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# Multiple choice question for engineering

## Set 1

1. Choose the correct option. Answer: b [Reason:] The point where the extension of major axis meets the curve is called vertex. The conic is defined as the locus of a point in such a way that the ratio of its distance from a fixed point and a fixed straight line is always constant. The ratio gives the eccentricity. The fixed point is called the focus and the fixed line is called directrix.

2. Match the following.
1. E < 1    i. Rectangular hyperbola
2. E = 1    ii. Hyperbola
3. E > 1    iii. Ellipse
4. E > 1    iv. Parabola
a) 1, i; 2, ii; 3, iii; 4, iv
b) 1, ii; 2, iii; 3, iv; 4, i
c) 1, iii; 2, iv; 3, ii; 4, i
d) 1, iv; 2, iii; 3, ii; 4, i

Answer: c [Reason:] The conic is defined as the locus of a point in such a way that the ratio of its distance from a fixed point and a fixed straight line is always constant. The fixed point is called the focus and the fixed line is called directrix. The change in ratio as given above results in different curves.

3. A plane is parallel to a base of regular cone and cuts at middle. The cross-section is __________
a) Circle
b) Parabola
c) Hyperbola
d) Ellipse

Answer: a [Reason:] A cone is formed by reducing the cross-section of circle the point. So there exist circles along the cone parallel to base. Since the given plane is parallel to base of the regular cone. The cross-section will be circle.

4. 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 [Reason:] 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.

5. The curve formed when eccentricity is equal to one is _________
a) Parabola
b) Circle
c) Semi-circle
d) Hyperbola

Answer: a [Reason:] The answer is parabola. Circle has an eccentricity of zero and semi circle is part of circle and hyper eccentricity is greater than one. 6. 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 [Reason:] 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 the cone the cross- section may be parabola or hyperbola. 7. A plane cuts the cylinder the plane is not parallel to the base and cuts all the generators. The Cross-section is _________
a) Circle
b) Ellipse
c) Parabola
d) Hyperbola

Answer: b [Reason:] Given is a plane which is inclined but cutting all the generators so it will be ellipse. Cutting of all generators gives us information that the cross-section will be closed curve and not parabola or hyperbola. Circle will form only if plane is parallel to base.

8. A plane cuts the cylinder and the plane is parallel to the base and cuts all the generators. The Cross-section is _________
a) Circle
b) Ellipse
c) Parabola
d) Rectangular hyperbola

Answer: a [Reason:] The plane which is parallel to base will definitely cut the cone at all generators. Here additional information also given that the plane is parallel to base so the cross-section will be circle. 9. The curve which has eccentricity zero is _______
a) Parabola
b) Ellipse
c) Hyperbola
d) Circle

Answer: d [Reason:] The eccentricity is the ratio of distance from a point on curve to focus and to distance from the point to directrix. For parabola it is 1 and for ellipse it is less than 1 and for hyperbola it is greater than 1. And for circle it is zero.

10. Rectangular hyperbola is one of the hyperbola but the asymptotes are perpendicular in case of rectangular hyperbola.
a) True
b) False

Answer: a [Reason:] 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 rectangular hyperbola.

## Set 2

1. Using how many methods can you draw perpendicular lines through a point within the lines?
a) 1
b) 2
c) 3
d) 4

Answer: c [Reason:] We can draw perpendicular lines using three methods. In one method, if the point is nearer to the centre of the line to which the perpendicular is to be made then we can use the bisector method where we cut two arcs on the line and from those intersections we cut another to the point.

2. How many ways can we draw parallel lines to an existing line?
a) 1
b) 2
c) 3
d) 4

Answer: b [Reason:] There are two ways by which we can draw parallel lines to an existing line. The first method is when we have to draw parallel lines to a line through a given point. The other method is to draw parallel lines to a line through a given distance.

3. While drawing perpendicular line through a point which is nearer to the middle of a given line, ______ is cut at two points on the line.
a) A circle
b) A square
c) A rectangle
d) An arc

Answer: d [Reason:] While drawing perpendicular line through a point which is nearer to the middle of a given line, an arc is cut at two points on the line. From these two intersection points, we draw other arcs with same radius and they are made to cut each other.

4. While drawing a perpendicular to a given line through a point nearer to the end of the line, which of the following properties of the circle is used?
a) The diameter of a circle always subtends an angle of 90˚ on the circumference.
b) The angle at the circumference is half the angle at the centre of the circle.
c) The summation of the opposite angles of a quadrilateral is always 180˚.
d) In an arc the angle subtended by any two points on the circumference is always same.

Answer: a [Reason:] While drawing a perpendicular to a given line through a point nearer to the end of the line, the geometric property of the circle that the diameter of a circle always subtends an angle of 90˚ on the circumference of the circle is used to draw the perpendicular line.

5. For drawing a perpendicular through a point outside a given line, which of the following method is used after drawing an arc from that point to the line intersecting at two points?
a) Angle bisector
b) Subtending an angle
c) Perpendicular bisector
d) Drawing a quadrilateral

Answer: c [Reason:] For drawing a perpendicular through a point outside a given line, an arc is drawn from that point to the line intersecting at two points. Then a perpendicular bisector is drawn between those points and thus making a perpendicular through the point outside the line.

6. While drawing a perpendicular to a line from a point within the line but nearer to the end of the line, all the arcs drawn in the process are of _______
b) Different radii but one
c) Same radii but one

Answer: d [Reason:] While drawing a perpendicular to a line from a point within a line but nearer to the end of the line, all the arcs drawn in the process are of same radii. There four arcs drawn in the process and all of them have the same radius.

7. In the given figure which of the following construction line is drawn first? a) Line AP
b) Arc DPC
c) Arc DQC
d) Line DC

Answer: b [Reason:] For drawing perpendicular to a given line through a point that is outside the line and is nearer to the end of the line we first cut an arc with radius equal to AD, keeping centre at A. then we draw another arc with radius DP keeping centre at P. Then join both intersection points we get the perpendicular.

8. For drawing parallel lines to a given line through a given point we make use of ____
a) Arcs
b) Triangles
c) Lines

Answer: a [Reason:] For drawing parallel lines to a given line through a given point we make use of arcs. By cutting the given line using an arc with centre as the given point and of convenient radius, then using the same radius cutting an arc with centre with the new intersection point and so on we make the parallel line.

9. Which of the following arcs is made first to draw a parallel line to the given line PQ? a) A
b) B
c) C
d) D

Answer: c [Reason:] The first arc drawn is C with centre A and any convenient radius. Then from C with the same radius another arc is drawn to the line PQ which cuts at D. And again from C another arc is drawn with radius equal to AD and it cuts at B and then A and B are joined giving the required parallel line.

10. While drawing a parallel line to the given line through a given distance, what all we need to draw?
b) Arcs and tangent
c) Tangents
d) Circles

Answer: b [Reason:] While drawing a parallel line to a given line through a given distance, we need to draw arcs and a tangent. The arcs are drawn on the same side of the given line and with radius as the given distance. Then a tangent is drawn joining both the arcs.

## Set 3

1. What happens to the voltage in a capacitive circuit when the frequency increases?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: b [Reason:] The capacitive reactance decreases as the frequency increases since they are in-versely proportional. The voltage is directly proportional to the capacitive reactance, hence it de-creases.

2. When voltage across a capacitor increases, what happens to the charge stored in it?
a) Increases
b) Decreases
c) Becomes zero
d) Cannot be determined

Answer: a [Reason:] When voltage across a capacitor increases, the charge stored in it also increases be-cause charge is directly proportional to voltage, capacitance being the constant of proportionality.

3. What happens to the current flow in a fully charged capacitor?
a) Current flow stops
b) Current flow doubles
c) Current flow becomes half its original value
d) Current flow becomes one-fourth its original value

Answer: a [Reason:] When a capacitor is fully charged, it does not store any more charge.There is no change in charge with time. Current is the rate of change of charge, hence it becomes zero, or stops.

4. What is the correct formula for capacitive reactance?
a) Xc=1/(2*f*pi*C)
b) Xc=(2*f*pi*C)
c) Xc=1/(f*pi*C)
d) Xc=I/(2*f*pi*C)

Answer: a [Reason:] The capacitive reactance Xc is the reciprocal of the product of the angular velocity and the capacitance. The angular velocity=2*pi*f, therefore Xc=1/(2*f*pi*C).

5. Calculate the capacitance of a capacitor that stores 80microC of charge and has a voltage of 4V.
a) 20F
b) 20microF
c) 10F
d) 10microF

Answer: b [Reason:] Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance. Hence C=Q/V. C=80microC/4V=20microF.

6. What happens to the current in a capacitive circuit when the frequency increases?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: a [Reason:] The capacitive reactance decreases as the frequency increases since they are in-versely proportional. The current is inversely proportional to the capacitive reactance, hence it in-creases.

7. Calculate the current in the capacitor having 2V supply voltage and 3F capacitance in 2seconds.
a) 2A
b) 5A
c) 6A
d) 3A

Answer: d [Reason:] Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance. Hence Q=CV. Q=3*2=6C. I=Q/t= 6/2=3A.

8. If 2V is supplied to a 3F capacitor, calculate the charge stored in the capacitor.
a) 1.5C
b) 6C
c) 2C
d) 3C

Answer: b [Reason:] Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance. Hence Q=CV. Q=3*2=6C.

9. A 30 microF capacitor is connected across a 400V, 50Hz supply. Calculate the capacitive reac-tance.
a) 102 ohm
b) 123.4 ohm
c) 106.2 ohm
d) 143.2 ohm

Answer: c [Reason:] We know that: Xc=1/(2*f*pi*C). Substituting the values from the given question, we get Xc= 106.2 ohm.

10. A 30 microF capacitor is connected across a 400V, 50Hz supply. Calculate the current.
a) 6.67A
b) 3.77A
c) 5.65A
d) 2.33A

Answer: b [Reason:] We know that: Xc=1/(2*f*pi*C). Substituting the values from the given question, we get Xc= 106.2 ohm. I=V/Xc, hence I= 3.77A.

## Set 4

1. The resistance of pure metals ___________
a) Increases with increase in temperature
b) Decreases with increase in temperature
c) Remains the same with increase in temperature
d) Becomes zero with increase in temperature

Answer: a [Reason:] In a conductor, the valence band and conduction band overlap each other, there is an excess of electrons in the conduction band. When the temperature increases, there is an overcrowding of electrons in the conduction band hence reducing the mobility and hence resistance increases.

2. The resistance of insulators __________
a) Increases with increase in temperature
b) Decreases with increase in temperature
c) Remains the same with increase in temperature
d) Becomes zero with increase in temperature

Answer: b [Reason:] In case of an insulator, the energy gap between the conduction band and the valence band is very large. When the temperature is increased, the electrons move from the conduction band to the valence band and hence it starts conducting. When conductance increases, resistance decreases, since C=1/R. Thus, when temperature increases, resistance decreases in insulators.

3. Which of the following statements are true about metals?
a) Metals have a positive temperature coefficient
b) Metals have a negative temperature coefficient
c) Metals have zero temperature coefficient
d) Metals have infinite temperature coefficient

Answer: a [Reason:] The resistance of metals increases with an increase in temperature thus, it has a positive temperature coefficient.

4. Which of the following statements are true about insulators?
a) Insulators have a positive temperature coefficient
b) Insulators have a negative temperature coefficient
c) Insulators have zero temperature coefficient
d) Insulators have infinite temperature coefficient

Answer: b [Reason:] Insulators have a negative temperature coefficient because as temperature increases, the resistance of insulators decreases.

5. What is the unit of temperature coefficient?

Answer: c [Reason:] R=Reff[1+temp. coeff(T-Teff)]. From the given expression: (R/Reff-1)/(T-Teff)= temp. coeff. Hence, the unit is the reciprocal of that of temperature= centigrade-1.

6. A copper coil has a resistance of 200 ohm when its mean temperature is 0 degree centigrade. Calculate the resistance of the coil when its mean temperature is 80 degree centigrade.
a) 268.5 ohm
b) 268.5 kilo-ohm
c) 286.5 ohm
d) 286.5 kilo-ohm

Answer: a [Reason:] The temperature coefficient of copper is 0.00428 centigrade-1 R1=R0(1+temp. coeff.*T1)= 200(1+0.00428*80)= 268.5 ohm.

7. The temperature of a coil cannot be measured by which of the following methods?
a) Thermometer
b) Increase in resistance of the coil
c) Thermo-junctions embedded in the coil
d) Caloriemeter

Answer: d [Reason:] Caloriemeter measures the amount of heat and not the temperature of coil coefficient. Temperature of a coil is mainly measured by thermometer.

8. The rise or fall in resistance with the rise in temperature depends on________
a) The property of the conductor material
b) The current in the metal
c) Both the given options
d) Does not depend on any factor

Answer: a [Reason:] The rise or fall in resistance with rise in temperature depends upon the property of the material. Hence it rises with temperature in metals and falls with temperature in insulators and semi-conductors.

9. If the temperature is increased in semi-conductors such that the resistance incessantly falls, it is termed as_______
a) Avalanche breakdown
b) Zener breakdown
c) Thermal runway
d) Avalanche runway

Answer c [Reason:] When the temperature keeps increasing, the resistance keeps falling continuously and hence the current to increase. This causes the heat in the semi-conductor to rise. This causes the temperature to increase further and the resistance to further decrease. This process continues and until there is sufficient heat to destroy the structure of the semi-conductor completely. This is known as thermal runway.

10. Materials having resistance almost equal to zero is_______
a) Semi-conductor
b) Conductor
c) Superconductors
d) Insulators

Answer: c [Reason:] When the temperature of a material falls to absolute zero, the resistance falls to zero and hence there are no I2R losses. Since resistance is zero, conductance is almost infinity and hence these materials are known as superconductors.

## Set 5

1. If the flow of electric current is parallel to the magnetic field, the force will be ______
a) Zero
b) Infinity
c) Maximum
d) Half the original value

Answer: a [Reason:] Force is a cross product. A cross product involves the sine of the angle between them. If two quantities are parallel to each other, the angle between them is zero. Sin(0) is zero, hence force is zero.

2. The force existing between two infinite parallel conductors is inversely proportional to ________
a) Radius of the conductors
b) Current in one of the conductors
c) The product of the current in the two conductors
d) The distance between the two conductors

Answer: d [Reason:] When current is flowing in two different conductors, the force between the two conductors is directly proportional to the product of the current in the two conductors and inversely proportional to the distance between the two conductors.

3. When the distance of operation between the two conductors increases, what happens to the force between the two conductors?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: b [Reason:] When the distance of separation increases, the force between the two conductors decrease because force between two conductors is inversely proportional to the distance of separation between them.

4. Which of the following is used to determine the direction of magnetic field in a current carrying conductor?
a) Left hand thumb rule
b) Right hand thumb rule
c) Right hand palm rule
d) Left hand palm rule

Answer: b [Reason:] The right hand thumb rule determines the direction of magnetic field in a current carrying conductor. The rule states that when we align our right thumb in the direction of the current and curl our fingers around it, the direction of our fingers is the direction of the magnetic field.

5. According to Flemming’s left hand rule, the index finger denotes ________
a) Direction of magnetic field
b) Direction of current
c) Direction of force
d) Direction of force as well as current

Answer: a [Reason:] According to Flemming’s left hand rule, the index finger denotes the direction of magnetic field, the thumb denoted the direction of force and the middle finger denoted the direction of current.

6. According to Flemming’s left hand rule, the middle finger denotes _________
a) Direction of magnetic field
b) Direction of current
c) Direction of force
d) Direction of force as well as current

Answer: b [Reason:] According to Flemming’s left hand rule, the index finger denotes the direction of magnetic field, the thumb denoted the direction of force and the middle finger denoted the direction of current.

7. According to Flemming’s left hand rule, the thumb denotes _________
a) Direction of magnetic field
b) Direction of current
c) Direction of force
d) Direction of force as well as current

Answer: c [Reason:] According to Flemming’s left hand rule, the index finger denotes the direction of magnetic field, the thumb denoted the direction of force and the middle finger denoted the direction of current.

8. The relation between the direction of force and the direction of magnetic field in a current carrying conductor is?
a) Same direction
b) Opposite direction
c) Perpendicular
d) Unrelated

Answer: c [Reason:] When a conductor carries a certain value of current, the force developed in the conductor, the current in the conductor and the magnetic field in the conductor are mutually perpendicular to each other.

9. The relation between the direction of current and the direction of magnetic field in a current carrying conductor is?
a) Same direction
b) Opposite direction
c) Perpendicular
d) Unrelated