Q. In how many ways can 3 red, 2 blue, and 1 green balls be arranged in a line?
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
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
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?
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?
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?
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?
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
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
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?
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
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
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 different objects be selected and arranged in a line?
-
A.
720
-
B.
600
-
C.
840
-
D.
960
Solution
The number of arrangements of 6 different objects is 6! = 720.
Correct Answer: A — 720
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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
-
C.
40320
-
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 filled first?
-
A.
σ2s
-
B.
σ*2s
-
C.
π2p
-
D.
σ2p
Solution
According to the Aufbau principle, the σ2s orbital is filled first before any other orbitals.
Correct Answer: A — σ2s
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Q. In molecular orbital theory, which of the following orbitals is the highest energy in O2?
-
A.
σ2p
-
B.
π2p
-
C.
σ2s
-
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?
-
A.
σ orbitals are always lower than π orbitals.
-
B.
π orbitals are always lower than σ orbitals.
-
C.
σ* orbitals are always higher than π* orbitals.
-
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?
-
A.
Neutrons
-
B.
Protons
-
C.
Electrons
-
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?
-
A.
Helium
-
B.
Neutrons
-
C.
Protons
-
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?
-
A.
Energy and neutrons
-
B.
Energy and protons
-
C.
Neutrons and electrons
-
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?
-
A.
High temperature and pressure
-
B.
Low temperature and pressure
-
C.
Magnetic fields
-
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?
-
A.
Ionization energy
-
B.
Binding energy
-
C.
Dissociation energy
-
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?
-
A.
To increase the speed of light.
-
B.
To minimize loss of light.
-
C.
To change the color of light.
-
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?
-
A.
Translational kinetic energy
-
B.
Rotational kinetic energy
-
C.
Potential energy
-
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:
-
A.
Maximum
-
B.
Zero
-
C.
Negative maximum
-
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
-
B.
Amplitude
-
C.
Halfway to amplitude
-
D.
None of the above
Solution
In SHM, acceleration is maximum at the amplitude (maximum displacement).
Correct Answer: B — Amplitude
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