Engineering & Architecture Admissions
Q. In an RLC series circuit, if the resistance is increased while keeping the inductance and capacitance constant, what happens to the quality factor (Q)?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
The quality factor (Q) is given by Q = (1/R)√(L/C). Increasing R decreases Q.
Correct Answer: B — Decreases
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Q. In an RLC series circuit, what is the condition for resonance?
A.
XL = XC
B.
R = 0
C.
XL > XC
D.
R > XL
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Solution
Resonance in an RLC series circuit occurs when the inductive reactance (X_L) equals the capacitive reactance (X_C), i.e., X_L = X_C.
Correct Answer: A — XL = XC
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Q. In beta decay, which particle is emitted from the nucleus?
A.
Alpha particle
B.
Beta particle
C.
Gamma ray
D.
Neutron
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Solution
In beta decay, a beta particle (which is an electron or positron) is emitted from the nucleus.
Correct Answer: B — Beta particle
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Q. In Biot-Savart Law, what does the term 'dL' represent?
A.
Element of current
B.
Element of length
C.
Element of magnetic field
D.
Element of charge
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Solution
In Biot-Savart Law, 'dL' represents an infinitesimal element of length along the current-carrying conductor.
Correct Answer: B — Element of length
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Q. In digital communication, what does the term 'bit rate' refer to?
A.
The number of bits transmitted per second
B.
The number of bits stored in a device
C.
The number of bits in a signal
D.
The number of bits required for modulation
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Solution
Bit rate is defined as the number of bits transmitted per second in a digital communication system.
Correct Answer: A — The number of bits transmitted per second
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Q. In double-slit diffraction, what is the effect of increasing the distance between the slits on the fringe width?
A.
Fringe width increases
B.
Fringe width decreases
C.
Fringe width remains constant
D.
Fringe width becomes zero
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Solution
Increasing the distance between the slits increases the fringe width because the angle of diffraction increases.
Correct Answer: A — Fringe width increases
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Q. In double-slit diffraction, what is the path difference for constructive interference at the first order maximum?
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Solution
For constructive interference, the path difference must be an integer multiple of the wavelength, so for the first order maximum, it is λ.
Correct Answer: B — λ
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Q. In electrochemistry, what does the term 'reduction' refer to?
A.
Loss of electrons
B.
Gain of electrons
C.
Loss of protons
D.
Gain of protons
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Solution
Reduction refers to the gain of electrons in a chemical reaction.
Correct Answer: B — Gain of electrons
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Q. In electromagnetic induction, what is the role of the changing magnetic field?
A.
It creates a static electric field
B.
It induces a current in a conductor
C.
It has no effect
D.
It increases resistance
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Solution
A changing magnetic field induces an electromotive force (EMF) in a conductor, leading to the flow of current.
Correct Answer: B — It induces a current in a conductor
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Q. In forced oscillations, what is the effect of increasing the amplitude of the driving force?
A.
Decreases the amplitude of oscillation
B.
Increases the amplitude of oscillation
C.
Has no effect on amplitude
D.
Causes the system to stop oscillating
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Solution
Increasing the amplitude of the driving force generally increases the amplitude of the forced oscillation.
Correct Answer: B — Increases the amplitude of oscillation
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Q. In forced oscillations, what is the phase difference between the driving force and the displacement at resonance?
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
270 degrees
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Solution
At resonance, the phase difference between the driving force and the displacement is 0 degrees, meaning they are in phase.
Correct Answer: A — 0 degrees
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Q. In heat exchangers, which process is primarily utilized?
A.
Conduction
B.
Convection
C.
Radiation
D.
All of the above
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Solution
Heat exchangers primarily utilize conduction, convection, and radiation for heat transfer.
Correct Answer: D — All of the above
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Q. In how many ways can 3 boys and 2 girls be seated in a row?
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Solution
The total number of arrangements is (3+2)! = 5! = 120.
Correct Answer: B — 60
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Q. In how many ways can 3 different colored balls be arranged in a line?
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Solution
The number of arrangements of 3 different colored balls is 3! = 6.
Correct Answer: A — 6
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Q. In how many ways can 3 different colored balls be chosen from a set of 7?
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Solution
The number of ways to choose 3 from 7 is given by C(7,3) = 7!/(3!4!) = 35.
Correct Answer: A — 35
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Q. In how many ways can 3 men and 2 women be arranged in a line if the men must be together?
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Solution
Treat the 3 men as one unit. So, we have 3 units (MMM, W, W). The arrangements = 3! * 3! = 36.
Correct Answer: B — 120
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Q. In how many ways can 3 red balls and 2 blue balls be arranged in a row?
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Solution
The total arrangements = 5! / (3! * 2!) = 10.
Correct Answer: A — 10
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Q. In how many ways can 3 red, 2 blue, and 1 green balls be arranged in a line?
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Solution
The total arrangements = 6! / (3! * 2! * 1!) = 60.
Correct Answer: B — 120
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Q. In how many ways can 4 different books be chosen from a shelf of 10 books?
A.
210
B.
120
C.
240
D.
300
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Solution
The number of ways to choose 4 books from 10 is C(10, 4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 4 different books be selected from a shelf of 10 books?
A.
210
B.
120
C.
240
D.
300
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Solution
The number of ways to choose 4 books from 10 is C(10,4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 4 different colored balls be arranged in a line?
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Solution
The number of arrangements is 4! = 24.
Correct Answer: B — 24
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Q. In how many ways can 4 different colored balls be placed in 3 different boxes?
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Solution
Each ball can go into any of the 3 boxes, so the total ways = 3^4 = 81.
Correct Answer: A — 81
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Q. In how many ways can 4 different prizes be awarded to 3 students?
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Solution
The number of ways is P(4, 3) = 4! / 1! = 24.
Correct Answer: C — 36
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Q. In how many ways can 4 different prizes be distributed among 3 students?
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Solution
Each prize can go to any of the 3 students, so the total ways = 3^4 = 81.
Correct Answer: A — 81
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Q. In how many ways can 4 students be selected from a group of 10?
A.
210
B.
120
C.
240
D.
300
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Solution
The number of ways to select 4 students from 10 is C(10,4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 5 different colored balls be arranged in a box?
A.
60
B.
120
C.
100
D.
80
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Solution
The number of arrangements is 5! = 120.
Correct Answer: B — 120
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Q. In how many ways can 5 different flags be arranged on a pole?
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Solution
The number of arrangements of 5 different flags is 5! = 120.
Correct Answer: A — 120
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Q. In how many ways can 5 different items be selected from 10 items?
A.
252
B.
120
C.
200
D.
300
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Solution
The number of ways to select 5 items from 10 is C(10, 5) = 252.
Correct Answer: A — 252
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Q. In how many ways can 5 different objects be selected from 10 objects?
A.
252
B.
120
C.
10
D.
100
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Solution
The number of ways to select 5 objects from 10 is 10C5 = 10! / (5! * 5!) = 252.
Correct Answer: A — 252
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Q. In how many ways can 6 people be divided into 2 groups of 3?
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Solution
The number of ways to divide 6 people into 2 groups of 3 is 6! / (3! * 3! * 2!) = 20.
Correct Answer: A — 20
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