Q. In how many ways can 7 people be divided into 3 groups if one group must have 3 people?
A.
210
B.
300
C.
420
D.
560
Show solution
Solution
Choose 3 people from 7: C(7, 3) = 35. The remaining 4 can be divided into 2 groups in 2 ways. Total = 35 * 2 = 70.
Correct Answer:
B
— 300
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Q. In how many ways can the letters of the word 'BOOK' be arranged? (2022)
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Solution
The word 'BOOK' has 4 letters with 'O' repeating. The number of arrangements is 4! / 2! = 12.
Correct Answer:
C
— 16
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Q. In how many ways can the letters of the word 'LEVEL' be arranged?
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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 how many ways can the letters of the word 'SCHOOL' be arranged?
A.
720
B.
360
C.
480
D.
600
Show solution
Solution
The word 'SCHOOL' has 6 letters with 'O' repeating 2 times. The arrangements are 6! / 2! = 360.
Correct Answer:
B
— 360
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Q. In how many years will a sum of money triple itself at 10% per annum compound interest? (2023)
A.
10 years
B.
12 years
C.
15 years
D.
20 years
Show solution
Solution
Using the formula A = P(1 + r)^n, we set 3P = P(1 + 0.1)^n. Solving gives n ≈ 12 years.
Correct Answer:
B
— 12 years
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Q. In how many years will a sum of money triple itself at a compound interest rate of 10% per annum?
A.
10 years
B.
12 years
C.
15 years
D.
20 years
Show solution
Solution
Using the formula A = P(1 + r)^n, we set A = 3P and solve for n, which gives approximately 12 years.
Correct Answer:
B
— 12 years
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Q. In humans, the allele for brown eyes (B) is dominant over the allele for blue eyes (b). What is the genotype of a person with blue eyes? (2019)
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Solution
A person with blue eyes must have the genotype bb, as blue is recessive.
Correct Answer:
C
— bb
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Q. In mathematical logic, what is a 'fallacy'?
A.
A valid argument that leads to a false conclusion.
B.
An error in reasoning that renders an argument invalid.
C.
A type of mathematical proof.
D.
A method for solving equations.
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Solution
A fallacy is an error in reasoning that renders an argument invalid, often leading to incorrect conclusions.
Correct Answer:
B
— An error in reasoning that renders an argument invalid.
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Q. In measurements, what does precision refer to? (2022)
A.
Closeness to the true value
B.
Consistency of repeated measurements
C.
Range of values
D.
Average of measurements
Show solution
Solution
Precision refers to the consistency of repeated measurements, regardless of their accuracy.
Correct Answer:
B
— Consistency of repeated measurements
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Q. In measurements, what does the term 'precision' refer to? (2022)
A.
Closeness to the true value
B.
Consistency of repeated measurements
C.
Range of values
D.
Average of measurements
Show solution
Solution
Precision refers to the consistency of repeated measurements, regardless of their accuracy.
Correct Answer:
B
— Consistency of repeated measurements
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Q. In Mendel's experiments, which trait was observed to be dominant in pea plants? (2018)
A.
Green seed color
B.
Yellow seed color
C.
Wrinkled seeds
D.
Short plants
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Solution
In Mendel's experiments, yellow seed color was observed to be the dominant trait in pea plants.
Correct Answer:
B
— Yellow seed color
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Q. In Mendel's experiments, which trait was observed to be dominant over the other? (2018)
A.
Green seed color
B.
Yellow seed color
C.
Round seed shape
D.
Wrinkled seed shape
Show solution
Solution
In Mendel's experiments, yellow seed color was observed to be dominant over green seed color.
Correct Answer:
B
— Yellow seed color
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Q. In meteorology, what does the term 'anemometer' refer to?
A.
A device to measure temperature
B.
A device to measure humidity
C.
A device to measure wind speed
D.
A device to measure atmospheric pressure
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Solution
An anemometer is a device used to measure wind speed.
Correct Answer:
C
— A device to measure wind speed
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Q. In meteorology, what does the term 'isobar' refer to?
A.
Line of equal temperature
B.
Line of equal pressure
C.
Line of equal humidity
D.
Line of equal wind speed
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Solution
An 'isobar' is a line on a weather map that connects points of equal atmospheric pressure.
Correct Answer:
B
— Line of equal pressure
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Q. In Microsoft Word, what is the shortcut key to save a document?
A.
Ctrl + S
B.
Ctrl + P
C.
Ctrl + C
D.
Ctrl + V
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Solution
The shortcut key to save a document in Microsoft Word is Ctrl + S.
Correct Answer:
A
— Ctrl + S
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Q. In Microsoft Word, which shortcut key is used to save a document? (2023)
A.
Ctrl + S
B.
Ctrl + P
C.
Ctrl + C
D.
Ctrl + V
Show solution
Solution
The shortcut key 'Ctrl + S' is used to save a document in Microsoft Word.
Correct Answer:
A
— Ctrl + S
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Q. In modern mathematics, what does the term 'topology' refer to?
A.
The study of shapes and their properties under continuous transformations.
B.
The analysis of numerical data.
C.
The calculation of areas and volumes.
D.
The study of algebraic structures.
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Solution
Topology is the branch of mathematics that studies the properties of space that are preserved under continuous transformations.
Correct Answer:
A
— The study of shapes and their properties under continuous transformations.
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Q. In modern mathematics, what is the importance of 'linear algebra'?
A.
It focuses solely on geometric shapes.
B.
It deals with vector spaces and linear mappings.
C.
It is irrelevant to real-world applications.
D.
It simplifies calculus problems.
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Solution
Linear algebra is important as it deals with vector spaces and linear mappings, which are foundational in various applications across mathematics and science.
Correct Answer:
B
— It deals with vector spaces and linear mappings.
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Q. In modern mathematics, what is the role of 'topology'?
A.
To study the properties of space that are preserved under continuous transformations
B.
To analyze numerical data
C.
To solve algebraic equations
D.
To explore geometric shapes
Show solution
Solution
Topology is the branch of mathematics that studies the properties of space that are preserved under continuous transformations.
Correct Answer:
A
— To study the properties of space that are preserved under continuous transformations
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Q. In modular arithmetic, what is the multiplicative inverse of 3 mod 11?
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Solution
The multiplicative inverse of 3 mod 11 is 4, since 3 * 4 ≡ 12 ≡ 1 (mod 11).
Correct Answer:
A
— 4
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Q. In modular arithmetic, what is the multiplicative inverse of 3 modulo 11?
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Solution
The multiplicative inverse of 3 mod 11 is 4, since (3 * 4) mod 11 = 12 mod 11 = 1.
Correct Answer:
B
— 7
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Q. In modular arithmetic, which of the following is a valid operation?
A.
Adding two numbers and taking mod
B.
Subtracting two numbers and taking mod
C.
Multiplying two numbers and taking mod
D.
All of the above
Show solution
Solution
All operations (addition, subtraction, multiplication) are valid in modular arithmetic.
Correct Answer:
D
— All of the above
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Q. In modular arithmetic, which of the following is true for any integer a?
A.
a mod 1 = 0
B.
a mod a = 1
C.
a mod 0 is undefined
D.
a mod 2 = 0 or 1
Show solution
Solution
For any integer a, a mod 2 will always yield either 0 or 1, depending on whether a is even or odd.
Correct Answer:
D
— a mod 2 = 0 or 1
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Q. In modular arithmetic, which of the following is true for any integer k?
A.
k mod 1 = 0
B.
k mod k = 1
C.
k mod 0 is undefined
D.
k mod k = 0
Show solution
Solution
For any integer k, k mod k = 0, as k is divisible by itself.
Correct Answer:
D
— k mod k = 0
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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
Show solution
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
Show solution
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.
Show solution
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, the mass of the products is less than the mass of the reactants. What is this mass difference converted into? (2019)
A.
Kinetic energy
B.
Potential energy
C.
Binding energy
D.
Radiation
Show solution
Solution
The mass difference in nuclear fission is converted into kinetic energy of the fission fragments, according to Einstein's equation E=mc².
Correct Answer:
A
— Kinetic energy
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Q. In nuclear fission, the mass of the products is less than the mass of the reactants. What is this mass difference called? (2019)
A.
Nuclear mass
B.
Binding energy
C.
Mass defect
D.
Fission energy
Show solution
Solution
The mass difference in nuclear fission is referred to as the mass defect, which is converted into energy according to Einstein's equation E=mc².
Correct Answer:
C
— Mass defect
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Q. In nuclear fission, what is released apart from energy?
A.
Neutrons
B.
Protons
C.
Electrons
D.
Photons
Show solution
Solution
Nuclear fission releases neutrons along with a significant amount of energy.
Correct Answer:
A
— Neutrons
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