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These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Civil Engineering .

1. |
## Perpendiculars can’t be drawn using |

A. | t- square |

B. | set-squares |

C. | pro- circle |

D. | protractor |

Answer» C. pro- circle | |

Explanation: t-square is meant for drawing a straight line and also perpendiculars. and also using set-squares we can draw |

2. |
## The length through perpendicular gives the shortest length from a point to the line. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: the statement given here is right. if we need the shortest distance from a point to the line, then drawing perpendicular along the point to a line is the best method. since the perpendicular is the line which has points equidistant from points either side of given line. |

3. |
## A Ogee curve is a |

A. | semi ellipse |

B. | continuous double curve with convex and concave |

C. | freehand curve which connects two parallel lines |

D. | semi hyperbola |

Answer» B. continuous double curve with convex and concave | |

Explanation: an ogee curve or a reverse curve is a combination of two same curves in which the second curve has a reverse shape to that of the first curve. any curve or line or mould consists of a continuous double curve with the upper part convex and lower part concave, like ‘’s’’. |

4. |
## How many pairs of parallel lines are there in regular Hexagon? |

A. | 2 |

B. | 3 |

C. | 6 |

D. | 1 |

Answer» B. 3 | |

Explanation: hexagon is a closed figure which has six sides, six corners. given is regular hexagon which means it has equal interior angles and equal side lengths. so, there will be 3 pair of parallel lines in a regular hexagon. |

5. |
## How many pairs of parallel lines are there in a regular pentagon? |

A. | 0 |

B. | 1 |

C. | 2 |

D. | 5 |

Answer» A. 0 | |

Explanation: pentagon is a closed figure which has five sides, five corners. given is regular pentagon which means it has equal interior angles and equal side lengths. since five is odd number so, there exists angles 36o, 72o, 108o, 144o, 180o with sides to horizontal. |

6. |
## How many external tangents are there for two circles? |

A. | 1 |

B. | 2 |

C. | 3 |

D. | 4 |

Answer» B. 2 | |

Explanation: external tangents are those which touch both the circles but they will not intersect in between the circles. the tangents touch at outmost points of circles that are ends of diameter if the circles have the same diameter. |

7. |
## How many internal tangents are there for two circles? |

A. | 4 |

B. | 3 |

C. | 2 |

D. | 1 |

Answer» C. 2 | |

Explanation: internal tangents are those which touch both the circle and also intersect each other on the line joining the centers of circles. and the internal tangents intersect each other at midpoint of line joining the center of circles only if circles have the same diameter. |

8. |
## For any point on any curve there exist two normals. |

A. | true |

B. | false |

Answer» B. false | |

Explanation: here we take point on the curve. there exist multiple tangents for some curve which are continuous, trigonometric curves, hyperbola etc. but for curves like circles, parabola, ellipse, cycloid etc. have only one tangent and normal. |

9. |
## There are 2 circles say A, B. A has 20 units radius and B has 10 units radius and distance from centers of A and B is 40 units. Where will be the intersection point of external tangents? |

A. | to the left of two circles |

B. | to the right of the two circles |

C. | middle of the two circles |

D. | they intersect at midpoint of line joining the centers |

Answer» B. to the right of the two circles | |

Explanation: a has 20 units radius and b has 10 units radius. so, the tangents go along the circles and meet at after the second circle that is b that is the right side of both circles. and we asked for external tangents so they meet away from the circles but not in between them. |

10. |
## There are 2 circles say A, B. A is smaller than B and they are not intersecting at any point. Where will be the intersection point of internal tangents for these circles? |

A. | to the left of two circles |

B. | to the right of the two circles |

C. | middle of the two circles |

D. | they intersect at midpoint of line joining the centers |

Answer» B. to the right of the two circles | |

Explanation: a is smaller than b so the intersection point of internal tangents will not be on the midpoint of the line joining the centers. and we asked for internal tangents so they will not meet away from the circles. |

11. |
## Which of the following is incorrect about Ellipse? |

A. | eccentricity is less than 1 |

B. | mathematical equation is x2 /a2 + y2/b2 = 1 |

C. | if a plane is parallel to axis of cone cuts the cone then the section gives ellipse |

D. | the sum of the distances from two focuses and any point on the ellipse is constant |

Answer» C. if a plane is parallel to axis of cone cuts the cone then the section gives ellipse | |

Explanation: if a plane is parallel to the axis of cone cuts the cone then the cross-section gives hyperbola. if the plane is parallel to base it gives circle. if the plane is inclined with an angle more than the external angle of cone it gives parabola. if the plane is inclined and cut every generators then it forms an ellipse. |

12. |
## Which of the following constructions doesn’t use elliptical curves? |

A. | cooling towers |

B. | dams |

C. | bridges |

D. | man-holes |

Answer» A. cooling towers | |

Explanation: cooling towers, water channels use hyperbolic curves as their design. |

13. |
## The line which passes through the focus and perpendicular to the major axis is |

A. | minor axis |

B. | latus rectum |

C. | directrix |

D. | tangent |

Answer» B. latus rectum | |

Explanation: the line bisecting the major axis at right angles and terminated by curve is called the minor axis. the line which passes through the focus and perpendicular to the major axis is latus rectum. tangent is the line which touches the curve at only one point. |

14. |
## Axes are called conjugate axes when they are parallel to the tangents drawn at their extremes. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: in ellipse there exist two axes (major and minor) which are perpendicular to each other, whose extremes have tangents parallel them. there exist two conjugate axes for ellipse and 1 for parabola and hyperbola. |

15. |
## Which of the following is not belonged to ellipse? |

A. | latus rectum |

B. | directrix |

C. | major axis |

D. | asymptotes |

Answer» D. asymptotes | |

Explanation: latus rectum is the line joining one of the foci and perpendicular to the major axis. asymptotes are the tangents which meet the hyperbola at infinite distance. major axis consists of foci and perpendicular to the minor axis. |

16. |
## In general method of drawing an ellipse, a vertical line called as is drawn first. |

A. | tangent |

B. | normal |

C. | major axis |

D. | directrix |

Answer» D. directrix | |

Explanation: in the general method of drawing an ellipse, a vertical line called as directrix is drawn first. the focus is drawn at a given distance from the directrix drawn. |

17. |
## If eccentricity of ellipse is 3/7, how many divisions will the line joining the directrix and the focus have in general method? |

A. | 10 |

B. | 7 |

C. | 3 |

D. | 5 |

Answer» A. 10 | |

Explanation: in the general method of drawing an ellipse, if eccentricity of the ellipse is given as 3/7 then the line joining the directrix and the focus will have 10 divisions. the number is derived by adding the numerator and denominator of the eccentricity. |

18. |
## In the general method of drawing an ellipse, after parting the line joining the directrix and the focus, a is made. |

A. | tangent |

B. | vertex |

C. | perpendicular bisector |

D. | normal |

Answer» B. vertex | |

Explanation: in the general method of drawing after parting the line joining the directrix and the focus, a vertex is made. an arc with a radius equal to the length between the vertex and the focus is drawn with the vertex as the centre. |

19. |
## An ellipse is defined as a curve traced by a point which has the sum of distances between any two fixed points always same in the same plane. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: an ellipse can also be defined as a curve that can be traced by a point moving in the same plane with the sum of the distances between any two fixed points always same. the two fixed points are called as a focus. |

20. |
## An ellipse has foci. |

A. | 1 |

B. | 2 |

C. | 3 |

D. | 4 |

Answer» B. 2 | |

Explanation: an ellipse has 2 foci. these foci are fixed in a plane. the sum of the distances of a point with the foci is always same. the ellipse can also be defined as the curved traced by the points which exhibit this property. |

21. |
## If information about the major and minor axes of ellipse is given then by how many methods can we draw the ellipse? |

A. | 2 |

B. | 3 |

C. | 4 |

D. | 5 |

Answer» D. 5 | |

Explanation: there are 5 methods by which we can draw an ellipse if we know the major and minor axes of that ellipse. those five methods are arcs of circles method, concentric circles method, loop of the thread method, oblong method, trammel method. |

22. |
## In arcs of circles method, the foci are constructed by drawing arcs with centre as one of the ends of the axis and the radius equal to the half of the axis. |

A. | minor, major |

B. | major, major |

C. | minor, minor |

D. | major, minor |

Answer» A. minor, major | |

Explanation: in arcs of circles method, the foci are constructed by drawing arcs with centre as one of the ends of the minor axis and the radius equal to the half of the major axis. this method is used when we know only major and minor axes of the ellipse. |

23. |
## If we know the major and minor axes of the ellipse, the first step of drawing the ellipse, we draw the axes each other. |

A. | parallel to |

B. | perpendicular bisecting |

C. | just touching |

D. | coinciding |

Answer» B. perpendicular bisecting | |

Explanation: if we know the major and minor axes of the ellipse, the first step of the drawing the ellipse is to draw the major and minor axes perpendicular bisecting each other. the major and the minor axes are perpendicular bisectors of each other. |

24. |
## Loop of the thread method is the practical application of method. |

A. | oblong method |

B. | trammel method |

C. | arcs of circles method |

D. | concentric method |

Answer» C. arcs of circles method | |

Explanation: loop of the thread method is the practical application of the arcs of circles method. the lengths of the ends of the minor axis are half of the length of the major axis. in this method, a pin is inserted at the foci point and the thread is tied to a pencil which is used to draw the curve. |

25. |
## Which of the following is incorrect about Parabola? |

A. | eccentricity is less than 1 |

B. | mathematical equation is x2 = 4ay |

C. | length of latus rectum is 4a |

D. | the distance from the focus to a vertex is equal to the perpendicular distance from a vertex to the directrix |

Answer» A. eccentricity is less than 1 | |

Explanation: the eccentricity is equal to one. that is the ratio of a perpendicular distance from point on curve to directrix is equal to distance from point to focus. the eccentricity is less than 1 for an ellipse, greater than one for hyperbola, zero for a circle, one for a parabola. |

26. |
## Which of the following constructions use parabolic curves? |

A. | cooling towers |

B. | water channels |

C. | light reflectors |

D. | man-holes |

Answer» C. light reflectors | |

Explanation: arches, bridges, sound reflectors, light reflectors etc use parabolic curves. cooling towers, water channels use hyperbolic curves as their design. arches, |

27. |
## The length of the latus rectum of the parabola y2 =ax is |

A. | 4a |

B. | a |

C. | a/4 |

D. | 2a |

Answer» B. a | |

Explanation: latus rectum is the line perpendicular to axis and passing through focus ends touching parabola. length of latus rectum of y2 =4ax, x2 =4ay is 4a; y2 =2ax, x2 |

28. |
## Which of the following is not a parabola equation? |

A. | x2 = 4ay |

B. | y2 – 8ax = 0 |

C. | x2 = by |

D. | x2 = 4ay2 |

Answer» D. x2 = 4ay2 | |

Explanation: the remaining represents different forms of parabola just by adjusting them we can get general notation of parabola but x2 = 4ay2 gives equation for hyperbola. and x2 + 4ay2 =1 gives equation for ellipse. |

29. |
## The parabola x2 = ay is symmetric about x- axis. |

A. | true |

B. | false |

Answer» B. false | |

Explanation: from the given parabolic equation x2 = ay we can easily say if we give y values to that equation we get two values for x so the given parabola is symmetric about y-axis. if the equation is y2 = ax then it is symmetric about x-axis. |

30. |
## Which of the following is not belonged to ellipse? |

A. | latus rectum |

B. | directrix |

C. | major axis |

D. | axis |

Answer» C. major axis | |

Explanation: latus rectum is the line joining one of the foci and perpendicular to the major axis. major axis and minor axis are in ellipse but in parabola, only one focus and one axis exist since eccentricity is equal to 1. |

31. |
## Which of the following is Hyperbola equation? |

A. | y2 + x2/b2 = 1 |

B. | x2= 1ay |

C. | x2 /a2 – y2/b2 = 1 |

D. | x2 + y2 = 1 |

Answer» C. x2 /a2 – y2/b2 = 1 | |

Explanation: the equation x2 + y2 = 1 gives a circle; if the x2 and y2 have same co- efficient then the equation gives circles. the equation x2= 1ay gives a parabola. the equation y2 + x2/b2 = 1 gives an ellipse. |

32. |
## Which of the following constructions use hyperbolic curves? |

A. | cooling towers |

B. | dams |

C. | bridges |

D. | man-holes |

Answer» A. cooling towers | |

Explanation: cooling towers, water channels use hyperbolic curves as their design. |

33. |
## The lines which touch the hyperbola at an infinite distance are |

A. | axes |

B. | tangents at vertex |

C. | latus rectum |

D. | asymptotes |

Answer» D. asymptotes | |

Explanation: axis is a line passing through the focuses of a hyperbola. the line which passes through the focus and perpendicular to the major axis is latus rectum. tangent is the line which touches the curve at only one point. |

34. |
## If the asymptotes are perpendicular to each other then the hyperbola is called rectangular hyperbola. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: in ellipse there exist two axes (major and minor) which are perpendicular to each other, whose extremes have tangents parallel them. there exist two conjugate axes for ellipse and 1 for parabola and hyperbola. |

35. |
## A straight line parallel to asymptote intersects the hyperbola at only one point. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: a straight line parallel to asymptote intersects the hyperbola at only one point. this says that the part of hyperbola will lay in between the parallel lines through outs its length after intersecting at one point. |

36. |
## The asymptotes of any hyperbola intersects at |

A. | on the directrix |

B. | on the axis |

C. | at focus |

D. | centre |

Answer» D. centre | |

Explanation: the asymptotes intersect at centre that is a midpoint of axis even for conjugate axis it is valid. along with the hyperbola asymptotes are also symmetric about both axes so they should meet at centre only. |

37. |
## is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. |

A. | cycloid |

B. | epicycloid |

C. | epitrochoid |

D. | trochoid |

Answer» D. trochoid | |

Explanation: cycloid form if generating point is on the circumference of generating a circle. epicycloid represents generating circle rolls on the directing circle. epitrochoid is that the generating point is within or outside the generating circle but generating circle rolls on directing circle. |

38. |
## is a curve generated by a point on the circumference of a circle, which rolls without slipping along another circle outside it. |

A. | trochoid |

B. | epicycloid |

C. | hypotrochoid |

D. | involute |

Answer» B. epicycloid | |

Explanation: trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. ‘hypo’ represents the generating circle is inside the directing circle. |

39. |
## is a curve generated by a point on the circumference of a circle which rolls without slipping on a straight line. |

A. | trochoid |

B. | epicycloid |

C. | cycloid |

D. | evolute |

Answer» C. cycloid | |

Explanation: trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line. ‘epi’ represents the directing path is a circle. |

40. |
## When the circle rolls along another circle inside it, the curve is called a |

A. | epicycloid |

B. | cycloid |

C. | trochoid |

D. | hypocycloid |

Answer» D. hypocycloid | |

Explanation: cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line. ‘epi’ represents the directing path is a circle. trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. ‘hypo’ represents the generating circle is inside the directing circle. |

41. |
## The generating circle will be inside the directing circle for |

A. | cycloid |

B. | inferior trochoid |

C. | inferior epitrochoid |

D. | hypocycloid |

Answer» D. hypocycloid | |

Explanation: the generating circle will be inside the directing circle for hypocycloid or hypotrochoid. trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line or over circle if not represented with hypo as a prefix. |

42. |
## The generating point is outside the generating circle for |

A. | cycloid |

B. | superior trochoid |

C. | inferior trochoid |

D. | epicycloid |

Answer» B. superior trochoid | |

Explanation: if the generating point is on the circumference of generating circle then the curve formed may be cycloids or hypocycloids. trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line or a circle. but here given is outside so it is superior trochoid. |

43. |
## Mathematical equation for Involute is |

A. | x = a cos3 θ |

B. | x = r cosθ + r θ sinθ |

C. | x = (a+b)cosθ – a cos(a+b⁄a θ) |

D. | y = a(1-cosθ) |

Answer» B. x = r cosθ + r θ sinθ | |

Explanation: x= a cos3 Ɵ is equation for hypocycloid, x= (a+ b) cosƟ – a cos ( (a+b)/aƟ) is equation for epicycloid, y = a (1- cosƟ) is equation for cycloid and x = r cosƟ |

44. |
## For inferior trochoid or inferior epitrochoid the curve touches the directing line or directing circle. |

A. | true |

B. | false |

Answer» B. false | |

Explanation: since in the inferior trochoids the generating point is inside the generating circle the path will be at a distance from directing line or circle even if the generating circle is inside or outside the directing circle. |

45. |
## ‘Hypo’ as prefix to cycloids give that the generating circle is inside the directing circle. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: ‘hypo’ represents the generating circle is inside the directing circle. ‘epi’ represents the directing path is a circle. trochoid represents the generating point is not on the circumference of generating a circle. |

46. |
## Which of the following represents an Archemedian spiral? |

A. | tornado |

B. | cyclone |

C. | mosquito coil |

D. | fibonacci series |

Answer» C. mosquito coil | |

Explanation: archemedian spiral is a curve traced out by a point moving in such a way that its movement towards or away from the pole is uniform with the increase of the vectorial angle from the starting line. it is generally used for teeth profiles of helical gears etc. |

47. |
## Which of the following does not represents an Archemedian spiral? |

A. | coils in heater |

B. | tendrils |

C. | spring |

D. | cyclone |

Answer» D. cyclone | |

Explanation: tendrils are a slender thread- like structures of a climbing plant, often |

48. |
## Match the following. Given points are about spirals. |

A. | 1, i; 2, ii; 3, iii; 4, iv |

B. | 1, ii; 2, iii; 3, i; 4, iv |

C. | 1, ii; 2, iv; 3, iii; 4, i |

D. | 1, iv; 2, i; 3, ii; 4, iii |

Answer» D. 1, iv; 2, i; 3, ii; 4, iii | |

Explanation: these are general structures we used to see in our daily life which have certain particular names when comes to |

49. |
## Fermat’s spiral iv. r=Ɵ1/2 |

A. | 1, i; 2, ii; 3, iii; 4, iv |

B. | 1, ii; 2, iii; 3, i; 4, iv |

C. | 1, iv; 2, i; 3, ii; 4, iii |

D. | 1, ii; 2, iv; 3, iii; 4, i |

Answer» C. 1, iv; 2, i; 3, ii; 4, iii | |

Explanation: the line joining any point on the curve with the pole is called radius vector. angle between radius vector and the line in its initial position is called vectorial angle. |

50. |
## Cyclone iv. Lituus spiral |

A. | 1, i; 2, ii; 3, iii; 4, iv |

B. | 1, ii; 2, iii; 3, i; 4, iv |

C. | 1, ii; 2, iv; 3, iii; 4, i |

D. | 1, iv; 2, i; 3, ii; 4, iii |

Answer» B. 1, ii; 2, iii; 3, i; 4, iv | |

Explanation: given are equations in polar |

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