Tuesday, May 12, 2009



1) A point P is 15 mm above the H.P. and 20 mm in front of the V.P. Another point Q is 25 mm behind the V.P. and 40 mm below the H.P. Draw projections of P and Q keeping the distance between their projectors equal to 90 mm. Draw straight lines joining (i) their top views (ii) their front views.
2) Two points A and B are in the H.P. The point A is 30 mm in front of the V.P., while B is behind the V.P. The distance between their projectors is 75 mm and the line joining their top views makes an angle of 45° with XY. Find the distance of the point B from the V.P.
3) A point P is 20 mm below H.P. and lies in the third quadrant. Its shortest distance from XY is 40 mm. Draw its projections.
4) A line AB 120 mm long is inclined at 45° to H.P. and 30° to V.P. It’s mid point C is in the V.P. and 20 mm above H.P. The end A is in the third quadrant and B is in the first quadrant. Draw the projections of the line.
5) The top view of a 75 mm long line PQ measures 50 mm. P is 50 mm infront of the V.P. and 15 mm below the H.P. Point Q is 15 mm infront of V.P. and is above the H.P. Draw the front view of PQ and find its inclinations with the H.P. and the V.P.
6) Draw the projections of a line AB, 90 mm long, it’s mid point M is 50 mm above H.P. and 40 mm infront of the V.P. The end A is 20 mm above H.P. and 10 mm infront of V.P. Show the inclinations of the line with H.P. & V.P.
7) A line AB 65 mm long has its end A 20 mm above the H.P. and 25 mm infront of the V.P. The end B is 40 mm above H.P. and 65 mm infront of the V.P. Draw the projections of AB and show its inclinations both actual and apparent with H.P. & V.P.
8) A Room measures 8 m long, 5 m wide and 4 m high. An electric bulb hangs in the centre of the ceiling and 1 m below it. A thin straight wire connects the bulb to a switch kept in one of corner of the room and 2 m above the floor. Draw the projections of the wire, also determine its true length and slope with the floor.
9) A regular Hexagon of 40 mm side has a corner on the H.P. It’s surface is inclined at 45° to the H.P. and the top view of the diagonal through the corner which is in the H.P. makes an angle of 60° with V.P. Draw its projections.
10) Draw the projections of a rhombus having diagonals 125 mm and 50 mm long, the smaller diagonal of which is parallel to both the principal planes, while the other is inclined at 30° to the H.P.
11) Draw the projections of a circle of 75 mm diameter having the end A of the diameter AB in the H.P. the end B in the V.P. and the surface is inclined at 30° to the H.P. & 60° to the V.P.
12) A semicircular plate of 80 mm diameter has its straight edge in the V.P. and inclined at 45° to the H.P. The surface of the plate makes an angle of 30° with the V.P. Draw the projections.
13) ABCDE is a regular pentagonal plate of 40 mm side and has its corner A on H.P. The plate is inclined to H.P. such that the top view lengths of edges AB and AE are each 35 mm. The side CD is parallel to the both the reference planes. Draw the projections of the plate and find its inclination with H.P.
14) A plate having shape of an isosceles triangle has base 50 mm long and altitude 70 mm. It is so placed that in the front view it is seen as an equilateral triangle of 50 mm sides, one side inclined at 45° to XY. Draw its top view.
15) a. A square pyramid, base 40 mm side and axis 65 mm long, has its base in the V.P. One edge of the base is inclined at 35° to the ground and a corner contained by that edge is on the ground. Draw its projections.
b. A tetrahedron of 5 cm long edges is resting on the ground on one of its faces, with an edge of that face parallel to the V.P. Draw its projections and measure the distance of its apex from the ground.
16) A frustum of hexagonal pyramid side of top and bottom 25 mm and 40 mm respectively with axis 50 mm height rests on its base in H.P. Its axis is parallel to V.P. Draw the orthographic projections and provide the isometric view of the solid.
17) A hexagonal pyramid side of the base 25 mm long and height 70 mm has one of its triangular faces perpendicular to the H.P. and inclined at 45° to the V.P. The base side of this triangular face is parallel to the H.P. Draw its projections.
18) Draw the projections of a cone, base 50 mm diameter and axis 75 mm long lying on a generator on the ground with the top view of the axis making an angle of 45° with the V.P.
19) a. A rectangular block 75 mm x 60 mm x 85 mm has a hole of 20 mm diameter drilled centrally through its largest faces. Draw the projection when the block has its 50 mm long edge parallel to the H.P. and perpendicular to the V.P. and axis of the hole inclined at 60° to the H.P.
b. Draw the projections of a square pyramid having one of its triangular faces in the V.P. and the axis parallel to and 40 mm above the H.P. base 30 mm side, axis 75 mm long.
20) Draw the isometric view of a Door-Steps having three steps of 22 cm tread and 15 cm rise. The steps measure 75 cm widthwise.
21) Draw the isometric view of a cylinder of base 50 mm diameter and 70 mm height when its base on H.P.(use four-centre method)
22) Draw the isometric projections of a cone of base 40 mm diameter and height 58 mm when it rests with its base on H.P.

22) Two points A and B are 50 mm apart. Draw the curve traced out by a point P moving in such a way that the difference between its distances from A and B is always constant and equal to 20 mm.
23) Draw a straight line AB of any length. Mark a point F, 75 mm from AB. Trace the paths of a point P moving in such a way that the ratio of its distance from the point F, to its distance from AB is 3:2. Plot at least 8 points. Name the curve. Draw a normal and a tangent to curve at a point on it, 50 mm from F.
24) Show by means of a drawing that when the diameter of the directing circle is twice that of the generating circle, the hypocycloid is straight line. Take the diameter of the generating circle equal to 60 mm.
25) A circle of 50 mm diameter, rolls on a horizontal line for half a revolution clockwise and then on a line inclined at 60 to the horizontal for another half clockwise. Draw the curve traced by a point P on the circumference of the circle, taking the top most point on the rolling circle as the initial position of the generating point.
26) Two straight lines OA and OB make an angle of 75° between them. P is a point 40 mm from OA and 50 mm from OB. Draw a hyperbola through P, with OA and OB as asymptotes, making at least ten points.

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