual length of the object is 3m?
a) 1:2
b) 1:0.2
c) 1:200
d) 1:20
View Answer
Answer: c
Explanation: The representative factor is the ratio of a length of the drawing to the actual length of an object. Hence for the line of length 15mm and the actual length 3m, R.F. = 15 ÷ 3000 = 1:200. The units of both the quantities should be same.
21. Which of the following is not a valid representative factor?
a) 1:2
b) 1:3
c) 2:5
d) 0:4
View Answer
Answer: d
Explanation: The representative factor cannot be zero. As the length of the drawing cannot be zero, having a value zero means that there is no drawing made. Representative factors are used to scale down or up the drawing from the actual object.
22. A line of length 4mm is represented by a line of 4cm. What is the representative factor?
a) 1:1
b) 10:1
c) 1:10
d) 1:100
View Answer
Answer: b
Explanation: The actual length of the object is 4mm and the length of the drawing is 4cm. From the formula for calculating the representative factor we get, R.F. = 4 ÷ 0.4 = 10. Hence the representative factor is 10:1.
23. What is the representative factor if sides of a square measuring 4cm in the drawing sheet while the actual length of the side of the square is 3m?
a) 1:0.75
b) 4:3
c) 1:75
d) 3:4
View Answer
Answer: c
Explanation: The length of the drawing is 4cm and the actual length of the drawing is 3m. By using the formula for calculating the representative factor we get the value of R.F. as 1:75. R.F. = 4 ÷ 300. The units of both the quantities should be the same.
24. What is the type of scale in which the representative fraction is 1:1?
a) Enlarged scale
b) Reduced scale
c) Full size scale
d) Graphical scale
View Answer
Answer: c
Explanation: A full size scale is a type of scale in which the length of the drawing and the actual length of the object is of the ratio 1:1. Hence by definition, its representative fraction is 1:1. In full size scale, the drawing is drawn with the actual measurements.
25. Which of the following representative fraction depicts an enlarging scale?
a) 1:0.2
b) 1:2
c) 1:3
d) 1:1
View Answer
Answer: a
Explanation: Enlarging scale means that the drawing is drawn with the bigger dimensions in comparison to the actual dimensions of the object. A representative fraction of 1:0.2 means 5:1, i.e. the drawing is five times bigger than the actual object. Hence the scale is enlarging scale.
26. Which of the following scales is a reducing scale?
a) 3:2
b) 1:3
c) 1:1
d) 1:0.4
View Answer
Answer: b
Explanation: The representative fraction 1:3 indicates that the dimension of the drawing is one-third of the actual object. Since the drawing is smaller than the actual object, this type of scale is called a reducing scale.
27. Which of the following is not an enlarging scale?
a) 2:1
b) 4:3
c) 3:5
d) 6:1
View Answer
Answer: c
Explanation: Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.
28. Which of the following scales is neither an enlarging nor a reducing scale?
a) 3:2
b) 1:4
c) 1:0.5
d) 1:1
View Answer
Answer: d
Explanation: A scale which is neither enlarging nor reducing is called as full size scale. The representative fraction of a full size scale is 1:1. In full size scale, the drawing is made just as the actual dimensions of the object.
29. A scale which is numerically represented on the drawing sheet is called as _____
a) Graphical scale
b) Engineer’s scale
c) Reducing scale
d) Full size scale
View Answer
Answer: b
Explanation: An engineer’s scale is the representation of the scale used in drawing on the drawing sheet numerically. For example, if the length of the drawing is 5 cm and the actual length is 10m, then it is numerically represented as 5cm = 10m.
30. Which of the following scale is used in survey maps?
a) Engineer’s scale
b) Diagonal scale
c) Graphical scale
d) Vernier scale
View Answer
Answer: c
Explanation: Graphical scales are used in survey maps. The graphical scale is drawn on the drawing. When the drawing ages, the engineer’s scale shrinks and may not give accurate results. Hence graphical scale is used as the drawing shrinks, the scale will also shrink.
31. What is the formula for calculating the length of the scale?
a) Minimum length to be measured x R.F.
b) Minimum length to be measured ÷ R.F.
c) Maximum length to be measured ÷ R.F.
d) Maximum length to be measured x R.F.
View Answer
Answer: d
Explanation: The length of the scale is calculated by using the following formula,
Length of the scale = R.F. x Maximum length to be measured.
32. Units of the measurements must be shown in the scale drawn.
a) True
b) False
View Answer
Answer: a
Explanation: Units of the scale must be clearly indicated on the drawing. This helps in clearing any misunderstanding concerning the different units used in the scale. The representative fraction should be mentioned in the drawing as well.
33. The minimum length to be shown must be known for drawing an unusual scale.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum length of the scale must be known to draw unusual scales on the drawing sheet. The representative fraction of the scale is also essential information. The units of the scale must be mentioned on the drawing.
34. What is the length of the scale, the representative fraction is 1:50000 and the scale must measure up to 25 km?
a) 5 x 10-4 cm
b) 50 cm
c) 5 cm
d) 0.5 cm
View Answer
Answer: b
Explanation: The formula for calculating the length of the scale is given by, Length of the scale = R.F. x maximum length to be measured; Hence length of the scale = 1 ÷ 50000 x 25 x 1000 x 100 = 50 cm. It is very important to note the units while calculating.
35. In a map, 30 miles is represented by 20 cm. What is the length of the kilometer scale if the maximum length to be measured is 10 km? (1 mile = 1.609 km)
a) 4.14 cm
b) 10.73 cm
c) 9.32 cm
d) 24.14 cm
View Answer
Answer: a
Explanation: The formula for calculating the length of the scale is given by; Length of the scale = R.F. x maximum length to be measured. Hence from the formula, length of the scale = 20 ÷ (30 x 1.609 x 1000 x 100) x 10 x 1000 x 100 = 4.14 cm.
36. What is the representative fraction of the kilometer scale if 20 miles is represented as 5 cm and maximum length to be measured is 5 km? (1 mile = 1.609 km)
a) 1:4
b) 1:643600
c) 1:1.287
d) 0.7768:1
View Answer
Answer: b
Explanation: The representative fraction is calculated by the formula, R.F. = length of the drawing ÷ actual length of the object. Here the length of the drawing is 5 cm and the actual length is 20 miles. In R.F. both quantities should be in the same unit. R.F. = 5 ÷ (20 x 1.609 x1000 x 100) = 1:643600.
37. What is not essential information to construct a scale from the following?
a) The R.F. of the scale
b) The units to represent
c) Length of scale
d) Maximum length
View Answer
Answer: c
Explanation: The length of the scale can be found using ’length of the scale = Representative fraction x Maximum length’. To draw drawing R.F (representative fraction), Units to represent (example: meters and centimeter or another if needed) and maximum length required is essential.
38. Which scale represents only two units or a unit and its sub-division?
a) Diagonal scale
b) Plane scale
c) Scale of chords
d) Vernier scale
View Answer
Answer: b
Explanation: A plain scale is constructed by dividing a line into the suitable number of equal parts or units, the first of which is sub-divided into smaller parts. Plain scales represent either two units or a unit and its sub-division.
39. Which scale is employed when we need to measure in three units?
a) Plane scale
b) Scale of chords
c) Vernier Scale
d) Diagonal scale
View Answer
Answer: d
Explanation: A diagonal scale is used when very small distances are to be accurately measured or when measurements are required in three units. Small divisions of short lines are obtained by the principle of diagonal scales.
40. We need a scale which has to show dm, cm and mm. Which scale do you prefer?
a) Diagonal scale
b) Plain scale
c) Vernier scale
d) Comparative scale
Answer: a
Explanation: Diagonal scale is meant for drawing scales which represents 3 units. A diagonal scale is used when very minute distances to be measured. Small divisions of short lines are obtained by the principle of the diagonal scale.
41. Which of the following statement is incorrect with regard to plain scales?
a) Plain scales represent two units
b) Zero should be placed between the units and its subdivisions
c) The representative factor should be mentioned below the scale
d) It can read up to three decimal places
View Answer
Answer: d
Explanation: Plane scales measure a unit and its subunits so it can represent only the first decimal place of measurement. In the construction of plain scales, all units are placed to the right side of the zero, which is called as the main scale and to the left of zero, sub-divisions of units are placed.
42. Diagonal scales can only measure the first decimal place of measurement.
a) False
b) True
View Answer
Answer: a
Explanation: Diagonal scales can measure even minute distances accurately to three decimal places. This is achieved through the principle of diagonal scale, using the principle of similar triangles, sub-divisions are again divided into the number of equal parts.
43. Put the statements in an order to divide the line AB into 10 parts using the principle of diagonal scales.
i. Number the division-points as 1, 2, 3, up to 9 starting from C and later join AC.
ii. Divide the line BC into 10 equal parts.
iii. Draw a perpendicular line BC TO the line AB.
iv. Hence 9’9 is 0.9AB and similarly, other 2’2 is 0.2AB.
v. Number the cutting points on AC as 1’, 2’, 3’ and so on up to 9’.
vi. Draw lines parallel to AB through the division-points.
a) i, iv, v, ii, vi, iii
b) i, v, vi, ii, iv, iii
c) iii, ii, i, vi, v, iv
d) i, ii, iii, iv, v, vi
View Answer
Answer: c
Explanation: In the principle of the diagonal scale we apply the concept of similar triangles. So, we need to draw a perpendicular to B, say BC and form a right angle triangle ABC. By dividing the line BC into 10 equal parts (required number of parts as mentioned in the question) and drawing lines parallel to AB through division points, all these lines give the measurement as 0.1AB, 0.2 AB, 0.3AB, 0.4AB and so on up to 0.9AB.
44. How can we decide the minimum length of a scale, when Representative factor (R.F) and the maximum length of measurement (L) are known?
a) Length of scale = R.F+L
b) Length of scale = R.F/L
c) Length of scale = R.F-L
d) Length of scale = R.F*L
View Answer
Answer: d
Explanation: We can draw the scale as long as possible but the minimum length of scale should be capable of measuring the maximum length of required measurement. We know R.F = (length of the drawing)/(Actual length of the object), Hence length of scale = R.F* maximum length of required measurement.
45. When the length of the line drawn is 2 mm, and the taken representative fraction is 1:2. Find the actual length of the line?
a) 1 mm
b) 0.5 mm
c) 4 mm
d) 3 mm
View Answer
Answer: c
Explanation: Representative fraction is the ratio of the length of the drawings to actual length, hence actual length = (length of the drawing)/R.F. Here R.F is 1:2 mm and length of the drawing is 2 mm, therefore the actual length of the line is 2*2 mm = 4 mm.
46. The maximum length is 50 m and length of scale is 10 cm. Find the Representative factor.
a) 1/50
b) 50
c) 500
d) 1/500
View Answer
Answer: d
Explanation: Length of the scale = Representative fraction x Maximum length, 10 cm = Representative fraction x 5000 cm, Representative factor = 1/500.
47. Given Representative factor as 4/50 and maximum length is 100 cm. Find the length of scale.
a) 8 cm
b) 10 cm
c) 9.7 cm
d) 12 cm
View Answer
Answer: b
Explanation: Length of the scale = Representative fraction x Maximum length, Length of scale = 4/50 x 100 cm, Length of scale= 8 cm.
48. Given, below are the steps related to constructing a scale of 1:50 to show meters and decimeters and the maximum length is 5 meters. Arrange the steps
i. Then divide the 1st part into 10 equal divisions
ii. Determining the length of scale 1/50 x 500 cm = 10 cm
iii. Determining R.F. here it is 1/50
iv. Draw a line 10 cm long and divide it to 5 equal parts
a) i, ii, iii, iv
b) iii, ii, iv, i
c) ii, iv, i, iii
d) iv, i, ii, iii
View Answer
Answer: b
Explanation: The general procedure involves finding R.F. at the 1st and next max length of scale and then dividing whole line into given number of units at last dividing the 1st part to number of sub-divisions that occur in the unit.
49. How many divisions a line has to be made if it is given to prepare plain scale up to 7 yards?
a) 8
b) 7
c) 6
d) It depends on R.F
View Answer
Answer: b
Explanation: Whatever the representative factor may given, we just require a number of units to divide the line in scale. Representative factor is only needed to find the length of the scale. Length of the scale = Representative fraction x Maximum length.
50. What is the length of the scale, representative fraction given is 3/40 and maximum length to be represented in scale is 100 cm?
a) 8.5 cm
b) 10 cm
c) 7.5 cm
d) 13.33
View Answer
Answer: c
Explanation: Length of the scale = Representative fraction x Maximum length. Length of the scale = 3/40 x 100 cm = 7.5 cm. That is to draw a scale for 100 cm with 3/40 R.F. We need to draw a 7.5 cm length line and divide to 10 decimeters.
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51. In preparing a plain scale of feet and yards, the first division is to be divided into how many sub-divisions?
a) 5
b) 3
c) 4
d) 10
View Answer
Answer: b
Explanation: Given that the plain scale is to be made with feet and yards. Generally, 1st part is divided into sub-divisions here is feet. We know 1 yard is equal to 3 feet, so 1st division should be divided into 3 sub-divisions.
52. In preparing a plain scale of feet and inches, how many sub-divisions do the first division is to be divided?
a) 10
b) 6
c) 12
d) 5
View Answer
Answer: c
Explanation: Given that the plain scale is to be made with feet and inches. Generally, 1st part is divided into sub-divisions here is inches. We know 1 feet is equal to 12 inches, so 1st division should be divided into 12 sub-divisions.
53. In preparing a plain scale of miles and furlongs, how many divisions do the first part is to be made?
a) 10
b) 12
c) 8
d) 6
View Answer
Answer: c
Explanation: Given that the plain scale is to be made with miles and furlongs. Generally, 1st part is divided into sub-divisions here is furlong. 1 mile is equal to 8 feet, so 1st division should be divided into 8 sub-divisions.
54. A plain scale is made to show 9 miles and sub division is furlong. To measure 3 miles and 6 furlongs how many divisions is to take on the right side of origin and how many division it is to take on the left side of origin?
a) 3, 6
b) 2, 4
c) 6, 3
d) 4, 2
View Answer
Answer: a
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side. Here it is asked to measure how many divisions do 3 miles takes. It is 3 and 6 furlongs take on left of the origin. It is 6.
55. A plain scale is made to show 7 yards and sub division is feet. To measure 2 feet, how many divisions it is to take on the left side of origin?
a) 1
b) 2
c) 3
d) 4
View Answer
Answer: b
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 2 feet takes. It is 2 from origin to left.
56. A plain scale is made to show 4 feet and sub division is inch. To measure 2 feet and 10 inches how many divisions is to take on the right side of origin?
a) 1
b) 2
c) 10
d) 9
View Answer
Answer: b
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 2 feet takes. It is 2 from origin to right.
57. A plain scale is made to show 8 meters and sub division is decimeters. To measure7 meters and 3 decimeters how many divisions is to take on the right side of origin and how many it is to take on the left side of origin?
a) 7, 3
b) 3, 7
c) 6, 4
d) 4, 6
View Answer
Answer: a
Explanation: Origin is at 1st division ending. 1st division is made to sub-divisions. From origin, it is divided into divisions on the right side and towards left 1st division is divided into sub-divisions. Here it is asked to measure how many divisions do 7 meters takes. It is 7 from origin to right. And 3 from origin to left.
58. A plain scale is made which shows 6 meters of maximum length and sub division is decimeter with a R.F. of 1 /60. How much length does the scale shows 4 m and 5 decimeters?
a) 4 m 5 dm
b) 4.5 m
c) 0.75 dm
d) 0.75 m
View Answer
Answer: b
Explanation: length of the scale = Representative fraction x Maximum length, length of scale =1/60 x 4.5 m = 0.075 m = 0.75 dm = 7.5 cm = 75 mm. (or) 1/60 x 4 m =0.0666 m + 1/60 x 5 dm = 0.083 dm, 0.666 dm + 0.08333 dm =0.7499 dm =7.5 cm = 75 mm.
59. A scale of 1:25 is to be constructed to show centimeters and it should be long enough to measure 10 meters. What is the length of the scale?
a) 4 cm
b) 0.4 cm
c) 40 cm
d) 400cm
View Answer
Answer: c
Explanation: The length of the scale is calculated as the product of the representative fraction and the maximum length to be measured. Hence, length of the scale = 1 ÷ 25 x 10 x 100 = 40 cm. While calculating it is very important to note the units of the dimensions.
60. From the following figure what is the maximum length that can be measured?
a) 11 dm
b) 10 dm
c) 13 dm
d) 12 dm
View Answer
Answer: d
Explanation: From the scale given in the figure it is clear that the maximum length that can be measured is 12 decimeters. It is clearly seen that we can measure 11 decimeters and then by adding 10 centimeters which is equal to one decimeter. Hence the maximum length is 12 dm.
61. What is the length of the scale? (R.F. = 1/5)
a) 2.4 cm
b) 24 cm
c) 240cm
d) 0.24cm
View Answer
Answer: b
Explanation: The length of the scale is calculated by the formula, length of the scale = R.F. x maximum length to be measured. Hence, length of centimeter scale = 1 ÷ 5 x 12 x 10 = 24 cm. Here, the representative factor is 1/5.
62. Using the given scale, we can measure 13.7 dm.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum length that can be measured is 12 dm. Any measurement beyond that using the given scale is not possible. As we can clearly see we can measure 11 dm and the rest 1 dm can be measured using 10 cm.
63. What is the least count of the given scale?
a) 1 cm
b) 0.1 cm
c) 1dm
d) 10 cm
View Answer
Answer: a
Explanation: The smallest value that can be measured is 1 cm or 0.1 dm. The maximum value that can be measured using the above scale is 12 dm. 10 cm equals to 1 dm. It is clear that 11 dm can be measured but in addition to it, we can measure 10 cm.
64. What is the maximum length that can be measured using the given scale?
a) 7 inches
b) 7 feet
c) 8 feet
d) 12 inches
View Answer
Answer: c
Explanation: It is clearly visible that the maximum length that can be measured using the given scale is 7 feet. The rest twelve inches can be measured. Since 12 inches = 1 foot, we can measure 1 foot in addition to the 7 feet. Hence we can measure 8 feet maximum using the above scale.
65. What is the scale in the following figure?
a) 1:2
b) 1:12
c) 1:4
d) 1:7
View Answer
Answer: b
Explanation: In the figure it is clearly shown that the representative factor is 1/12. Hence the scale is 1:12. The representative fraction is measured as the length of the drawing divided by the actual length of the object.
66. What is the length of the scale?
a) 7 feet
b) 7 inches
c) 8 feet
d) 8 inches
View Answer
Answer: d
Explanation: The length of the scale is calculated as, length of the scale = representative fraction x maximum length to be measured. Hence length of the scale = 1 ÷ 12 x 8 x 12 = 8 inches. While calculating, the units are to be noted.
67. What is the least count of the given scale?
a) 3“
b) 1“
c) 12”
d) 7”
View Answer
Answer: b
Explanation: The least count is the minimum amount of length that can be measured. Here in the given scale, the least count is 1 inch or one twelfth of a foot = 1/12th foot. The maximum length that can be measured is 8 feet.
68. From the given scale we can measure 3 feet 10”.
a) True
b) False
View Answer
Answer: a
Explanation: From the given scale we easily measure 3 feet. In addition to that we can measure 10 inches using the inches scale. In this type of plain scale we can measure using both feet and inches as 12 inches = 1 foot.
69. Which of the following scales is used when there are three units that need to be measured?
a) Plain scale
b) Comparative scale
c) Diagonal scale
d) Vernier scale
View Answer
Answer: c
Explanation: Diagonal scale is used when three different units of measurements are needed to be measured. With the help of this scale, we can get the reading in three different units. This scale also helps in accurate measurement of minute divisions.
70. Which of the following scales is used to accurately measure minute divisions?
a) Plain scale
b) Diagonal scale
c) Scale of chords
d) Comparative scale
View Answer
Answer: b
Explanation: Minute divisions are accurately measured by using diagonal scales. Diagonal scales are also when three different units of measurements are needed to be measured. With the help of these scales, we can get a relation between three different units.
71. What is the length of AB in the following scale?
a) 2.74 m
b) 3.74 m
c) 2.47 m
d) 3.47 m
View Answer
Answer: a
Explanation: Reading of the diagonal involves reading in three ways. The first measurement is taken in the meters scale, the second is from the decimeters scale and the third is from the centimeters scale. Hence in meters scale, the value is 2 m from 0; in decimeters scale, the value is 7 dm and in the centimeters scale, the value is 4 cm. Hence length of AB = 2.74 m.
72. What is the maximum length of the given scale?
a) 3 dm
b) 4 dm
c) 3 m
d) 4 m
View Answer
Answer: d
Explanation: The maximum length that can be measured using the given scale is 4 meters. It is clear that wee can measure 3 m from the meters scale. The rest 1 meter is measured as 10 decimeter. Hence 3 + 1 = 4 meters is the maximum length.
73. If the given scale is 1: 60, what is the length of the scale?
a) 6.67dm
b) 0.67 cm
c) 6.67 cm
d) 66.67 cm
View Answer
Answer: c
Explanation: The length of the scale is determined by the formula, length of the scale = representative fraction x maximum length to be measured, that is, length of the scale = 1 ÷ 60 x 4 x 100 = 6.67 cm. Hence the length of the scale is 6.67 cm.
74. From the given scale, we can measure 4.56 m.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum length that can be measured is 4 meters. Hence any value beyond 4.00 meters cannot be measured using the above scale. Measuring a value in diagonal scale, the line needs to coincide with one of the line in the scale and not go beyond it.
75. From the given scale below, what is the length of PQ?
a) 3 yd 2 ft 0”
b) 3 yd 1 ft 10”
c) 3 yd 0 ft 10”
d) 4 yd 2 ft 0”
View Answer
Answer: b
Explanation: The distance from the 0 on the horizontal to the point Q is 3 yards. In the feet scale, the point P lies on 1 feet and in the inches scale, the point P lies on 10 inches. Hence, the length of PQ is 3 yards 1 foot 10 inches.
76. What is the maximum length that can be measured using the given scale?
a) 6 yards
b) 5 yards
c) 6 feet
d) 15 feet
View Answer
Answer: a
Explanation: It is clear that we can measure up to 5 yards directly. But in addition to the five yards, we have 3 feet in the feet scale which equals to one yard. Hence the maximum length that can be measured is 6 yards.
77. What is the length of the scale, if the scale is 1:30?
a) 0.6 yard
b) 7.2 feet
c) 0.2 feet
d) 7.2 inches
View Answer
Answer: d
Explanation: The length of the scale is measured as; length of the scale = representative fraction x maximum length to be measured. Hence, length of the scale = 1 ÷ 30 x 6 x 3 x 12 = 7.2 inches. Representative fraction for the scale 1:30 is 1/30.
78. From the given scale, we can measure 5 yards 3 feet and 0 inches.
a) True
b) False
View Answer
Answer: a
Explanation: We can measure 5 yards and 3 feet using the given scale, as 5 yards are clearly indicated on the yards scale and 3 feet is also indicated on the feet scale. 3 feet equals 1 yard. Hence, 5 yard 3 feet is nothing but 6 yards and that is the maximum length that can be measured by the scale.
79. The diagonal scales are used when measurements are required in _____ units.
a) 1
b) 2
c) 3
d) 4
View Answer
Answer: c
Explanation: Using plain scale we can accommodate 2 units (example: yard, feet). But with the diagonal scale we can accommodate 3 units (example: yard, feet and inch). It is possible by the principle of diagonal division.
80. If a diagonal scale is to be made with a meter, decimeter and centimeter then, how many divisions it has to be made vertically?
a) 3
b) 5
c) 10
d) 9
View Answer
Answer: c
Explanation: Vertical divisions are related to how many centimeters take a decimeter. It is 10. Or anywhere in a diagonal scales vertical division are dependent of 2nd and 3rd unit which we use in drawing diagonal scale.
81. If a diagonal scale is to be made with a yard, feet and inch then, how many divisions it has to be made vertically?
a) 3
b) 12
c) 10
d) 6
View Answer
Answer: b
Explanation: Vertical divisions are related to how many inches take a foot. It is 12. Or anywhere in the diagonal scales vertical division are dependent of 2nd and 3rd unit which we use in drawing diagonal scale.
82. Arrange the steps involved in drawing the diagonal scale.
i) Dividing vertically and joining the points from subdivisions to successive next subdivisions on the last vertical line.
ii) Finding length of scale
iii) Finding R.F.
iv) Dividing horizontally and subdividing the 1st part.
a) i, ii, iii, iv
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, i, iv, iii
View Answer
Answer: b
Explanation: General procedure in preparing graphical scales includes finding representative fraction at first and then finding length of scale. Next dividing horizontally, sub-dividing the 1st division which is common in plain and diagonal scale. In diagonal scales the fourth step as said above places prominent role.
83. A plot of 35,000 sq m is drawn on map as plot of 14 cm and 5 cm. Find the R.F.
a) 1/35000
b) 1/50000
c) 1/34930
d) 1/2236
View Answer
Answer: d
Explanation: Area of plot in drawing is 14 x 5 = 70 sq cm (equivalent to 35000 sq m). So 1 sq cm =35000/70 = 500 sq m. 1 cm = square root of 500 m = 22.3 m (equivalent to 1 cm). Representative fraction = 1/ (22.36 m) =1/ (2236 cm).
84. Diagonal scale follows the principle of similar triangles.
a) True
b) False
View Answer
Answer: a
Explanation: Diagonal scale follows the principle of similar triangles where a short length is divided into a number of divisions in which sides are proportional which produces interpolated values in between the 1st least number in a unit to 0.
85. We can draw diagonal scale for meter, feet, inch.
a) True
b) False
View Answer
Answer: b
Explanation: There exists a particular order in selecting 1st, 2nd and 3rd unit while drawing diagonal scale that is 1st should have a higher quantity of all three, 3rd should have least quantity of all three and 2nd should be middle in them. And there exits at least appreciable multiples among themselves
86. Which of the following scales is used to accurately measure minute divisions?
a) Plain scale
b) Diagonal scale
c) Scale of chords
d) Comparative scale
View Answer
Answer: b
Explanation: Minute divisions are accurately measured by using diagonal scales. Diagonal scales are also when three different units of measurements are needed to be measured. With the help of these scales, we can get a relation between three different units.
