McqMate

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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 |

51. |
## Logarithmic spiral is also called Equiangular spiral. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: the logarithmic spiral is also known as equiangular spiral because of its property that the angle which the tangent at any point on the curve makes with the radius vector at that point is constant. the values of vectorial angles are in arithmetical progression. |

52. |
## In logarithmic Spiral, the radius vectors are in arithmetical progression. |

A. | true |

B. | false |

Answer» B. false | |

Explanation: in the logarithmic spiral, the values of vectorial angles are in arithmetical progression and radius vectors are in the geometrical progression that is the lengths of consecutive radius vectors enclosing equal angles are always constant. |

53. |
## The mosquito coil we generally see in house hold purposes and heating coils in electrical heater etc are generally which spiral. |

A. | logarithmic spiral |

B. | equiangular spiral |

C. | fibonacci spiral |

D. | archemedian spiral |

Answer» D. archemedian spiral | |

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. the use of this curve is made in teeth profiles of helical gears, profiles of cam etc. |

54. |
## The sections cut by a plane on a right circular cone are called as |

A. | parabolic sections |

B. | conic sections |

C. | elliptical sections |

D. | hyperbolic sections |

Answer» B. conic sections | |

Explanation: the sections cut by a plane on a right circular cone are called as conic sections or conics. the plane cuts the cone on different angles with respect to the axis of the cone to produce different conic sections. |

55. |
## Which of the following is a conic section? |

A. | circle |

B. | rectangle |

C. | triangle |

D. | square |

Answer» A. circle | |

Explanation: circle is a conic section. when the plane cuts the right circular cone at right angles with the axis of the cone, the shape obtained is called as a circle. if the angle is oblique we get the other parts of the conic sections. |

56. |
## In conics, the is revolving to form two anti-parallel cones joined at the apex. |

A. | ellipse |

B. | circle |

C. | generator |

D. | parabola |

Answer» C. generator | |

Explanation: in conics, the generator is revolving to form two anti-parallel cones joined at the apex. the plane is then made to cut these cones and we get different conic sections. if we cut at right angles with respect to the axis of the cone we get a circle. |

57. |
## While cutting, if the plane is at an angle and it cuts all the generators, then the conic formed is called as |

A. | circle |

B. | ellipse |

C. | parabola |

D. | hyperbola |

Answer» B. ellipse | |

Explanation: if the plane cuts all the generators and is at an angle to the axis of the cone, then the resulting conic section is called as an ellipse. if the cutting angle was right angle and the plane cuts all the generators then the conic formed would be circle. |

58. |
## When the plane cuts the cone at angle parallel to the axis of the cone, then is formed. |

A. | hyperbola |

B. | parabola |

C. | circle |

D. | ellipse |

Answer» A. hyperbola | |

Explanation: when the plane cuts the cone at an angle parallel to the axis of the cone, then the resulting conic section is called as a hyperbola. if the plane cuts the cone at an angle with respect to the axis of the cone then the resulting conic sections are called as ellipse and parabola. |

59. |
## Which of the following is not a conic section? |

A. | apex |

B. | hyperbola |

C. | ellipse |

D. | parabola |

Answer» A. apex | |

Explanation: conic sections are formed when a plane cuts through the cone at an angle with respect to the axis of the cone. if the angle is right angle then the conics is a circle, if the angle is oblique then the resulting conics are parabola and ellipse. |

60. |
## The locus of point moving in a plane such that the distance between a fixed point and a fixed straight line is constant is called as |

A. | conic |

B. | rectangle |

C. | square |

D. | polygon |

Answer» A. conic | |

Explanation: the locus of a point moving in a plane such that the distance between a fixed point and a fixed straight line is always constant. the fixed straight line is called as directrix and the fixed point is called as the focus. |

61. |
## The ratio of the distance from the focus to the distance from the directrix is called as eccentricity. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: the ratio of the distance from the focus to the distance from the directrix is called eccentricity. it is denoted as e. the value of eccentricity can give information regarding which type of conics it is. |

62. |
## Which of the following conics has an eccentricity of unity? |

A. | circle |

B. | parabola |

C. | hyperbola |

D. | ellipse |

Answer» B. parabola | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. it is denoted as e. the value of eccentricity can give information regarding which type of conics it is. the eccentricity of a parabola is the unity that is 1. |

63. |
## Which of the following has an eccentricity less than one? |

A. | circle |

B. | parabola |

C. | hyperbola |

D. | ellipse |

Answer» D. ellipse | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. it is denoted as e. the value of eccentricity can give information regarding which type of conics it is. the eccentricity of an ellipse is less than one. |

64. |
## If the distance from the focus is 10 units and the distance from the directrix is 30 units, then what is the eccentricity? |

A. | 0.3333 |

B. | 0.8333 |

C. | 1.6667 |

D. | 0.0333 |

Answer» A. 0.3333 | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. hence from the formula of eccentricity, e = 10 ÷ 30 = 0.3333. since the value of eccentricity is less than one the conic is an ellipse. |

65. |
## If the value of eccentricity is 12, then what is the name of the conic? |

A. | ellipse |

B. | hyperbola |

C. | parabola |

D. | circle |

Answer» B. hyperbola | |

Explanation: eccentricity is defined as the ration of the distance from the focus to the distance from the directrix. it is denoted as e. if the value of eccentricity is greater than unity then the conic section is called as a hyperbola. |

66. |
## If the distance from the focus is 3 units and the distance from the directrix is 3 units, then how much is the eccentricity? |

A. | infinity |

B. | zero |

C. | unity |

D. | less than one |

Answer» C. unity | |

Explanation: eccentricity is defined as the ration of the distance from the focus to the distance from the directrix and it is denoted as |

67. |
## If the distance from the focus is 2 mm and the distance from the directrix is 0.5 mm then what is the name of the conic section? |

A. | circle |

B. | ellipse |

C. | parabola |

D. | hyperbola |

Answer» D. hyperbola | |

Explanation: the eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. it is denoted as e. if the value of the eccentricity is greater than unity then the conic section is called as a hyperbola. |

68. |
## Which of the following is a conic section? |

A. | apex |

B. | circle |

C. | rectangle |

D. | square |

Answer» B. circle | |

Explanation: conic sections are formed when a plane cuts through the cone at an angle with respect to the axis of the cone. if the angle is right angle then the conics is a circle, if the angle is oblique then the resulting conics are parabola and ellipse. |

69. |
## If the distance from the focus is 10 units and the distance from the directrix is 30 units, then what is the name of the conic? |

A. | circle |

B. | parabola |

C. | hyperbola |

D. | ellipse |

Answer» D. ellipse | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. hence from the formula of eccentricity, e = 10 ÷ 30 = 0.3333. since the value of eccentricity is less than one the conic is an ellipse. |

70. |
## If the distance from the focus is 2 mm and the distance from the directrix is 0.5 mm then what is the value of eccentricity? |

A. | 0.4 |

B. | 4 |

C. | 0.04 |

D. | 40 |

Answer» B. 4 | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. therefore, by definition, e = 2 ÷ 0.5 = 4. hence the conic section is called as hyperbola. |

71. |
## If the distance from the focus is 3 units and the distance from the directrix is 3 units, then what is the name of the conic section? |

A. | ellipse |

B. | hyperbola |

C. | circle |

D. | parabola |

Answer» D. parabola | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. therefore, by definition, e = 3 ÷ 3 = 1. hence the conic section is called as a parabola. |

72. |
## If the distance from the directrix is 5 units and the distance from the focus is 3 units then what is the name of the conic section? |

A. | ellipse |

B. | parabola |

C. | hyperbola |

D. | circle |

Answer» A. ellipse | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. hence, by definition, e = 3 ÷ 5 = 0.6. hence the conic section is called an ellipse. |

73. |
## If the distance from a fixed point is greater than the distance from a fixed straight line then what is the name of the conic section? |

A. | parabola |

B. | circle |

C. | hyperbola |

D. | ellipse |

Answer» C. hyperbola | |

Explanation: the fixed point is called as focus and the fixed straight line is called as directrix. eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. if e is greater than one then the conic section is called as a hyperbola. |

74. |
## If the distance from a fixed straight line is equal to the distance from a fixed point then what is the name of the conic section? |

A. | ellipse |

B. | parabola |

C. | hyperbola |

D. | circle |

Answer» B. parabola | |

Explanation: the fixed straight line is called as directrix and the fixed point is called as a focus. eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. |

75. |
## If the distance from the directrix is greater than the distance from the focus then what is the value of eccentricity? |

A. | unity |

B. | less than one |

C. | greater than one |

D. | zero |

Answer» B. less than one | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. therefore, by definition the value of eccentricity is less than one hence the conic section is an ellipse. |

76. |
## If the distance from the directrix is 5 units and the distance from the focus is 3 units then what is the value of eccentricity? |

A. | 1.667 |

B. | 0.833 |

C. | 0.60 |

D. | 0.667 |

Answer» C. 0.60 | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. therefore, by definition, e = 3 ÷ 5 = 0.6. hence the conic section is called an ellipse. |

77. |
## If the distance from a fixed straight line is 5mm and the distance from a fixed point is 14mm then what is the name of the conic section? |

A. | hyperbola |

B. | parabola |

C. | ellipse |

D. | circle |

Answer» A. hyperbola | |

Explanation: the fixed straight line is called directrix and the fixed point is called as a focus. eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. |

78. |
## If the distance from the directrix is greater than the distance from the focus then what is the name of the conic section? |

A. | hyperbola |

B. | parabola |

C. | ellipse |

D. | circle |

Answer» C. ellipse | |

Explanation: eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. therefore, by definition the value of eccentricity is less than one hence the conic section is an ellipse. |

79. |
## If the distance from a fixed straight line is equal to the distance from a fixed point then what is the value of eccentricity? |

A. | unity |

B. | greater than one |

C. | infinity |

D. | zero |

Answer» A. unity | |

Explanation: the fixed straight line is called as directrix and the fixed point is called as a focus. eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. |

80. |
## If the distance from a fixed point is greater than the distance from a fixed straight line then what is the value of eccentricity? |

A. | unity |

B. | infinity |

C. | zero |

D. | greater than one |

Answer» D. greater than one | |

Explanation: the fixed point is called as focus and the fixed straight line is called as directrix. eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix and it is denoted by e. |

81. |
## The cross-section is a when a plane is inclined to the axis and cuts all the generators of a regular cone. |

A. | rectangular hyperbola |

B. | hyperbola |

C. | circle |

D. | ellipse |

Answer» D. ellipse | |

Explanation: a cone is a solid or hollow object which tapers from a circular base to a point. here given an inclined plane which cuts all the generators of a regular cone. so the cross-section will definitely ellipse. |

82. |
## The curve formed when eccentricity is equal to one is |

A. | parabola |

B. | circle |

C. | semi-circle |

D. | hyperbola |

Answer» A. parabola | |

Explanation: the answer is parabola. circle has an eccentricity of zero and semi circle is part of circle and hyper eccentricity is greater than one. |

83. |
## The cross-section gives a when the cutting plane is parallel to axis of cone. |

A. | parabola |

B. | hyperbola |

C. | circle |

D. | ellipse |

Answer» B. hyperbola | |

Explanation: if the cutting plane makes angle less than exterior angle of the cone the cross- section gives a ellipse. if the cutting plane makes angle greater than the exterior angle of |

84. |
## The curve which has eccentricity zero is |

A. | parabola |

B. | ellipse |

C. | hyperbola |

D. | circle |

Answer» D. circle | |

Explanation: the eccentricity is the ratio of a distance from a point on the curve to focus and to distance from the point to directrix. |

85. |
## Rectangular hyperbola is one of the hyperbola but the asymptotes are perpendicular in case of rectangular hyperbola. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: asymptotes are the tangents which meet the curve hyperbola at infinite distance. if the asymptotes are perpendicular to each other then hyperbola takes the name of a rectangular hyperbola. |

86. |
## The straight lines which are drawn from various points on the contour of an object to meet a plane are called as |

A. | connecting lines |

B. | projectors |

C. | perpendicular lines |

D. | hidden lines. |

Answer» B. projectors | |

Explanation: the object will generally kept at a distance from planes so to represent the shape in that view projectors are drawn perpendicular to plane in orthographic projection. projectors are simply called lines of sights when an observer looks towards an object from infinity. |

87. |
## When the projectors are parallel to each other and also perpendicular to the plane, the projection is called |

A. | perspective projection |

B. | oblique projection |

C. | isometric projection |

D. | orthographic projection |

Answer» D. orthographic projection | |

Explanation: in orthographic projection, the projectors are parallel to each other and also perpendicular to the plane but in oblique projection, the projectors are inclined to the plane of projection and projectors are parallel to each other. |

88. |
## In the Oblique projection an object is represented by how many views? |

A. | one view |

B. | two views |

C. | three views |

D. | four views |

Answer» A. one view | |

Explanation: oblique projection is one method of pictorial projection. oblique projection shows three dimensional objects on the projection plane in one view only. this |

89. |
## The object we see in our surrounding usually without drawing came under which projection? |

A. | perspective projection |

B. | oblique projection |

C. | isometric projection |

D. | orthographic projection |

Answer» A. perspective projection | |

Explanation: perspective projection gives the view of an object on a plane surface, called the picture plane, as it would appear to the eye when viewed from a fixed position. it may also be defined as the figure formed on the projection plane when visual rays from the eye to the object cut the plane. |

90. |
## In orthographic projection, each projection view represents how many dimensions of an object? |

A. | 1 |

B. | 2 |

C. | 3 |

D. | 0 |

Answer» B. 2 | |

Explanation: in orthographic projection and oblique projection the projection planes which represent one view of an object only shows width, height; width, thickness; height, thickness only but in isometric and perspective projections width, height and thickness can also be viewed. |

91. |
## In orthographic projection an object is represented by two or three views on different planes which |

A. | gives views from different angles from different directions |

B. | are mutually perpendicular projection planes |

C. | are parallel along one direction but at different cross-section |

D. | are obtained by taking prints from 2 or 3 sides of object |

Answer» B. are mutually perpendicular projection planes | |

Explanation: by viewing in mutual perpendicular planes- vertical plane, horizontal plane, profile plane which indirectly gives us front view in x-direction, top-view in y –direction and thickness in z- direction which are mutually perpendicular. ortho means perpendicular. |

92. |
## To represent the object on paper by orthographic projection the horizontal plane (H.P) should be placed in which way? |

A. | the h.p is turned in a clockwise direction up to 90 degrees |

B. | the h.p is turned in anti-clockwise direction up to 90 degrees |

C. | h.p plane is placed to left side of vertical plane parallel to it |

D. | h.p plane is placed to right side of vertical plane parallel to it |

Answer» A. the h.p is turned in a clockwise direction up to 90 degrees | |

Explanation: the vertical plane and horizontal plane are perpendicular planes intersected at reference line. so on paper to represent perpendicular planes any of the planes should arrange to get a real picture of required projection. |

93. |
## The hidden parts inside or back side of object while represented in orthographic projection are represented by which line? |

A. | continuous thick line |

B. | continuous thin line |

C. | dashed thin line |

D. | long-break line |

Answer» C. dashed thin line | |

Explanation: continuous thick line is used for visible outlines, visible edges, crests of screw threads, limits of full depth thread etc. continuous thin line is used for extension, projection, short centre, leader, reference lines, imaginary lines of intersection etc. |

94. |
## Orthographic projection is the representation of two or more views on the mutual perpendicular projection planes. |

A. | true |

B. | false |

Answer» A. true | |

Explanation: orthographic projection is the representation of two or more views on the mutual perpendicular projection planes. but for oblique projection, the object is viewed in only one view. and in isometric view the object is kept resting on the ground on one of its corners with a solid diagonal perpendicular to the v.p. |

95. |
## In perspective projection and oblique projection, the projectors are not parallel to each other. |

A. | true |

B. | false |

Answer» B. false | |

Explanation: in oblique projection the projectors are parallel to each other but inclined to projection plane but in perspective projection all the projectors are not parallel to each other and so to projection plane. |

96. |
## What is additional 3rd view on orthographic projection in general for simple objects? |

A. | front view |

B. | top view |

C. | side view |

D. | view at 45 degrees perpendicular to horizontal plane |

Answer» C. side view | |

Explanation: in general for simple objects engineers use only front view and top view or else front view and side view or else top view and side view. if every view is visualized side view gives height and thickness of object. |

97. |
## The front view of an object is shown on which plane? |

A. | profile plane |

B. | vertical plane |

C. | horizontal plane |

D. | parallel plane |

Answer» B. vertical plane | |

Explanation: the front view will be represented on vertical plane, top view will be represented on horizontal plane and side view will be shown on profile plane. the front view shows height and width of object. |

98. |
## The Top view of an object is shown on which plane? |

A. | profile plane |

B. | vertical plane |

C. | horizontal plane |

D. | parallel plane |

Answer» C. horizontal plane | |

Explanation: the front view will be shown on vertical plane, top view will be represented on horizontal plane and side view will be represents on profile plane. the top view gives thickness and width of the object. |

99. |
## The side view of an object is shown on which plane? |

A. | profile plane |

B. | vertical plane |

C. | horizontal plane |

D. | parallel plane |

Answer» A. profile plane | |

Explanation: the front view will be represents on vertical plane, top view will be shown on horizontal plane and side view will be represents on profile plane. the side view gives height and thickness of object. |

100. |
## The 3rd quadrant is in which position? |

A. | below h.p, behind v.p |

B. | above h.p, behind v.p |

C. | above h.p, in-front of v.p |

D. | below h.p, in-front of v.p |

Answer» A. below h.p, behind v.p | |

Explanation: the position of reference planes will be similar to quadrants in x, y plane co-ordinate system. as the 3rd quadrant lies below the x-axis and behind the y-axis here also the 3rd quadrant is below h.p, behind v.p. |

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