# Multiple choice question for engineering

## Set 1

1. Steps are given to determine the centre of curvature at a given point on a conic. Arrange the steps. Let P be the given point on the conic and F is the focus.

Join P with F.

Draw a line NR perpendicular to PN and cutting PF or PF-extended at R.

Draw a line RO perpendicular to PR and cutting PN-extended at O which is centre of curvature.

At P, draw a normal PN, cutting the axis at N.

a) i, iv, ii, iii

b) iv, i, iii, ii

c) iii, i, iv, ii

d) ii, iv, i, iii

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2. Steps are given to determine the centre of curvature at a given point on an Ellipse. Arrange the steps. Let P be the given point on the conic and F and F1 are the foci.

i. Produce F1G to H so that GH = VF. Join H with F.

ii. Then O is the required centre of curvature.

iii. Draw a line GO parallel to HF and intersecting the axis at O.

iv. Draw a line F1G inclines to the axis and equal to VF1.

a) i, iv, ii, iii

b) iv, i, iii, ii

c) iii, i, iv, ii

d) ii, iv, i, iii

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3. Steps are given to determine the centre of curvature at a given point on an Ellipse. Arrange the steps. Let P be the given point on the conic and F is one of the focus.

i. Join A with C.

ii. Then O1 and O2 are the centres of curvature when the point P is at A and C respectively.

iii. Draw a rectangle AOCE in which AO = ½ major axis and CO = ½ minor axis.

iv. Through E, draw a line perpendicular to AC and cutting the major axis at O1 and the minor axis O2.

a) i, iv, ii, iii

b) iv, i, iii, ii

c) iii, i, iv, ii

d) ii, iv, i, iii

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4. Steps are given to determine the centre of curvature at a given point on a hyperbola. Arrange the steps. Let P be the given point on the conic, V is vertex and F and F1 are the foci.

i. Draw a line GO parallel to HF and cutting the axis at O.

ii. Draw a line F1G inclined to the axis and equal to FV1.

iii. Then O is the centre of curvature at the vertex V.

iv. On F1G, mark a point H such that HG = VF. Join H with F.

a) i, iv, ii, iii

b) iv, i, iii, ii

c) iii, i, iv, ii

d) ii, iv, i, iii

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5. Steps are given to draw the evolute of a cycloid. Arrange the steps.

i. Mark a point P on the cycloid and draw the normal PN to it.

ii. Similarly, mark a number of points on the cycloid and determine centres of curvature at these points.

iii. The curve drawn through these centres is the evolute of the cycloid. It is an equal cycloid.

iv. Produce PN to Op so that NOp = PN. Op is the centre of curvature at the point P.

a) i, iv, ii, iii

b) iv, i, iii, ii

c) iii, i, iv, ii

d) ii, iv, i, iii

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6. Steps are given to draw the evolute of a hypocycloid. Arrange the steps.

i. Draw the diameter PQ of the rolling circle. Join Q with O, the centre of the directing circle.

ii. Mark a number of points on the hypocycloid and similarly, obtain centres of curvature at these points. The curve drawn through these centres is the evolute of the hypocycloid.

iii. Produce PN to cut OQ- produced at Op, which is the centre of curvature at the point P.

iv. Mark a point P on the hypocycloid and draw the normal PN to it.

a) i, iv, ii, iii

b) iv, i, iii, ii

c) iii, i, iv, ii

d) ii, iv, i, iii

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7. The evolute of the involute of a circle is the circle itself.

a) True

b) False

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8. The difference between two consecutive crest/root of a screw is called __________

a) Helix

b) Mean diameter

c) Pitch

d) Revolution

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9. Pitch of the given bolt is 10 mm. The bolt completed the ½ revolution in forward direction. How much the bolt advances through axis?

a) 10 mm

b) 5 mm

c) 2.5 mm

d) 20 mm

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10. Helix angle can be expressed as tanӨ = __________________

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11. Number of revolutions are 10 and pitch is 2mm. Find the length of spring.

a) 10

b) 40

c) 30

d) 20

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12. Length of spring is 5cm and pitch measured is 4mm. Find the number of revolutions.

a) 20

b) 12.5

c) 13

d) 12

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## Set 2

1. A Spring is made of wire whose cross-section is a square of 15 mm side. Inner diameter of spring is 60 mm then outer diameter will be _________

a) 45

b) 75

c) 90

d) 80

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2. A Spring is made of wire whose cross-section is an equilateral triangle of 8 mm side. Inner diameter of spring is 40 mm then outer diameter will be _________

a) 57.88 mm

b) 54.88 mm

c) 60 mm

d) 56 mm

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3. Spring index = _________________

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4. Mean diameter of coil is given as 100 mm and diameter of wire is 5 mm. Spring index is________

a) 40

b) 30

c) 25

d) 20

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5. Spring index is given as 12.5 and diameter of wire given is 5 mm. Mean diameter of coil is _______

a) 60 mm

b) 62.5 mm

c) 6 cm

d) 56.2 mm

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6. Spring index is given as 15 and mean diameter of coil is 90 mm. Diameter of wire is __________

a) 6 mm

b) 5 mm

c) 7 mm

d) 8 mm

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7. Mean diameter of coil is 170 mm and spring index is 17. Diameter of wire is _________

a) 1 cm

b) 5 mm

c) 153 mm

d) 1.5 cm

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8. Diameter of wire is 7.5 mm and spring index is 15. Outer diameter of the coil is ___________

a) 112.5 mm

b) 120 mm

c) 1.2 cm

d) 20 cm

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9. Mean diameter of coil is 100 mm and inner diameter is 95 mm, spring index is __________

a) 10

b) 5

c) 12

d) 15

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10. Outer diameter is 95 mm and inner diameter is 88 mm. Mean diameter is ________

a) 90 mm

b) 91.5 mm

c) 95.1 mm

d) 88 mm

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11. Inner diameter of the coil is 70 mm and diameter of wire is 8 mm, spring index is ________

a) 9.25

b) 8.75

c) 9.75

d) 7.8

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12. Spring index is 10 and diameter of wire is 10 mm. Outer diameter of coil is __________

a) 100 mm

b) 90 mm

c) 110 mm

d) 120 mm

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## Set 3

1. Which of the following is Hyperbola equation?

a) y^{2} + x^{2}/b^{2} = 1

b) x^{2}= 1ay

c) x^{2} /a^{2} – y^{2}/b^{2} = 1

d) X^{2} + Y^{2} = 1

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^{2}+ y

^{2}= 1 gives a circle; if the x

^{2}and y

^{2}have same co-efficient then the equation gives circles. The equation x

^{2}= 1ay gives a parabola. The equation y

^{2}+ x

^{2}/b

^{2}= 1 gives an ellipse.

2. Which of the following constructions use hyperbolic curves?

a) Cooling towers

b) Dams

c) Bridges

d) Man-holes

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3. The lines which touch the hyperbola at infinite distance are ________

a) Axes

b) Tangents at vertex

c) Latus rectum

d) Asymptotes

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4. Which of the following is the eccentricity for hyperbola?

a) 1

b) 3/2

c) 2/3

d) 1/2

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5. If the asymptotes are perpendicular to each other then the hyperbola is called rectangular hyperbola.

a) True

b) False

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6. A straight line parallel to asymptote intersects the hyperbola at only one point.

a) True

b) False

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7. Steps are given to locate the directrix of hyperbola when axis and foci are given. Arrange the steps.

i. Draw a line joining A with the other Focus F.

ii. Draw the bisector of angle FAF1, cutting the axis at a point B.

iii. Perpendicular to axis at B gives directrix.

iv. From the first focus F1 draw a perpendicular to touch hyperbola at A.

a) i, ii, iii, iv

b) ii, iv, i, iii

c) iii, iv, i, ii

d) iv, i, ii, iii

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8. Steps are given to locate asymptotes of hyperbola if its axis and focus are given. Arrange the steps.

i. Draw a perpendicular AB to axis at vertex.

ii. OG and OE are required asymptotes.

iii. With O midpoint of axis (centre) taking radius as OF (F is focus) draw arcs cutting AB at E, G.

iv. Join O, G and O, E.

a) i, iii, iv, ii

b) ii, iv, i, iii

c) iii, iv, i, ii

d) iv, i, ii, iii

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9. The asymptotes of any hyperbola intersects at __________

a) On the directrix

b) On the axis

c) At focus

d) Centre

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## Set 4

1. Mathematical equation for Involute is ___________

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2. Steps are given to draw involute of given circle. Arrange the steps f C is the centre of circle and P be the end of the thread (starting point).

i. Draw a line PQ, tangent to the circle and equal to the circumference of the circle.

ii. Draw the involute through the points P1, P2, P3 ……..etc.

iii. Divide PQ and the circle into 12 equal parts.

iv. Draw tangents at points 1, 2, 3 etc. and mark on them points P1, P2, P3 etc. such that 1P1 =P1l, 2P2 = P2l, 3P3= P3l etc.

a) ii, i, iv, iii

b) iii, i , iv, ii

c) i, iii, iv, ii

d) iv, iii, i, ii

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3. Steps are given to draw tangent and normal to the involute of a circle (center is C) at a point N on it. Arrange the steps.

i. With CN as diameter describe a semi-circle cutting the circle at M.

ii. Draw a line joining C and N.

iii. Draw a line perpendicular to NM and passing through N which is tangent.

iv. Draw a line through N and M. This line is normal.

a) ii, i, iv, iii

b) iii, i , iv, ii

c) i, iii, iv, ii

d) iv, iii, i, ii

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4. Steps given are to draw an involute of a given square ABCD. Arrange the steps.

i. With B as centre and radius BP1 (BA+ AD) draw an arc to cut the line CB-produced at P2.

ii. The curve thus obtained is the involute of the square.

iii. With centre A and radius AD, draw an arc to cut the line BA-produced at a point P1.

iv. Similarly, with centres C and D and radii CP2 and DP3 respectively, draw arcs to cut DC-produced at P3 and AD-produced at P4.

a) ii, i, iv, iii

b) iii, i , iv, ii

c) i, iii, iv, ii

d) iv, iii, i, ii

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5. Steps given are to draw an involute of a given triangle ABC. Arrange the steps.

i. With C as centre and radius C1 draw arc cutting AC-extended at 2.

ii. With A as center and radius A2 draw an arc cutting BA- extended at 3 completing involute.

iii. B as centre with radius AB draw an arc cutting the BC- extended at 1.

iv. Draw the given triangle with corners A, B, C.

a) ii, i, iv, iii

b) iii, i , iv, ii

c) i, iii, iv, ii

d) iv, iii, i, ii

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6. Steps given are to draw an involute of a given pentagon ABCDE. Arrange the steps.

i. B as centre and radius AB, draw an arc cutting BC –extended at 1.

ii. The curve thus obtained is the involute of the pentagon.

iii. C as centre and radius C1, draw an arc cutting CD extended at 2.

iv. Similarly, D, E, A as centres and radius D2, E3, A4, draw arcs cutting DE, EA, AB at 3, 4, 5 respectively.

a) ii, i, iv, iii

b) iii, i , iv, ii

c) i, iii, iv, ii

d) iv, iii, i, ii

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7. For inferior trochoid or inferior epitrochoid the curve touches the directing line or directing circle.

a) True

b) False

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

a) True

b) False

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## Set 5

1. Which of the following is incorrect about Ellipse?

a) Eccentricity is less than 1

b) Mathematical equation is x^{2} = 4ay

c) Length of latus rectum is 4a

d) The distance from focus to vertex is equal to perpendicular distance from vertex to directrix

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2. Which of the following constructions use parabolic curves?

a) Cooling towers

b) Water channels

c) Light reflectors

d) Man-holes

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3. The length of the latus rectum of the parabola y2 =ax is ______

a) 4a

b) a

c) a/4

d) 2a

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^{2}=4ax, x

^{2}=4ay is 4a; y

^{2}=2ax, x

^{2}=2ay is 2a; y

^{2}=ax, x

^{2}=ay is a.

4. Which of the following is not a parabola equation?

a) x^{2} = 4ay

b) y^{2} – 8ax = 0

c) x^{2} = by

d) x^{2} = 4ay^{2}

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^{2}= 4ay

^{2}gives equation for hyperbola. And x

^{2}+ 4ay

^{2}=1 gives equation for ellipse.

5. The parabola x^{2} = ay is symmetric about x-axis.

a) True

b) False

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^{2}= 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 y

^{2}= ax then it is symmetric about x-axis.

6. Steps are given to find the axis of a parabola. Arrange the steps.

i. Draw a perpendicular GH to EF which cuts parabola.

ii. Draw AB and CD parallel chords to given parabola at some distance apart from each other.

iii. The perpendicular bisector of GH gives axis of that parabola.

iv. Draw a line EF joining the midpoints lo AB and CD.

a) i, ii, iii, iv

b) ii, iv, i, iii

c) iii, iv, i, ii

d) iv, i, ii, iii

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7. Steps are given to find focus for a parabola. Arrange the steps.

i. Draw a perpendicular bisector EF to BP, Intersecting the axis at a point F.

ii. Then F is the focus of parabola.

iii. Mark any point P on the parabola and draw a perpendicular PA to the axis.

iv. Mark a point B on the on the axis such that BV = VA (V is vertex of parabola). Join B and P.

a) i, ii, iii, iv

b) ii, iv, i, iii

c) iii, iv, i, ii

d) iv, i, ii, iii

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8. Which of the following is not belonged to ellipse?

a) Latus rectum

b) Directrix

c) Major axis

d) Axis