250+ TOP MCQs on Curves Used in Engineering Practice and Answers

Civil Engineering Drawing Multiple Choice Questions on “Curves Used in Engineering Practice”.

1. Parabolic curves is not used in ________
a) Arches
b) Bridges
c) Sound reflectors

3. When the point is within the circle, the curve is called an ________
a) Inferior trochoid
b) Superior trochoid
c) Inscribed trochoid
d) Superior trochiod

Answer: a

5. For eccentricity in ellipse (e) which relation is correct?
a) e < 1
b) e = 1
c) e > 1
d) e = ∞

Answer: a
Clarification: Eccentricity can be defined as a parameter associated with every conic section. It can be thought of a measure of how much the conic section deviates from being circular. When (e < 1 Ellipse), (e = 1 Parabola), (e > 1 Hyperbola), (e = ∞ straight line), (e = 0 Circle).

6. When a uniform and flexible chain hangs from two pegs, its weight is uniformly distributed along its length. The shape it takes is called a _________
a) Catenary
b) Parabola
c) Hyperbola
d) Ellipse

Answer: a

7. A curve defined by an equation x2/a2 + y2/b2 = 1 is known as ________
a) Ellipse
b) Directrix
c) Parabola
d) Hyperbola

Answer: a

8. The curve generated by a point on the circumference of a circle, rolling along another circle inside it, is called a ________
a) Epicycloid
b) Epitrochoid
c) Hypocycloid
d) Trochoid

Answer: c

9. The curve generated by a point fixed to a circle outside its circumference as it rolls along a straight line is called a _________
a) Inferior epitrochoid
b) Superior trochoid
c) Inferior trochoid
d) Superior epitrochoid

Answer: b

10. The curve generated by a point fixed to a circle outside its circumference s it rolls along a circle outside it, is called _______________
a) Inferior epitrochoid
b) Superior trochoid
c) Inferior trochoid
d) Superior Epitrochoid

Answer: d
Clarification: An epitrochoid is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle.

11. Which of the following is not true regarding concentric and eccentric circles?
a) Concentric circles have a common centre point
b) Eccentric circles have no common centre point
c) Concentric circles have no common centre point
d) Two or more circles with a common centre point are called concentric

Answer: d

12. Which of the following is not present in a circle?
a) Angle
b) Centre
c) Sector
d) Eccentricity

Answer: d
Clarification: Eccentricity can be defined as a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular. Options like angle, centre and sector are there in a circle except the eccentricity.

250+ TOP MCQs on Estimate of Single & Double Room Building and Answers

Civil Engineering Drawing Multiple Choice Questions on “Estimate of Single & Double Room Building”.

1. For 100 sq. m cement concrete (1 : 2: 4) 4 cm thick floor, the quantity of cement required, is _______
a) 0.90 m3
b) 0.94 m3
c) 0.98 m3
d) 0.98 m3

Answer: b
Clarification: Volume – area * thickness.
So, 100 *.04 = 4 cubic metre, 10% for uneven surface.
4 * 10% = .04 = 4.4cubic metre.
50% for dry mortar, 4.4 * 50% = 2.2.
= 6.6cubic meter.
Cement = 6.6/(1 + 2 + 4) = .94 cubic meter.

2. For the construction of buildings, the subheads of the estimate are ________
a) Earthwork, Concrete work, Brick work
b) Plastering or pointing, finishing, water supply and sanitary work
c) Brickwork Flooring, Wood work, Steel work
d) Earthwork, concrete work, brick work, plastering, water supply and steel work

Answer: d
Clarification: This method is suitable for walls of similar cross sections. Here the total centre line length is multiplied by breadth and depth of respective item to get the total quantity at a time. When cross walls or partitions or verandah walls join with main wall, the centre line length gets reduced by half of breadth for each junction. Such junction or joints are studied carefully while calculating total centre line length. The estimates prepared by this method are most accurate and quick.

3. The ‘centre line method’ is specially adopted for estimating?
a) Circular buildings
b) Hexagonal buildings
c) Other geometrical shaped buildings
d) Circular, hexagonal and other geometric shapes

Answer: d
Clarification: By center-line method, estimate for earthwork, concrete work or brick work for all walls of the building can be done at a time. If there are junctions, it needs to be carefully calculated deducting the widths. By long wall and short wall method, each wall is estimated separately. In centerline method, it can be prepared quickly eliminating lengthy mathematical calculations. In Center-line method, estimate can’t be physically measured at site where as it can be done for Long wall short wall method. Center-line method is preferred for preparing estimates and long wall short wall method is preferred for entering measurements in measurement book.

4. Referring to the figure below, pick up the correct statement from the following.

a) The total length of centre line of four walls is 20 m
b) Length of long wall out-to-out is 6.80 m
c) Length of short walls in-to-in is 3.20 m
d) Total length of four wall – 20 m, length of short wall – 6.8 m

Answer: d
Clarification: Total length is (long wall) 6.80. So, centre to centre length 6.80-80 = 6, 2 wall so 6+6 = 12.
Total length of short wall 4.80. So, centre to centre length 4.80-80 = 4, 2 wall so 4+4 = 8. Total length of center to centre 4 wall = 20 m.
Length of short wall in-to-in is 4.80-(80+80) = 3.20 m.

5. The expected out turn for earth work in excavation in ordinary soil per labourer per day is _____
a) 1 cum
b) 2 cum
c) 3 cum
d) 4 cum

Answer: c
Clarification: Sand = 4 cum
Ordinary soil = 3 cum
Compacted soil = 2 cum
Rock = 1 cum.

6. The expected out turn of half brick partition wall per mason per day is _________
a) 1.5 m3
b) 2.0 m3
c) 4.0 m2
d) 5.0 m2

Answer: d
Clarification: The out-turn of work per artisan varies to some extent according to the nature, size, height, situation, location, etc., In bigger cities where specialized and experienced labour is available the out-turn is greater than small towns and country sides. In well-organized work less labour is required.

7. The floor area includes the area of the balcony up to _________
a) 50 %
b) 60 %
c) 70 %
d) 45 %

Answer: a
Clarification: Carpet Area is the area enclosed within the walls, actual area to lay the carpet. Built up Area is the carpet area plus the thickness of outer walls and the balcony. Super Built up Area is the built up area plus proportionate area of common areas such as the lobby, lifts shaft, stairs, etc.
In architectural, construction, and real estate, floor area, floor space, or floor space is the area (measured as square feet or square metres) taken up by a building or part of it. Gross floor area (GFA) – The total floor area contained within the building measured to the external face of the external walls.

8. The measurement is made for stone work in square metre in case of ________
a) Wall facing
b) Columns, lintels, copings
c) Footings
d) Building work

Answer: a
Clarification: Stone blocks used in masonry can be dressed or rough, though in both examples: corners, door and window jambs, and similar areas are usually dressed. Stone masonry utilizing dressed stones is known as ashlar masonry, whereas masonry using irregularly shaped stones is known as rubble masonry. Both rubble and ashlar masonry can be laid in coursed rows of even height through the careful selection or cutting of stones, but a great deal of stone masonry is uncoursed.

250+ TOP MCQs on Railway Line and Answers

Civil Engineering Drawing Multiple Choice Questions on “Railway Line”.

1. ______ percentage of Indian rails routes are electrified.
a) 66%
b) 25%
c) 45%
d) 76%

Answer: c
Clarification: It is the fourth largest railway network in the world by size, comprising 119,630 kilometres (74,330 mi) of total track and 92,081 km (57,216 mi) of running track over a route of 66,687 km (41,437 mi) at the end of 2015-16. Forty-five percentage of its routes are electrified, using entirely 25 kV AC electric traction. The track is mostly broad gauge with small stretches of metre and narrow gauge track. 37% of the tracks are double or multiple tracked.

2. ____________ is the predominant gauge used by Indian railways.
a) Broad gauge
b) Narrow gauge
c) Metre gauge
d) Standard gauge

Answer: a
Clarification: Indian gauge 1,676 mm (5 ft 6 in) (a broad gauge) is the predominant gauge used by IR.
Broad Gauge: width 1676 mm to 1524 mm or 5’6” to 5’0”
Standard Gauge: width 1435 mm and 1451 mm or 4′-8⅟2”
Metre Gauge: width 1067 mm, 1000 mm and 915 mm or 3′-6”, 3′-33/8” and 3′-0”
Narrow Gauge: width 762 mm and 610 mm or 2′-6” and 2′-0”.

3. Sleepers (ties) are mostly made up of _______________
a) wood
b) prestressed concrete
c) metal
d) steak

Answer: b
Clarification: Prestressed concrete is a form of concrete used in construction which is “pre-stressed” by being placed under compression prior to supporting any loads beyond its own dead weight. This compression is produced by the tensioning of high-strength “tendons” located within or adjacent to the concrete volume and is done to improve the performance of the concrete in service.

4. __________ forms the trackbed upon which railroad ties (sleepers) are laid.
a) Track ballast
b) Concrete ballast
c) Rail ballast
d) Wooden ballast

Answer: a
Clarification: It is packed between, below, and around the ties. It is used to bear the load from the railroad ties, to facilitate drainage of water, and also to keep down vegetation that might interfere with the track structure. This also serves to hold the track in place as the trains roll by. It is typically made of crushed stone, although ballast has sometimes consisted of other, less suitable materials, for example burnt clay. The term “ballast” comes from a nautical term for the stones used to stabilize a ship.

5. The shape of ballast should be _____________
a) triangular
b) irregular
c) spherical
d) longitudinal

Answer: b
Clarification: Stones must be irregularly cut, with sharp edges, so that they properly interlock and grip the ties in order to fully secure them against movement; spherical stones cannot do this. In order to let the stones fully settle and interlock, speed limits are often lowered on sections of track for a period of time after new ballast has been laid.

6. In this form of track, the rails are welded together by utilising flash butt welding to form one continuous rail that may be several kilometres long, this type of rail is called __________
a) Continuous jointed rail
b) Merged rail
c) Continuous welded rail
d) Continuous welded rail

Answer: c
Clarification: In this form of track, the rails are welded together by utilising flash butt welding to form one continuous rail that may be several kilometres long. Because there are few joints, this form of track is very strong, gives a smooth ride, and needs less maintenance; trains can travel on it at higher speeds and with less friction. Welded rails are more expensive to lay than jointed tracks, but have much lower maintenance costs.

7. The distance shown by red line represents ______________

a) separation
b) parallel way
c) height
d) gauge

Answer: d
Clarification: During the early days of rail, there was considerable variation in the gauge used by different systems. Today, 54.8% of the world’s railways use a gauge of 1,435 mm (4 ft 8 (frac{1}{2}) in), known as standard or international gauge. Gauges wider than standard gauge are called broad gauge; narrower, narrow gauge. Some stretches of track are dual gauge, with three (or sometimes four) parallel rails in place of the usual two, to allow trains of two different gauges to use the same track.

8. The surface of the head of each of the two rails can be maintained by using a ___________
a) rail header
b) rail trimmer
c) rail grinder
d) rail cutter

Answer: c
Clarification: A rail grinder (or rail grinder) is a maintenance of way vehicle or train used to restore the profile and remove irregularities from worn tracks to extend its life and to improve the ride of trains using the track. Rail grinders were developed to increase the lifespan of the tracks being serviced for rail corrugation. Rail grinding is a process that is done to stop the deformation due to use and friction on railroad tracks by removing deformations and corrosion.

9. The track and ballast form the ______________
a) Temporary way
b) True way
c) Rigid way
d) Permanent way

Answer: d
Clarification: The permanent way is the elements of railway lines: generally the pairs of rails typically laid on the sleepers (“ties” in American parlance) embedded in ballast, intended to carry the ordinary trains of a railway. It is described as permanent way because in the earlier days of railway construction, contractors often laid a temporary track to transport spoil and materials about the site; when this work was substantially completed, the temporary track was taken up and the permanent way installed.

10. The longest railway platforms is ______________
a) State Street subway, Chicago
b) Gorakhpur railway station, UP
c) Kharagpur, West Bengal
d) Kollam Junction, Kerala

Answer: b
Clarification: • Gorakhpur railway station, Uttar Pradesh, India:1,366.33 m (4,483 ft) (longest in the world).
• Kollam Junction, Kerala, India:1,180.5 m (3,873 ft)
• Kharagpur, West Bengal, India: 1,072.5 m (3,519 ft)
• State Street subway, Chicago, Illinois, US: 1,067 m (3,501 ft) (longest in North America)
• Bilaspur railway station, Chhattisgarh, India: 802 m (2,631 ft).

250+ TOP MCQs on Earthwork, Concrete and R.C.C. work and Answers

Civil Engineering Drawing Multiple Choice Questions on “Earthwork, Concrete and R.C.C. work”.

1. _______________ are engineering works created through the processing of parts of the earth’s surface involving quantities of soil or unformed rock.
a) Surfacework
b) Landwork
c) Earthworks
d) Hosework
Answer: c
Clarification: Typical earthworks include roads, railway beds, causeways, dams, levees, canals, and berms. Other common earthworks are land grading to reconfigure the topography of a site, or to stabilize slopes.

2. An ___________________ beam is one in which the tension capacity of the tensile reinforcement is smaller than the combined compression capacity of the concrete and the compression steel (under-reinforced at tensile face).
a) extra-reinforced
b) less-reinforced
c) under-reinforced
d) over-reinforced
Answer: c
Clarification: When the reinforced concrete element is subject to increasing bending moment, the tension steel yields while the concrete does not reach its ultimate failure condition. As the tension steel yields and stretches, an “under-reinforced” concrete also yields in a ductile manner, exhibiting a large deformation and warning before its ultimate failure. In this case the yield stress of the steel governs the design.

3. When aggregate is mixed together with dry Portland cement and water, the mixture forms a fluid _________ that is easily poured and moulded into shape.
a) curry
b) furry
c) slurry
d) gel
Answer: c
Clarification: A slurry is a thin sloppy mud or cement or, in extended use, any fluid mixture of a pulverized solid with a liquid (usually water), often used as a convenient way of handling solids in bulk. Slurries behave in some ways like thick fluids, flowing under gravity and are also capable of being pumped if not too thick.

4. Excavation may be classified by type of material- Earth excavation ________ excavation, rock excavation, muck excavation, unclassified excavation.
a) bottom soil
b) sub-soil
c) topsoil
d) surface soil
Answer: c
Clarification: Topsoil is the upper, outermost layer of soil, usually the top 2 inches (5.1 cm) to 8 inches (20 cm). It has the highest concentration of organic matter and microorganisms and is where most of the Earth’s biological soil activity occurs. Four elements constitute the composition of soil. Those elements are mineral particles, organic matter, water, and air. The volume of top soil consists of 50 to 80% of these particles which form the skeletal structure of most soils.

5. Heavy construction equipment is usually used due to the amounts of material to be moved – up to millions of cubic metres.
a) True
b) False
Answer: a
Clarification: Earthwork construction was revolutionized by the development of the (Fresno) scraper and other earth-moving machines such as the loader, the dump truck, the grader, the bulldozer, the backhoe, and the dragline excavator.

6. In the past, earthwork excavating calculations were done by hand using a slide rule and with methods such as Simpson’s rule.
a) True
b) False
Answer: a
Clarification: In numerical analysis, Simpson’s rule is a method for numerical integration, the numerical approximation of definite integrals. The slide rule, also known colloquially in the United States as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as exponents, roots, logarithms and trigonometry, but typically not for addition or subtraction.

7. A mixture of bentonite and water used to make slurry walls.
a) True
b) False
Answer: a
Clarification: Bentonite is an absorbent aluminium phyllosilicate clay consisting mostly of montmorillonite. It was named by Wilbur C. Knight in 1898 after the Cretaceous Benton Shale near Rock River, Wyoming.

8. Manure slurry, a mixture of animal waste, organic matter, and sometimes water often known simply as “slurry” in agricultural use, used as fertilizer after ageing in a slurry pit.
a) True
b) False
Answer: a
Clarification: A slurry pit, also known as a farm slurry pit, slurry tank, slurry lagoon or slurry store, is a hole, dam, or circular concrete structure where farmers gather all their animal waste together with other unusable organic matter, such as hay and water run off from washing down dairies, stables, and barns, in order to convert it, over a lengthy period of time, into fertilizer that can eventually be reused on their lands to fertilize crops.

9. Chemical admixture may accelerate or slow down the rate at which the concrete hardens.
a) True
b) False
Answer: a
Clarification: Chemical admixtures are added to achieve varied properties. These ingredients may accelerate or slow down the rate at which the concrete hardens, and impart many other useful properties including increased tensile strength, entrainment of air and water resistance.

10. Concrete can be formulated with high tensile strength, but always has lower compressive strength.
a) True
b) False
Answer: b
Clarification: Reinforcement is often included in concrete. Concrete can be formulated with high compressive strength, but always has lower tensile strength. For this reason it is usually reinforced with materials that are strong in tension, typically steel rebar.

11. Reinforced concrete (RC) is a composite material in which concrete’s relatively low tensile strength and ductility are counteracted by the inclusion of reinforcement having higher tensile strength or ductility.
a) True
b) False
Answer: a
Clarification: The reinforcement is usually, though not necessarily, steel reinforcing bars (rebar) and is usually embedded passively in the concrete before the concrete sets. Reinforcing schemes are generally designed to resist tensile stresses in particular regions of the concrete that might cause unacceptable cracking and/or structural failure. Modern reinforced concrete can contain varied reinforcing materials made of steel, polymers or alternate composite material in conjunction with rebar or not.

12. Reinforced concrete can be classified as precast or postcast concrete.
a) True
b) False
Answer: b
Clarification: Reinforced concrete can be classified as precast or cast-in-place concrete. Designing and implementing the most efficient floor system is key to creating optimal building structures. Small changes in the design of a floor system can have significant impact on material costs, construction schedule, ultimate strength, operating costs, occupancy levels and end use of a building.

13. The coefficient of thermal expansion of concrete is very small to that of steel, eliminating large internal stresses due to differences in thermal expansion or contraction.
a) True
b) False
Answer: b
Clarification: The coefficient of thermal expansion of concrete is similar to that of steel, eliminating large internal stresses due to differences in thermal expansion or contraction.

14. The reinforcement in an RC structure, such as a steel bar, has to undergo the same strain or deformation as the surrounding concrete in order to prevent discontinuity, slip or separation of the two materials under load.
a) True
b) False
Answer: a
Clarification: Maintaining composite action requires transfer of load between the concrete and steel. The direct stress is transferred from the concrete to the bar interface so as to change the tensile stress in the reinforcing bar along its length, this load transfer is achieved by means of bond (anchorage) and is idealized as a continuous stress field that develops in the vicinity of the steel-concrete interface.

15. Prestressing concrete is a technique that decreases the load-bearing strength of concrete beams.
a) True
b) False
Answer: b
Clarification: Prestressing concrete is a technique that greatly increases the load-bearing strength of concrete beams.

250+ TOP MCQs on Accounts and Answers

Civil Engineering Drawing Multiple Choice Questions on “Accounts”.

1. In P.W.D who is the primary disbursing officer who is supplied with cheque books on district treasuries of India.
a) S.D.O’s
b) Divisional officer
c) Chief Minister
d) Manager of bank
Answer: b
Clarification: He makes payments to contractors against proper bills by issuing cheques. He also obtains money by presentation of cheque and keep in his cash chest for making petty cash payments as and when required.

2. Which is not a transaction type of Public work office grouped under?
a) Expenditure heads
b) Revenue heads
c) Remittance heads
d) Credit heads
Answer: d
Clarification: The transaction under each of these groups of heads are further sub-divided for the purpose of accounts. In the case of expenditure and revenue heads, the main unit of classification is known as the major head.

3. The latrine seat with flushing cistern, flushing pipes are, etc., are usually taken as ______ set for estimation.
a) equal
b) one
c) two
d) separate
Answer: b
Clarification: A latrine is a toilet or an even simpler facility that is used as a toilet within a sanitation system. For example, it can be a communal trench in the earth in a camp to be used as emergency sanitation, a hole in the ground (pit latrine), or more advanced designs, including pour-flush systems.
The term “latrine” is still commonly used in emergency sanitation situations, as well as in army camps. Nowadays, the word “toilet” is more commonly used than “latrine”, except for simple systems like “pit latrine” or “trench latrine”.
The use of latrines was a major advance in sanitation over more basic practices such as open defecation and helped control the spread of many waterborne diseases.

4. According to ISI method of measurement, the order of the sequence is ___________
a) length, breadth, height
b) breadth, height, Length
c) height, Length, breadth
d) width, Length, breadth
Answer: a
Clarification: The first dimension is length (L). Length is always the longest side of the box that has a flap. The second dimension is width (W). Width is the second longest side with a flap. The third dimension is height (H). Height is the only dimension without a flap.

5. The area of a sloping surface of a protective embankment of mean height d, side slopes S: 1 and length L is _________
a) d x d x s
b) (d2 x (ds)2)1/2
c) L.D (1 + s2)1/2
d) 2 L.D (1 + s2)1/2
Answer: c
Clarification: An embankment dam is a large artificial dam. It is typically created by the placement and compaction of a complex semi-plastic mound of various compositions of soil, sand, clay, or rock. It has a semi-pervious waterproof natural covering for its surface and a dense, impervious core. This makes such a dam impervious to surface or seepage erosion. Such a dam is composed of fragmented independent material particles. The friction and interaction of particles binds the particles together into a stable mass rather than by the use of a cementing substance.

6. For 100 sq. m cement concrete (1 : 2: 4) 4 cm thick floor, the quantity of cement required, is ________
a) 0.90 m3
b) 0.94 m3
c) 0.98 m3
d) 0.98 m3
Answer: b
Clarification: Volume – area * thickness.
So, 100*.04 = 4 cubic metre, 10% for uneven surface.
4 * 10% = .04 = 4.4cubic metre.
50% for dry mortar, 4.4 * 50% = 2.2.
= 6.6cubic meter.
Cement = 6.6/(1 + 2 + 4) = .94 cubic meter.

7. The measurement is made for stone work in square metre in case of __________
a) wall facing
b) columns, lintels, copings
c) fotings
d) building work
Answer: a
Clarification: Stone blocks used in masonry can be dressed or rough, though in both examples: corners, door and window jambs, and similar areas are usually dressed. Stone masonry utilizing dressed stones is known as ashlar masonry, whereas masonry using irregularly shaped stones is known as rubble masonry. Both rubble and ashlar masonry can be laid in coursed rows of even height through the careful selection or cutting of stones, but a great deal of stone masonry is uncoursed.

250+ TOP MCQs on Loci of Points and Answers

Civil Engineering Drawing Multiple Choice Questions on “Loci of Points”.

1. The locus of a point P moving in a plane about another point O in such a way that its distance from it is constant, is called _________
a) Arc
b) Angle
c) Circle
d) Perpendicular bisector

Answer: c
Clarification: According to locus postulate: The locus of a point P moving in a lane about another point in such a way that its distance from it is constant, is a circle of some radius.

2. The locus of a point equidistant from two fixed points A and B in the same plane, is the called ___________
a) Straight line
b) Angle
c) Circle
d) Perpendicular bisector

Answer: d
Clarification: According to locus postulate: The locus of a point equidistant from two fixed points A and B in the same plane, is the perpendicular bisector of the line joining the two points.

3. The locus of a point equidistant from two fixed non-parallel straight line AB and CD is known as _______________
a) Straight line
b) Angular bisector
c) Circle
d) Perpendicular bisector

Answer: b
Clarification: According to locus postulate: The locus of a point equidistant from two fixed non-parallel straight lines AB and CD will be a straight line bisecting the angle between them.

4. Using ruler and compass how will you construct ∆ABC, if AB=3.5, BC=6 and angle ABC=60o?
a) Draw line BC=6 cm and an angle CBA=600. Cut off AB=3.5. Join AC, triangle ABC is the required triangle
b) Draw line BC=6 cm and AB= 3.5 and then angle ABC=60o, ABC is the required triangle
c) Draw line AB= 3.5cm and cut off AB = 6 cm at any point and make angle CBA=600
d) Draw angle CBA= 600 and make

Answer: a

5. Given 2 points A and B, what is the locus of points P so that angle APB is a right angle?
a) A square with points A and B
b) The circle with diameter AB
c) A rectangle with side A and B
d) A semi-circle with diameter AB

Answer: b

6. For all value of the co-ordinates of a moving point Pare (a cos θ, b sin θ); what will be the equation to the locus of P?
a) x2/a2 + y2/b2 = 0
b) x2/b2 + y2/a2 = 0
c) x2/b2 + y2/a2 = 1
d) x2/a2 + y2/b2 = 1

Answer: d
Clarification: Let (x, y) be the co-ordinates of any point on the locus traced out by the moving point P. Then we shall have
x = a cos θ or x/a = cos θ and y = b sin θ or, y/b = sin θ
x2/a2 + y2/b2 = cos2 θ + sin2 θ or, x2/a2 + y2/b2 = 1
which is the required equation to the locus of P.

7. What curve does the locus represent if the locus of a moving point which is always equidistant from the points (2, -1) and (3, 2)?
a) Hyperbola
b) Straight line
c) Ellipse
d) Circle

Answer: b
Clarification: Let A (2, -1) and B (3, 2) be the given points and (x, y) be the co-ordinates of a point P on the required locus. Then,
PA2 = (x – 2)2 + (y + 1)2 and PB2 = (x – 3)2 + (y – 2)2

By problem, PA = PB or, PA2 = PB2

or, (x – 2)2 + (y + 1)2 = (x – 3)2 + (y – 2)2 or, x2 – 4x + 4 + y2 + 2y + 1 = x2 – 6x + 9 + y2 – 4y + 4
or, 2x + 6y = 8 or, x + 3y = 4 ……… (1)
Clearly, equation (1) is a first degree equation in x and y; hence, the locus of P is a straight line whose equation is x + 3y = 4.

8. A point moves in such a manner that three times of its abscissa is greater by 5 than two times of its ordinate; find the equation of its locus.
a) 3y-2y=5
b) 3x-2y=5
c) 2x+3y=5
d) 2x-3y=5

Answer: b
Clarification: Here the terms abscissa and ordinate are the coordinates of a point in a two- dimensional rectangular Cartesian coordinate system where abscissa represents x-axis and ordinate as y-axis. So according to the given question the equation is as follows: 3x-2y=5.

9. What will be the geometry made by a locus of a swimmer maintaining the same distant from the lighthouse?
a) Square
b) Rectangle
c) Circle
d) Triangle

Answer: c

10. Which statement is correct for the locus shown in the figure below?

a) A point P moving in a plane about another point in such a way that its distance is constant
b) A point P moving in a plane about a fixed line as an arc with same centre
c) A point P moving in a plane about another point in such a way that its distance from a fixed line AB is constant
d) A point equidistant from two fixed non-parallel lines AB and CD in the same plane

Answer: b
Clarification: As per arc postulate regarding locus it is stated as: When the fixed line is an arc of a circle, the locus will be another arc drawn through same centre. Here fixed line is an arc AB and the locus drawn is an arc representing the circumference, produced due to point P.

11. Four bar mechanism is generally used in ___________________
a) Bicycle
b) Fan
c) Train suspension
d) Rickshaw

Answer: c

12. Chords which are ___________ from the centre are equal.
a) unequal
b) equidistant
c) one third
d) two third

Answer: b