Engineering & Architecture Admissions
Q. In how many ways can 5 different objects be selected from 10 objects?
-
A.
252
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B.
120
-
C.
10
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D.
100
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?
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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Q. In how many ways can 7 different items be selected and arranged in a line?
-
A.
5040
-
B.
720
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C.
40320
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D.
10080
Solution
The number of arrangements of 7 different items is 7! = 5040.
Correct Answer: C — 40320
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Q. In how many ways can 7 different objects be arranged in a circle?
-
A.
720
-
B.
5040
-
C.
7200
-
D.
600
Solution
The number of arrangements in a circle is (n-1)! = 6! = 720.
Correct Answer: B — 5040
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Q. In how many ways can the letters of the word 'LEVEL' be arranged?
Solution
The word 'LEVEL' has 5 letters with 'L' and 'E' repeating. The arrangements = 5! / (2! * 2!) = 30.
Correct Answer: B — 30
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Q. In molecular orbital theory, which of the following orbitals is the highest energy in O2?
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A.
σ2p
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B.
π2p
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C.
σ2s
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D.
π2s
Solution
In O2, the π2p orbitals are the highest energy orbitals.
Correct Answer: B — π2p
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Q. In molecular orbital theory, which of the following statements is correct regarding the energy levels of orbitals?
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A.
σ orbitals are always lower than π orbitals.
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B.
π orbitals are always lower than σ orbitals.
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C.
σ* orbitals are always higher than π* orbitals.
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D.
Energy levels can vary based on the atoms involved.
Solution
The energy levels of molecular orbitals can vary depending on the specific atoms and their electronegativities.
Correct Answer: D — Energy levels can vary based on the atoms involved.
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Q. In nuclear fission, what is released apart from energy?
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A.
Neutrons
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B.
Protons
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C.
Electrons
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D.
Photons
Solution
Nuclear fission releases neutrons along with a significant amount of energy.
Correct Answer: A — Neutrons
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Q. In nuclear fission, what is the primary product of the reaction?
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A.
Helium
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B.
Neutrons
-
C.
Protons
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D.
Alpha particles
Solution
In nuclear fission, the primary products are neutrons, which can further induce fission in nearby nuclei.
Correct Answer: B — Neutrons
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Q. In nuclear fission, what is the primary product?
-
A.
Helium
-
B.
Neutrons
-
C.
Protons
-
D.
Alpha particles
Solution
Nuclear fission primarily produces neutrons along with other fission products.
Correct Answer: B — Neutrons
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Q. In nuclear fission, what is typically released as a result of the reaction?
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A.
Energy and neutrons
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B.
Energy and protons
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C.
Neutrons and electrons
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D.
Protons and energy
Solution
Nuclear fission releases a significant amount of energy and additional neutrons, which can induce further fission reactions.
Correct Answer: A — Energy and neutrons
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Q. In nuclear fusion, what is typically required to overcome the repulsion between nuclei?
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A.
High temperature and pressure
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B.
Low temperature and pressure
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C.
Magnetic fields
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D.
Chemical reactions
Solution
Nuclear fusion requires high temperature and pressure to overcome the electrostatic repulsion between positively charged nuclei.
Correct Answer: A — High temperature and pressure
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Q. In nuclear reactions, what is the term for the energy required to remove a nucleon from the nucleus?
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A.
Ionization energy
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B.
Binding energy
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C.
Dissociation energy
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D.
Activation energy
Solution
The binding energy is the energy required to remove a nucleon from the nucleus, reflecting the stability of the nucleus.
Correct Answer: B — Binding energy
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Q. In optical fibers, total internal reflection is utilized. What is the primary reason for this?
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A.
To increase the speed of light.
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B.
To minimize loss of light.
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C.
To change the color of light.
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D.
To focus light.
Solution
Total internal reflection in optical fibers minimizes the loss of light as it allows light to be guided through the fiber with minimal attenuation.
Correct Answer: B — To minimize loss of light.
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Q. In rolling motion, which type of energy is associated with the rotation of the object?
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A.
Translational kinetic energy
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B.
Rotational kinetic energy
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C.
Potential energy
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D.
Elastic potential energy
Solution
Rotational kinetic energy is associated with the rotation of the object in rolling motion.
Correct Answer: B — Rotational kinetic energy
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Q. In simple harmonic motion, the acceleration is maximum when the displacement is:
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A.
Maximum
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B.
Zero
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C.
Negative maximum
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D.
None of the above
Solution
In SHM, acceleration is maximum at maximum displacement (A).
Correct Answer: A — Maximum
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Q. In simple harmonic motion, the acceleration of the particle is maximum when it is at which position?
-
A.
Mean position
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B.
Amplitude
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C.
Halfway to amplitude
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D.
None of the above
Solution
In SHM, acceleration is maximum at the amplitude (maximum displacement).
Correct Answer: B — Amplitude
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Q. In simple harmonic motion, the maximum displacement from the mean position is called what?
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A.
Amplitude
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B.
Frequency
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C.
Period
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D.
Wavelength
Solution
The maximum displacement from the mean position in simple harmonic motion is called amplitude.
Correct Answer: A — Amplitude
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Q. In simple harmonic motion, the maximum speed occurs at which point?
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A.
At the mean position
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B.
At the amplitude
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C.
At one-fourth of the amplitude
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D.
At three-fourths of the amplitude
Solution
The maximum speed in SHM occurs at the mean position where the displacement is zero.
Correct Answer: A — At the mean position
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Q. In simple harmonic motion, the restoring force is directly proportional to which of the following?
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A.
Displacement
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B.
Velocity
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C.
Acceleration
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D.
Mass
Solution
The restoring force is directly proportional to the displacement from the mean position.
Correct Answer: A — Displacement
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Q. In simple harmonic motion, the total mechanical energy is conserved. What forms of energy are involved?
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A.
Kinetic and Potential Energy
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B.
Kinetic and Thermal Energy
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C.
Potential and Thermal Energy
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D.
Only Kinetic Energy
Solution
In SHM, the total mechanical energy is the sum of kinetic and potential energy, which remains constant.
Correct Answer: A — Kinetic and Potential Energy
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Q. In simple harmonic motion, the velocity of the particle is maximum when it is at which position?
-
A.
Mean position
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B.
Maximum displacement
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C.
Equilibrium position
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D.
None of the above
Solution
In simple harmonic motion, the velocity is maximum at the mean position where the displacement is zero.
Correct Answer: A — Mean position
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Q. In the Biot-Savart Law, what does the term 'dl' represent?
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A.
The length of the wire segment
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B.
The distance from the wire to the point of interest
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C.
The current flowing through the wire
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D.
The angle between the wire and the point
Solution
'dl' represents the infinitesimal length of the wire segment that contributes to the magnetic field at a point.
Correct Answer: A — The length of the wire segment
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Q. In the Bohr model of the hydrogen atom, what is the energy of the electron in the n=2 level?
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A.
-13.6 eV
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B.
-3.4 eV
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C.
-1.51 eV
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D.
0 eV
Solution
The energy of an electron in the nth level of hydrogen is given by E_n = -13.6 eV/n². For n=2, E_2 = -13.6 eV/2² = -3.4 eV.
Correct Answer: B — -3.4 eV
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Q. In the Bohr model of the hydrogen atom, what is the radius of the first orbit?
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A.
0.0529 nm
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B.
0.1 nm
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C.
0.529 nm
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D.
0.529 pm
Solution
The radius of the first orbit in the Bohr model is 0.529 Å or 0.0529 nm.
Correct Answer: C — 0.529 nm
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Q. In the complex [Ni(CO)4], what is the hybridization of the nickel atom?
-
A.
sp
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B.
sp2
-
C.
sp3
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D.
d2sp3
Solution
Nickel in [Ni(CO)4] undergoes sp3 hybridization as it forms four sigma bonds with CO ligands.
Correct Answer: C — sp3
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Q. In the context of adsorption, what does the term 'saturation' refer to?
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A.
Complete coverage of the adsorbent surface
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B.
Maximum temperature for adsorption
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C.
Equilibrium state of adsorption and desorption
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D.
None of the above
Solution
Saturation refers to the complete coverage of the adsorbent surface by the adsorbate.
Correct Answer: A — Complete coverage of the adsorbent surface
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Q. In the context of diffraction, what does the term 'angular width' refer to?
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A.
The angle between the first and second minima
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B.
The angle of incidence
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C.
The angle of reflection
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D.
The angle of diffraction
Solution
Angular width refers to the angle between the first and second minima in a diffraction pattern.
Correct Answer: A — The angle between the first and second minima
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Q. In the context of diffraction, what does the term 'coherence' refer to?
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A.
The ability of waves to interfere
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B.
The speed of light
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C.
The intensity of light
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D.
The wavelength of light
Solution
Coherence refers to the ability of waves to maintain a constant phase relationship, which is essential for producing clear interference patterns.
Correct Answer: A — The ability of waves to interfere
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Q. In the context of diffraction, what does the term 'resolution' refer to?
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A.
The ability to distinguish between two closely spaced objects
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B.
The intensity of the diffracted light
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C.
The wavelength of the light used
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D.
The width of the slit
Solution
Resolution refers to the ability to distinguish between two closely spaced objects, which is affected by diffraction.
Correct Answer: A — The ability to distinguish between two closely spaced objects
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