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# Multiple choice question for engineering

## Set 1

1. An equilateral triangle of side 10 cm is held parallel to horizontal plane and base is parallel to xy reference line. The length of line from front view will be _____
a) 8.66 cm
b) 10 cm
c) 0 cm
d) 12.47 cm

Answer: b [Reason:] Just by visualizing we can get picture and then as the base is parallel to xy reference plane the side view and front view will be a line and front view gives line of length equal to side of triangle given and side view gives the height of triangle.

2. A square of side 10 cm is held parallel to vertical plane and one diagonal is perpendicular to xy reference plane. The length of line in top view will be ________
a) 10 cm
b) 14.14 cm
c) 7.07 cm
d) 0 cm

Answer: b [Reason:] Given the square is parallel to vertical plane ad diagonal is perpendicular to xy reference plane the top view and side gives a line and both of same length which is equal to diagonal length L= 2 x √(52+52 ) = 14.14 cm.

3. A hexagon is placed parallel to vertical plane which of the following projection is true?
a) Front view-line, top view- hexagon
b) Front view- hexagon, top view- line
c) Front view –line, top view-line
d) Top view- hexagon, side view- line

Answer: b [Reason:] Given a hexagon parallel to vertical plane so the plane containing hexagon in perpendicular to horizontal plane and profile plane. The top view and side view gives a line and front view gives the true shape and size of hexagon.

4. A pentagon is placed parallel to horizontal plane which of the following projection is true?
a) Front view-line, top view- pentagon
b) Front view- pentagon, top view- line
c) Front view –line, top view-line
d) Top view- line, side view- line

Answer: a [Reason:] Given a pentagon parallel to horizontal plane so the plane containing pentagon in perpendicular to vertical plane and profile plane. The front view and side view gives a line and top view gives the true shape and size of pentagon.

5. A rectangle is placed parallel to profile plane which of the following projection is true?
a) Front view-line, top view- rectangle
b) Front view- rectangle, top view- line
c) Front view –line, top view-line
d) Top view- rectangle, side view- line

Answer: c [Reason:] Given a rectangle parallel to profile plane so the plane containing rectangle in perpendicular to horizontal plane and vertical plane. The top view and front view gives a line and side view gives the true shape and size of hexagon.

6. A circle is placed parallel to vertical plane which of the following projection is false?
a) Front view-circle, top view- line
b) Length in top view and side view will be same
c) Circle is perpendicular to horizontal plane
d) The traces of plane containing this circle intersect at xy reference line

Answer: d [Reason:] Given a circle parallel to vertical plane so the plane containing circle in perpendicular to horizontal plane and profile plane. The top view and side view gives a line and front view gives the true shape and size of circle. The traces will intersect at line formed by intersection of profile plane and horizontal plane.

7. An ellipse is placed parallel to vertical plane which of the following projection is false?
a) Front view-ellipse, top view- line
b) Length in top view and side view will be same
c) Ellipse is perpendicular to horizontal plane
d) The traces of plane containing this circle will not intersect at xy reference line

Answer: b [Reason:] Given an ellipse parallel to vertical plane so the plane containing ellipse in perpendicular to horizontal plane and profile plane. The top view and side view gives a line and front view gives the true shape and size of hexagon. As the object is ellipse which has major and minor axis the views show different lengths.

8. While drawing projections if a triangle is parallel to horizontal plane, top should be drawn first and projections are drawn to it to get front view.
a) True
b) False

Answer: a [Reason:] Given a triangle parallel to horizontal plane so the front view and side view gives a line and top view gives the true shape and size of triangle so top view should be drawn first with specifications given and then projections to further gives the front view.

9. If a plane is parallel to one of the reference plane then the projection onto the other reference planes would be a line.
a) True
b) False

Answer: a [Reason:] If a plane is only parallel to vertical plane then it is perpendicular to horizontal plane and profile plane. The top view and side view gives a line and front view gives the true shape and size of plane.

10. An equilateral triangle of side 10 cm is held parallel to horizontal plane and base is parallel to xy reference line. The length of line from side view will be _____
a) 8.66 cm
b) 10 cm
c) 0 cm
d) 12.47 cm

Answer: a [Reason:] Just by visualizing we can get picture and then as the base is parallel to xy reference plane the side view and front view will be a line and front view gives line of length equal to side of triangle given and side view gives the height of triangle.

11. A square of side 10 cm is held parallel to vertical plane and one diagonal is making 45 degrees with xy reference plane. The length of line in top view will be ________
a) 10 cm
b) 14.14 cm
c) 7.07 cm
d) 0 cm

Answer: a [Reason:] Given the square is parallel to vertical plane ad diagonal is making 45 degrees with xy reference plane the top view and side gives a line and both of same length which is equal to length of side of square because in square angle between the diagonal and side is 45 degrees.

12. The top view, front view and side view of a triangle parallel to vertical plane, circle parallel to profile plane and rectangle parallel to horizontal plane respectively are ___________
a) line, circle, line
b) triangle, line, rectangle
c) triangle, line, line
d) line, line, line

Answer: d [Reason:] If a plane is parallel to vertical plane then the top view and side view gives a line and front view gives the true shape. If a plane is parallel to horizontal plane then the front view and side view gives a line and top view gives the true shape. If a plane is parallel to profile plane then the top view and front view gives a line and side view gives the true shape.

## Set 2

1. Which of the following is not the definition of center of gravity?
a) A point on which whole weight if body balances
b) A point through which the resultant of forces of gravity of every particle in body acts
c) It is also called center of mass
d) The point in the body where the gravity becomes zero

Answer: d [Reason:] The center of gravity is defined as point on which whole weight if body balances (or) a point through which the resultant of forces of gravity of every particle in body acts. It is also called center of mass. It may not necessarily lie within the body.

2. The center of gravity of a triangle is on ______
a) centroid
b) circum center
c) in center
d) ortho center

Answer: a [Reason:] The center of gravity is defined as point on which whole weight if body balances (or) a point through which the resultant of forces of gravity of every particle in body acts. For planar objects like triangle the center of gravity will be at its centroid.

3. Given steps in procedure to find the center of gravity of the quadrilateral ABCD. Arrange the steps.
i. Draw lines joining G1 with G2 and G3 with G4.
ii. In given quadrilateral draw diagonal BD and locate centers of gravity G1, G2 of triangles BCD and ABD.
iii. The point of intersection of lines G1G2 and G3G4 gives the center of gravity of the quadrilateral ABCD.
iv. Similarly draw the diagonal AC and determine the centers of gravity G3, G4 of triangles ABC and ADC.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii

Answer: b [Reason:] Given is irregular quadrilateral so first we have to make it to regular simpler shapes like triangle and the finding center of gravity for those and intersection of forces acting gives the center of gravity of whole.

4. Given steps in procedure to find the center of gravity of the trapezium ABCD. Arrange the steps.
i. Join E and F which intersects the line PQ at G. G is center of gravity.
ii. Similarly produce CD to a point F so that FD=AB.
iii. Draw a line joining the midpoints P and Q of the parallel sides AB and DC respectively.
iv. Produce AB to a point E so that BE=DC.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, ii, i
d) iii, i, ii, iv

Answer: c [Reason:] Given is trapezium and the steps given are for finding the center of gravity in simple way. In this the parallel lines are extended up to the length of their opposite sides and intersection of line joining ends and line joining midpoints of parallel lines gives the center of gravity.

5. The center of gravity of an equilateral triangle is on its circum center.
a) True
b) False

Answer: a [Reason:] For equilateral triangle the centroid and circum center and in center coincides so as the centre of gravity is the centroid for any triangle but here comes center of gravity also coincides with all other 3 points.

6. The center of gravity of a circular ring will be a ______________
a) line which acts as axis of that ring
b) point anywhere in its inner circumference
c) point at center of ring
d) point on centroid of cross section of ring

Answer: c [Reason:] The center of gravity is defined as point on which whole weight if body balances (or) a point through which the resultant of forces of gravity of every particle in body acts. It is also called center of mass. It may not necessarily lie within the body.

7. For symmetrical objects the center of gravity lies at intersection of axes.
a) True
b) False

Answer: a [Reason:] The center of gravity is defined as point on which whole weight if body balances (or) a point through which the resultant of forces of gravity of every particle in body acts. It may not necessarily lie within the body.

8. The center of gravity of a right angled triangle having h as height and b as base length and vertex at 90 degrees is at origin.
a) (h/3,b/3)
b) (b/4,h/4)
c) (b/3,h/3)
d) (h/2,b/2)

Answer: c [Reason:] Given is a right angled triangle having h as height and b as base length and vertex at 90 degrees is at origin. The center of gravity coincides with the centroid of the triangle the given answer is the centroid for such a triangle.

9. Which of the following game make use of center of gravity?
a) Caroms
b) Seesaw
c) Tic-Tac-Toe
d) Swing

Answer: b [Reason:] The center of gravity is defined as point on which whole weight if body balances (or) a point through which the resultant of forces of gravity of every particle in body acts. It is also called center of mass.

10. The center of gravity of a rectangle having h as height and w as width, one of its vertex is origin and its width is along x-axis is _____________
a) (w/3,h/3)
b) (w/4,h/4)
c) (h/2,w/2)
d) (w/2,h/2)

Answer: d [Reason:] Given a rectangle having h as height and w as width, one of its vertices is origin and its width is along x-axis which is symmetric planar object and for symmetrical objects the center of gravity lies at intersection of axes.

## Set 3

1. The commands Erase, Copy, Mirror, Trim, Extend, Break etc belongs to which tool bar?
a) Layer tool bar
b) Style tool bar
c) Modify tool bar
d) Draw tool bar

Answer: c [Reason:] The commands Erase, Copy, Mirror, Trim, Extend, Break, Join, Scale, Array etc belongs to ‘Modify tool bar’. The commands Donut, Block, Spline, Hatch, Rectangle, Ellipse, Polygon, and Arc etc belong to ‘Draw tool bar’.

2. The commands Donut, Block, Spline, Polygon, and Arc etc belong to which tool bar?
a) Layer tool bar
b) Style tool bar
c) Modify tool bar
d) Draw tool bar

Answer: d [Reason:] The commands Erase, Copy, Mirror, Trim, Extend, Break, Join, Scale, Array etc belongs to ‘Modify tool bar’. The commands Donut, Block, Spline, Hatch, Rectangle, Ellipse, Polygon, and Arc etc belong to ‘Draw tool bar’.

3. The command which works on two lines or a single poly line to create a beveled edge is __________
a) Chamfer
b) Fillet
c) Stretch
d) Extend

Answer: a [Reason:] Chamfer works on two lines or a single poly line to create a beveled edge. Fillet is used to create a round corner between two lines. Stretch command can either lengthen entities or shorten them and thus their shapes.

4. The command which is used to create a round corner between two lines is __________
a) Chamfer
b) Fillet
c) Stretch
d) Extend

Answer: b [Reason:] Fillet is used to create a round corner between two lines. Chamfer works on two lines or a single poly line to create a beveled edge. Stretch command can either lengthen entities or shorten them and thus their shapes.

5. The command ‘Oops’ is used to ______________
a) create one or more copies of selected objects at another location
b) creates mirror image of selected objects about specified line
c) retrieves all objects erased by the last erase
d) deletes the selected entities

Answer: c [Reason:] The command ‘Oops’ is used to retrieves all objects erased by the last erase. Mirror is used to creates mirror image of selected objects about specified line. Command copy creates one or more copies of selected objects at another location.

6. The command ‘pedit’ is used for _______________
a) erases a portion of line, arc, circle or a 2D poly line between two selected points
b) reverses the effects of a series of previously used commands
c) breaking a poly line into individual segments
d) editing of poly line properties

Answer: d [Reason:] The command ‘pedit’ is used for editing of poly line properties. Command ‘U’ is used for reverses the effects of a series of previously used commands. Command ‘break’ is used for erases a portion of line, arc, circle or a 2D poly line between two selected points.

7. The command ‘break’ is used for ____________________
a) erases a portion of line, arc, circle or a 2D poly line between two selected points
b) reverses the effects of a series of previously used commands
c) breaking a poly line into individual segments
d) editing of poly line properties

Answer: a [Reason:] The command ‘break’ is used for erases a portion of line, arc, circle or a 2D poly line between two selected points. Command ‘pedit’ is used for editing of poly line properties. Command ‘U’ is used for reverses the effects of a series of previously used commands.

8. The command ‘U’ is used for _____________________
a) erases a portion of line, arc, circle or a 2D poly line between two selected points
b) reverses the effects of a series of previously used commands
c) breaking a poly line into individual segments
d) editing of poly line properties

Answer: b [Reason:] The command ‘U’ is used for reverses the effects of a series of previously used commands. Command ‘pedit’ is used for editing of poly line properties. Command ‘break’ is used for erases a portion of line, arc, circle or a 2D poly line between two selected points.

9. The command ‘Explode’ is used for _________________________
a) erases a portion of line, arc, circle or a 2D poly line between two selected points
b) reverses the effects of a series of previously used commands
c) breaking a poly line into individual segments
d) editing of poly line properties

Answer: c [Reason:] The command ‘Explode’ is used for breaking a poly line into individual segments. Command ‘pedit’ is used for editing of poly line properties. Command ‘U’ is used for reverses the effects of a series of previously used commands.

10. The command which is used to set a new coordinate system by shifting the working XY plane to be desired location is?
a) 3DFACE
b) VPOINT
c) UCS
d) ELEV

Answer: c [Reason:] UCS is used to set a new coordinate system by shifting the working XY plane to be desired location. 3DFACE is used for making planar unmeshed surfaces that have three or four sides. VPOINT is used to set the viewpoint in 3D space for viewing the 3D models.

11. The command which is used for making planar unmeshed surfaces that have three or four sides is ______________
a) 3DFACE
b) VPOINT
c) UCS
d) ELEV

Answer: a [Reason:] 3DFACE is used for making planar unmeshed surfaces that have three or four sides. VPOINT is used to set the viewpoint in 3D space for viewing the 3D models. UCS is used to set a new coordinate system by shifting the working XY plane to be desired location.

12. The command which is used to set the viewpoint in 3D space for viewing the 3D models is _____________
a) 3DFACE
b) VPOINT
c) UCS
d) ELEV

Answer: b [Reason:] VPOINT is used to set the viewpoint in 3D space for viewing the 3D models. 3DFACE is used for making planar unmeshed surfaces that have three or four sides. UCS is used to set a new coordinate system by shifting the working XY plane to be desired location.

13. The command which is used to set elevation and thickness properties for 2D wireframe objects such as line, point, circle, polygon, arc is ____________
a) 3DFACE
b) VPOINT
c) UCS
d) ELEV

Answer: d [Reason:] ELEV is used to set elevation and thickness properties for 2D wireframe objects such as line, point, circle, polygon and arc. 3DFACE is used for making planar unmeshed surfaces that have three or four sides.

14. The command which identifies the points on drawing entities that are visible on screen is ________ and this option allows the user to pick-up the points very accurately with respect to drawing displayed.
a) OSNAP
b) TABSURF
c) SNAP
d) GRID

Answer: a [Reason:] The command which identifies the points on drawing entities that are visible on screen is OSNAP. This option allows the user to pick-up the points very accurately with respect to drawing displayed.

## Set 4

1. ___________ 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 [Reason:] Cycloid form if generating point is on the circumference of generating circle. Epicycloid represents generating circle rolls on directing circle. Epitrochoid is that the generating point is within or outside the generating circle but generating circle rolls on directing circle.

2. ___________ 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 [Reason:] 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.

3. __________ 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 [Reason:] 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 circle.

4. When the circle rolls along another circle inside it, the curve is called a __________
a) Epicycloid
b) Cycloid
c) Trochoid
d) Hypocycloid

Answer: d [Reason:] 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 circle. 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.

5. Match the following

1.Generating point is within the circumference of circle and generating circle rolls on straight line.i.Inferior trochoid
2.Generating point is on the circumference of circle and generating circle rolls on straight line.ii.Epicycloid
3.Generating point is outside the circumference of circle and generating circle rolls on straight line. iii. Cycloid
4.Generating point is on the circumference of circle and generating circle rolls along another circle outside it.iv. Superior trochoid

a) 1, i; 2, iii; 3, iv; 4, ii
b) 1, ii; 2, iii; 3, i; 4, iv
c) 1, ii; 2, iv; 3, iii; 4, i
d) 1, iv; 2, iii; 3, ii; 4, i

Answer: a [Reason:] Trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. Inferior or superior depends on whether the generating point in within or outside the generating circle. If directing path is straight line then the curve is cycloid.

6. Match the following

 1 Generating point is within the circumference of circle and generating circle rolls on another circle outside it i. Superior Epitrochoid 2 Generating point is within or outside the circumference of circle and generating circle rolls inside another circle. ii. Inferior Epitrochoid 3 Generating point is outside the circumference of circle and generating circle rolls on another circle outside it. iii. Hypotrochoid 4 Generating point is on the circumference of circle and generating circle rolls along another circle inside it. iv. Hypocycloid

a) 1, i; 2, iii; 3, iv; 4, ii
b) 1, ii; 2, iii; 3, i; 4, iv
c) 1, ii; 2, iv; 3, iii; 4, i
d) 1, iv; 2, iii; 3, ii; 4, i

Answer: b [Reason:] Inferior or superior depends on whether the generating point in within or outside the generating circle. ‘Hypo’ represents the generating circle is inside the directing circle. Trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line.

7. Steps are given to find the normal and tangent for a cycloid. Arrange the steps if C is the centre for generating circle and PA is the directing line. N is the point on cycloid.
i. Through M, draw a line MO perpendicular to the directing line PA and cutting at O.
ii. With centre N and radius equal to radius of generating circle, draw an arc cutting locus of C at M.
iii. Draw a perpendicular to ON at N which is tangent.
iv. Draw a line joining O and N which is normal.
a) iii, i, iv, ii
b) ii, i, iv, iii
c) iv, ii, i, iii
d) i, iv, iii, ii

Answer: b [Reason:] The normal at any point on a cycloidal curve will pass through the corresponding point of contact between the generating circle and the directing line. So with help of locus of centre of generating circle we found the normal and then tangent.

8. Steps are given to find the normal and tangent to an epicycloid. Arrange the steps if C is the centre for generating circle and O is the centre of directing cycle. N is the point on epicycloid.
i. Draw a line through O and D cutting directing circle at M.
ii. Draw perpendicular to MN at N. We get tangent.
iii. With centre N and radius equal to radius of generating circle, draw an arc cutting the locus of C at D.
iv. Draw a line joining M and N which is normal.
a) iii, i, iv, ii
b) ii, i, iv, iii
c) iv, ii, i, iii
d) i, iv, iii, ii

Answer: a [Reason:] The normal at any point on an epicycloidal curve will pass through the corresponding point of contact between the generating circle and the directing circle. And also with help of locus of centre of generating circle we found the normal and then tangent.

9. The generating circle will be inside the directing circle for _________
a) Cycloid
b) Inferior trochoid
c) Inferior epitrochoid
d) Hypocycloid

Answer: d [Reason:] 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 prefix.

10. The generating point is outside the generating circle for____________
a) Cycloid
b) Superior Trochoid
c) Inferior Trochoid
d) Epicycloid

Answer: b [Reason:] 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.

## Set 5

1. 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 ellipse is constant

Answer: c [Reason:] If a plane is parallel to 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 angle more than external angle of cone it gives parabola. If the plane is inclined and cut every generators then it forms a ellipse.

2. Which of the following constructions doesn’t use elliptical curves?
a) Cooling towers
b) Dams
c) Bridges
d) Man-holes

Answer: a [Reason:] Cooling towers, water channels use Hyperbolic curves as their design. Arches, Bridges, sound reflectors, light reflectors etc use parabolic curves. Arches, bridges, dams, monuments, man-holes, glands and stuffing boxes etc use elliptical curves.

3. The line which passes through the focus and perpendicular to major axis is ________
a) Minor axis
b) Latus rectum
c) Directrix
d) Tangent

Answer: b [Reason:] 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 major axis is latus rectum. Tangent is the line which touches the curve at only one point.

4. Which of the following is the eccentricity for ellipse?
a) 1
b) 3/2
c) 2/3
d) 5/2

Answer: c [Reason:] The eccentricity for ellipse is always less than 1. The eccentricity is always 1 for any parabola. The eccentricity is always 0 for a circle. The eccentricity for a hyperbola is always greater than 1.

5. Axes are called conjugate axes when they are parallel to the tangents drawn at their extremes.
a) True
b) False

Answer: a [Reason:] 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.

6. Steps are given to draw an ellipse by loop of the thread method. Arrange the steps.
i. Check whether the length of the thread is enough to touch the end of minor axis.
ii. Draw two axes AB and CD intersecting at O. Locate the foci F1 and F2.
iii. Move the pencil around the foci, maintaining an even tension in the thread throughout and obtain the ellipse.
iv. Insert a pin at each focus-point and tie a piece of thread in the form of a loop around the pins.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii

Answer: b [Reason:] This is the easiest method of drawing ellipse if we know the distance between the foci and minor axis, major axis. It is possible since ellipse can be traced by a point, moving in the same plane as and in such a way that the sum of its distances from two foci is always the same.

7. Steps are given to draw an ellipse by trammel method. Arrange the steps.
i. Place the trammel so that R is on the minor axis CD and Q on the major axis AB. Then P will be on ellipse.
ii. Draw two axes AB and CD intersecting each other at O.
iii. By moving the trammel to new positions, always keeping R on CD and Q on AB, obtain other points and join those to get ellipse.
iv. Along the edge of a strip of paper which may be used as a trammel, mark PQ equal to half the minor axis and PR equal to half of major axis.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii

Answer: b [Reason:] This method uses the trammels PQ and PR which ends Q and R should be placed on major axis and minor axis respectively. It is possible since ellipse can be traced by a point, moving in the same plane as and in such a way that the sum of its distances from two foci is always the same.

8. Steps are given to draw a normal and a tangent to the ellipse at a point Q on it. Arrange the steps.
i. Draw a line ST through Q and perpendicular to NM.
ii. ST is the required tangent.
iii. Join Q with the foci F1 and F2.
iv. Draw a line NM bisecting the angle between the lines drawn before which is normal.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii

Answer: c [Reason:] Tangents are the lines which touch the curves at only one point. Normals are perpendiculars of tangents. As in the circles first we found the normal using foci (centre in circle) and then perpendicular at given point gives tangent.

9. Which of the following is not belonged to ellipse?
a) Latus rectum
b) Directrix
c) Major axis
d) Asymptotes