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# Multiple choice question for engineering

## Set 1

1. The total path length is always equal to the magnitude of the displacement vector of a particle. True or false?
a) True
b) False

Answer: b [Reason:] The displacement depends only on the end points while the path length depends on the actual path. The two quantities are equal only if the direction of motion of the object does not change. In all other cases, path length is greater than the magnitude of displacement.

2. A passenger arriving in a new town wishes to go from the station to a hotel located 10km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23km long and reaches the hotel in 28 minutes, what is the average speed of the taxi?
a) 21.43km/h
b) 75km/h
c) 49.3km/h
d) 21km/h

Answer: c [Reason:] Magnitude of displacement = 10km Total path length = 23km Time taken = 28mins = 28/60h = 7/15h Average speed = (Total path lenght)/(Time taken) = 23/(7/15) = 49.3km/h

3. The net acceleration of a particle in circular motion is
a) Towards the centre
c) Irregular
d) Circular in motion

Answer: a [Reason:] The net acceleration of a particle in circular motion is towards the centre only if its speed is constant.

4. Scalar quantity is conserved in a process. True or false?
a) True
b) False

Answer: b [Reason:] Scalar quantities like kinetic energy are not conserved in an inelastic collision. Moreover, vector quantities like linear momentum are conserved.

5. A projectile fired from the ground follows a parabolic path. At what position will the speed of projectile be minimum?
a) At the top of the path
b) At the beginning of the path
c) While travelling along the path
d) Never

Answer: a [Reason:] The speed of the projectile will be minimum at the top of the path. This is because horizontal component of velocity will remain constant throughout the motion whereas the vertical component of the velocity is zero at the top.

6. Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?
a) The faster one
b) Depends on their mass
c) The slower one
d) Both will reach simultaneously

Answer: d [Reason:] Both the bullets will reach simultaneously because T = √(2h/g) Time t does not depend on horizontal speed.

7. Three particles A,B and C are projected from the same point with the same initial speed making angles 30°,45° and 60° respectively with the horizontal. Which of the following statements is correct?
a) A, B and C have unequal ranges
b) Ranges of A and C are equal and less than that of B
c) Ranges of A and C are equal and greater than that of B
d) A, B and C have equal ranges

Answer: b [Reason:] RA = (u2 sin60°)/g = √3/2 u2/g RB = (u2 sin90°)/g = u2/g Rc = (u2 sin120°)/g = √3/2 u2/g Ranges A and C are equal but less than that of B

8. A body executing uniform circular motion has at any instant is velocity vector and acceleration vector
a) Along the same direction
b) In opposite direction
c) Normal to each other
d) Not related to each other

Answer: c [Reason:] Velocity is along the tangent to the circular path and acceleration vector is along the radius. Thus a body executing uniform circular motion at any instant has velocity vector and acceleration vector normal to each other.

9. Two vectors have a resultant equal to either. The angle between them is
a) 60°
b) 120°
c) 90°
d) 100°

Answer: b [Reason:] R = √(P2+Q2+2PQcosθ) p2 = 2p2 (1+cosθ) 1+cosθ = 1/2 Cosθ = -1/2 = cos 120° θ = 120°

10. A body A is dropped from vertically from the top of a tower. If another identical body is thrown horizontally from the same point at the same instant, then
a) A will reach the ground earlier
b) B will reach the ground earlier than A
c) Both A and B will reach the ground simultaneously
d) Depends on external factors

Answer: c [Reason:] Both A and B will reach the ground simultaneously. Both have zero initial velocity and cover the same height under the acceleration due to gravity.

11. Which of the following is constant in a projectile motion?
a) Horizontal component
b) Vertical component
c) Velocity of projection
d) Acceleration of projected object

Answer: a [Reason:] Horizontal component is constant in a projectile motion. It is not affected by the force of gravity.

12. At the highest point of projectile, its velocity and acceleration are at angle of
a) 0°
b) 45°
c) 90°
d) 180°

Answer: c [Reason:] At the highest point of projectile, it has only horizontal velocity while the acceleration due to gravity acts vertically downwards. Therefore they are at an angle of 90°

13. An aeroplane flying horizontally with a speed of 360km/h releases a bomb at a height of 490m form the ground. If g=9.8m/s2, it will strike the ground at
a) 10km
b) 100km
c) 1km
d) 16km

Answer: c [Reason:] Time taken by the bomb to fall through a height of 490m, t = √(2h/g) = √((2×490)/9.8)=10s Distance at which the bomb strikes the ground = Horizontal velocity × time = 1km

14. A stone tied to the end of string 80cm long is whirled in horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of acceleration of the stone?
a) 680 cm/s2
b) 860 cm/s2
c) 720 cm/s2
d) 990 cm/s2

Answer: d [Reason:] a = rω2 = r(2πn/t)2 a = (80×4×(22/7)2×142)/142 = 990cm/s2

## Set 2

1. Which method can be used to distinguish between the two types of carriers?
a) Hall effect
b) Rayleigh method
c) Doppler effect
d) Fermi effect

Answer: a [Reason:] When a conductor carrying current is placed in a transverse magnetic field, an electric field is produced inside the conductor in a direction normal to both the current and the magnetic field. This phenomenon is known as Hall Effect.

2. Find the resistance of an intrinsic Ge rod cm long, 1mm wide and 1mm thick at 300K.
a) 2.32 ohm
b) 5314 ohm
c) 4310 ohm
d) 431 ohm

Answer: c [Reason:] Conductivity of an intrinsic semiconductor = nieeh) Conductivity = 2.32 Resistance = ρl/A = l/(conductivy ×A) Resistance = 4310 ohm

3. A semiconducting crystal 12mm long, 5mm wide and 1mm thick has a magnetic flux density of 0.5Wb/m2 applied from front to back perpendicular to largest faces. When a current of 20mA flows length wise through the specimen, the voltage measured across its width is found to be 37μV. What is the Hall coefficient of this semiconductor?
a) 37×10-6 m3/C
b) 3.7×10-6 m3/C
c) 3.7×106 m3/C
d) 0

Answer: b [Reason:] Hall coefficient = (VH b)/(IH B) Hall coefficient = 3.7×10-6 m3/C

4. The intrinsic carrier density at room temperature in Ge is 2.37×1019/m3. If the electron and hole mobilities are 0.38 and 0.18 m2/Vs respectively. Calculate its resistivity.
a) 0.18ohm m
b) 0.460ohm m
c) 0.4587ohm m
d) 0.709ohm m

Answer: d [Reason:] Conductivity = nieeh) Conductivity = 2.12352/ohm m Resistivity = 1/Conductivity Resistivity = 0.4709ohm m

5. A silicon plate of thickness 1mm, breadth 10mm and length 100mm is placed in a magnetic field of 0.5 Wb/m2 acting perpendicular to its thickness. If 10-3 A current flows along its length, calculate the Hall voltage developed, if the Hall coefficient is 3.66×104 m3/Coulomb.
a) 1.83×10-3Volts
b) 3.66×10-4Volts
c) 0.5Volts
d) 25.150Volts

Answer: a [Reason:] VH = (RH IH B)/t VH = 1.83×10-3 Volts

6. The conductivity of germanium at 20°C is 2/ohm m. What is its conductivity at 40°C? Eg=0.72eV
a) 1.38×10-23/Ohm m
b) 1.0002/ Ohm m
c) 293/ Ohm m
d) 313/ Ohm m

Answer: b [Reason:] σ = Ce(-E/2KT) σ1/σ2 = e(-E/2KT)/e(-E/2KT) σ2 = 1.0002/ Ohm m

7. What is the Fermi energy of a n-type semiconductor?
a) E
b) E(F )= (Ec+ Ev)/2
c) EF = (Ec+ Ed)/2
d) EF = (Ev+ Ea)/2

Answer: c [Reason:] The Fermi energy level of n-type semiconductor lies exactly between the acceptor energy level and the maximum energy level of valence band. Therefore the Fermi energy level of n-type semiconductor is EF = (Ec+ Ed)/2.

8. EF = (Ec+ Ev)/2, this represents the Fermi energy level of which of the following?
a) Extrinsic semiconductor
b) N-type semiconductor
c) P-type semiconductor
d) Intrinsic semiconductor

Answer: d [Reason:] The Fermi energy of an intrinsic semiconductor is EF = (Ec+ Ev)/2. That is the Fermi energy level exactly lies between the lowest energy level of conduction band and highest energy level of valence band.

9. For semiconductors, the resistivity is inversely proportional to the temperature for semiconducting materials. True or false?
a) True
b) False

Answer: a [Reason:] For semiconductors, the resistivity is inversely proportional to the temperature of material, that is, it has negative temperature coefficient. When the temperature of the semiconductor is increased, large numbers of charge carriers are produced due to the breaking of covalent bonds. These charge carriers move freely, hence conductivity increases and therefore the resistivity decreases.

## Set 3

1. Every simple harmonic motion is periodic motion, but every periodic motion need not be simple harmonic motion. True or false?
a) True
b) False

Answer: a [Reason:] Every simple harmonic motion is periodic motion, but every periodic motion need not be simple harmonic motion. For example, when the motion of the earth around the sun is a periodic motion, but not simple harmonic motion as the back and forth motion is not taking place.

2. A pendulum watch can be used in an artificial satellite. True or false?
a) True
b) False

Answer: b [Reason:] A pendulum watch cannot be used in an artificial satellite. In an artificial satellite, a body is in a state of weightlessness, that is g=0. T=2π√(l/g)=∞ Inside the satellite the pendulum does not oscillate. Hence a pendulum watch cannot be used in an artificial satellite.

3. A spring of force constant k is cut into two pieces, such that one piece is double the length of the other. Then the long piece will have a force constant of
a) (2/3) k
b) (3/2) k
c) 3k
d) 6k

Answer: b [Reason:] Force constant, k = F/x The length of the long piece is 2x/3 So, its force constant is k=F/(2x/3)=3F/2x=3/2×k

4. In a simple harmonic oscillator, at the mean position
a) Kinetic energy in minimum, potential energy is maximum
b) Both kinetic and potential energies are maximum
c) Kinetic energy is maximum, potential energy is minimum
d) Both kinetic and potential energies are minimum

Answer: c [Reason:] At mean position, the kinetic energy is maximum and potential energy is minimum.

5. What is the maximum acceleration of the particle executing the simple harmonic motion, y = 2sin[(πt/2)+φ], where y is in cm?
a) π/2 cm/s2
b) π2/2 cm/s2
c) π/4 cm/s2
d) π2/4 cm/s2

6. When the maximum kinetic energy of a simple pendulum is K, then what is its displacement (in terms of amplitude a) when its kinetic energy is K/2?
a) a/√2
b) a/2
c) a/√3
d) a/3

Answer: a [Reason:] Here Kmax=1/2×ka2=K Let 1/2×ky2=K/2=1/2×1/2×ka2 y=a/√2

7. The mass and the radius of a planet are twice that of earth. Then, period of oscillation of a second pendulum on that planet will be
a) 1/√2s
b) 2√2s
c) 2s
d) 1/2s

Answer: b [Reason:] On earth, g=GM/R2 On planet, g=G2M/(4R)2 =g/2 T/T=√(g/g)=√((g/g)/2)=√2 T=√2×T=2√2 s

8. In case of a forced vibration, the resonance wave becomes very sharp when the
a) Applied periodic force is small
b) Quality factor is small
c) Damping force is small
d) Restoring force is small

Answer: c [Reason:] Lesser the damping force, more sharp is the resonance peak.

9. Statement: In simple harmonic motion, the motion is to and fro and periodic [Reason:] Velocity of the particle,
v=ω√(a2-x2 )
Where x is displacement.
a) Both statement and reason are true and reason is the correct explanation of the statement
b) Both statement and reason are true but reason is not the correct explanation of the statement
c) Statement is true, but reason is false
d) Statement and reason are false

Answer: b [Reason:] Both statement and reason are true but the reason is not a correct explanation. Simple harmonic motion is a periodic motion in which acceleration is proportional to displacement from mean position and acceleration acts in the opposite direction of displacement

10. If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will
a) Increase
b) Decrease
c) Remains the same
d) First increases and then decreases

Answer: c [Reason:] Time period, T=2π√(l/g) is independent of the mass of the bob.

## Set 4

1. In the upper part of atmosphere, the kinetic temperature of air is of the order 1000K. Therefore one feels extremely hot. True or false?
a) True
b) False

Answer: b [Reason:] As we go up the atmosphere, the number of air molecules per unit volume decreases. The quantity oh heat per unit volume or the heat density is low. But the translational kinetic energy per molecule is quite large. As the kinetic temperature is the measure of translational kinetic energy, so the kinetic temperature is quite high in the upper atmosphere but one feels severe cold there due to low density.

2. What type of motion is associated with the molecules of gas?
a) Newton’s law of motion
b) Conservative motion
c) Linear motion
d) Brownian motion

Answer: d [Reason:] Brownian motion is associated with the molecules of a gas. In this motion any particular molecule will follow a zigzag path due to the collisions with the other molecules or with the walls of the container.

3. At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be 1920ms-1. The gas is
a) H2
b) F2
c) O2
d) Cl2

Answer: a [Reason:] vrms=√(3RT/M) M=3RT/(vrms)2 =(3×8.3×300)/(1920)2 =2 Hence the gas is H2

4. A vessel contains a mixture of 1 mole of oxygen and 2 moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O2 molecule to that per N2 molecule is
a) 1:1
b) 1: 2
c) 2:1
d) Depends on the moment of inertia of the two molecules

Answer: d [Reason:] Both gases are diatomic. Both have two rotational degrees of freedom at 300K. Average rotational kinetic energy per molecule of each gas will be same=2×1/2 kT=1kT Hence the required ratio is 1:1

5. Statement: For an ideal gas at constant temperature, the product of the pressure and volume is a constant [Reason:] The mean square velocity of the molecules is inversely proportional to mass.
a) Both statement and reason are true and explanation is the correct explanation of the statement
b) Both statement and reason are true but explanation is not correct explanation of the statement
c) Statement it true but reason is false
d) Both statement and reason are false

Answer: b [Reason:] Both the statement and reason are true but the explanation is not a correct explanation of the statement. According to Boyle’s law, PV=constant, at a given temperature.

6. An ant is walking on the horizontal surface. The number of degrees of freedom of ant will be
a) 1
b) 2
c) 3
d) 6

Answer: b [Reason:] As the ant can move on a plane, it has 2 degrees of freedom

7. The number of degrees of freedom for a diatomic gas molecule is
a) 2
b) 3
c) 5
d) 6

Answer: c [Reason:] A diatomic molecule has 3 degrees of freedom due to translator motion and 2 degrees of motion due to rotator motion

8. A gas at one atmosphere and having volume 100ml is mixed with another gas of equal moles at 0.5atm and having volume 50ml in flask of one litre, what is the final pressure?
a) 0.5atm
b) 1atm
c) 0.75atm
d) 0.125atm

Answer: d [Reason:] Total number of moles is conserved. (P1 V1)/RT+(P2 V2)/RT=PV/RT (1×100)/RT+(0.5×50)/RT=(P×1000)/RT P=0.125atm

9. Temperature of oxygen kept in a vessel is raised by 1°C at constant volume. Heat supplied to the gas may be taken partly as translational and partly rotational kinetic energies. Their respective shares are
a) 60%, 40%
b) 50%, 50%
c) 100%, zero
d) 40%, 60%

Answer: a [Reason:] A diatomic oxygen molecule has 3 degrees of freedom due to translator motion and 2 degrees of freedom due to rotator motion. Their associated kinetic energies will be in the ratio 3:2 or 60% and 40%

10. An ideal gas is heated from 27°C to 627°C at constant pressure. If initial volume was 4m3, then the final volume of the gas will be
a) 2m3
b) 4m3
c) 6m3
d) 12m3

Answer: d [Reason:] Using Charle’s law, V1/T1 =V2/T2 V2=T2/T1 ×V1=((273+627))/((273+27) )×4=900/300×4=12m3

## Set 5

1. The restraint imposed on the behavior of water is dependent on which of the following factors?
a) Nature and binding capacity of polar residues
b) Configuration of hydrophobic and hydrophilic areas
c) Mechanism which alter the structure of water
d) All of the mentioned

Answer: d [Reason:] All of the mentioned impose restraint on the behavior of water.

2. Which of the following is an advantage of semi moist food?
a) Ease in packaging and storage
b) Low in moisture, less bulky
c) Direct consumption and texture closer to normal food than dehydrated food
d) All of the mentioned

Answer: d [Reason:] All of the mentioned are advantages of semi moist food.

3. Which of the following law gives the relationship between the moles of water and the moles of solute in a solution and its water activity?
a) Hallinan law
b) Burgess law
c) Raoult’s law
d) None of the mentioned

Answer: c [Reason:] Raoult’s law gives the relationship between the moles of water and the moles of solute in a solution and its water activity.

4. Rice has a higher water activity than apples.
a) True
b) False

Answer: b [Reason:] Rice has a lesser water activity than apples. Apples contain higher water per 100 grams of dry material.

5. As the moisture content of a food decreases, a restraint is observed on the vapor pressure which is evident from the water activity.
a) True
b) False

Answer: a [Reason:] As the moisture content of a food decreases, a restraint is observed on the vapor pressure which is evident from the water activity.

6. Statement 1: When there is equilibrium between the vapor pressure and the percentage relative humidity, water activity is directly proportional to the percentage relative humidity.
Statement 2: Even a water activity as high as 0.85 for food items is considered to be very dry for substances.
a) True, False
b) True, True
c) False, False
d) False, True

Answer: b [Reason:] When there is equilibrium between the vapor pressure and the percentage relative humidity, water activity is directly proportional to the percentage relative humidity. Even a water activity as high as 0.85 for food items is considered to be very dry for substances.

7. Which of the following is true when a solute is added to water?
a) Concentration of water is reduced
b) Interaction with solute may break or increase the water structures
c) Both of the mentioned
d) Neither of the mentioned

Answer: c [Reason:] When a solute is added to water, concentration of water is reduced and interaction with solute may break or increase the water structures.

8. Statement 1: Sodium chloride has a higher water activity than sucrose.
Statement 2: Sucrose creates structures in water and reduces water activity below what they should be based on concentration alone.
a) True, False
b) True, True
c) False, False
d) False, True

Answer: b [Reason:] Sodium chloride has a higher water activity than sucrose. This is because, sucrose creates structures in water and reduces water activity below what they should be based on concentration alone.

9. Statement 1: Just like the vapor pressure on an individual component is higher than when it is in bulk, the water activity is low when in bulk.
Statement 2: Water activity is directly proportional to the surface tension and molecular weight of water and inversely proportional to density of water.
a) True, False
b) True, True
c) False, False
d) False, True

Answer: b [Reason:] Just like the vapor pressure on an individual component is higher than when it is in bulk, the water activity is low when in bulk. Water activity is directly proportional to the surface tension and molecular weight of water and inversely proportional to density of water.

10. If a dehydrated porous absorptive food is soaked in a solution whose viscosity is not too high to penetrate, then the food will absorb an amount of solution approximately equal to the amount of water it would normally absorb.
a) True
b) False

Answer: a [Reason:] If a dehydrated porous absorptive food is soaked in a solution whose viscosity is not too high to penetrate, then the food will absorb an amount of solution approximately equal to the amount of water it would normally absorb.

11. Semi moist food items work on the principle that the additives will diffuse into the food to an extent that the final concentration in the food and in the solution will be similar.
a) True
b) False

Answer: a [Reason:] Semi moist food items work on the principle that the additives will diffuse into the food to an extent that the final concentration in the food and in the solution will be similar.

12. Semi moist food items work on the principle of equilibrium, that is at a dry state, the food items absorb the solution and in the wet state, water is washed out with another liquid by diffusion.
a) True
b) False

Answer: a [Reason:] Semi moist food items work on the principle of equilibrium, that is at a dry state, the food items absorb the solution and in the wet state, water is washed out with another liquid by diffusion.

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