Q. In how many ways can 4 different books be arranged on a shelf?
Show solution
Solution
The number of arrangements of 4 different books is 4! = 24.
Correct Answer:
B
— 24
Learn More →
Q. In how many ways can 4 different fruits be selected from a basket of 10 fruits?
A.
210
B.
120
C.
240
D.
300
Show solution
Solution
The number of ways to choose 4 fruits from 10 is given by 10C4 = 210.
Correct Answer:
A
— 210
Learn More →
Q. In how many ways can 4 different gifts be distributed among 3 children if each child can receive any number of gifts?
Show solution
Solution
Each gift can go to any of the 3 children, so the total ways are 3^4 = 81.
Correct Answer:
A
— 81
Learn More →
Q. In how many ways can 4 different gifts be distributed among 3 children?
Show solution
Solution
Each gift can go to any of the 3 children, so the total ways are 3^4 = 81.
Correct Answer:
A
— 81
Learn More →
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
Learn More →
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
Learn More →
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
Learn More →
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.
Show solution
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.
Learn More →
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.
Show solution
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.
Learn More →
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.
Show solution
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.
Learn More →
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
Learn More →
Q. In modular arithmetic, what is the multiplicative inverse of 3 mod 11?
Show solution
Solution
The multiplicative inverse of 3 mod 11 is 4, since 3 * 4 ≡ 12 ≡ 1 (mod 11).
Correct Answer:
A
— 4
Learn More →
Q. In modular arithmetic, what is the multiplicative inverse of 3 modulo 11?
Show solution
Solution
The multiplicative inverse of 3 mod 11 is 4, since (3 * 4) mod 11 = 12 mod 11 = 1.
Correct Answer:
B
— 7
Learn More →
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
Learn More →
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
Learn More →
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
Learn More →
Q. In polynomial long division, what is the first step when dividing 2x^3 + 3x^2 - x + 4 by x + 2?
A.
Divide the leading term of the dividend by the leading term of the divisor.
B.
Multiply the entire divisor by the first term of the quotient.
C.
Subtract the product from the dividend.
D.
Bring down the next term from the dividend.
Show solution
Solution
The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor.
Correct Answer:
A
— Divide the leading term of the dividend by the leading term of the divisor.
Learn More →
Q. In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x?
A.
Divide the leading term of the dividend by the leading term of the divisor.
B.
Multiply the divisor by the leading term of the dividend.
C.
Subtract the product from the dividend.
D.
Write down the remainder.
Show solution
Solution
The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor.
Correct Answer:
A
— Divide the leading term of the dividend by the leading term of the divisor.
Learn More →
Q. In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x + 1?
A.
Multiply the divisor by the leading term of the dividend.
B.
Subtract the product from the dividend.
C.
Identify the degree of both polynomials.
D.
Write the remainder.
Show solution
Solution
The first step in polynomial long division is to multiply the divisor by the leading term of the dividend.
Correct Answer:
A
— Multiply the divisor by the leading term of the dividend.
Learn More →
Q. In polynomial long division, what is the first step when dividing 4x^3 by 2x?
A.
Multiply 2x by 2x^2.
B.
Subtract 2x from 4x^3.
C.
Divide 4 by 2.
D.
Add the exponents.
Show solution
Solution
The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor, which in this case is 4x^3 ÷ 2x = 2x^2.
Correct Answer:
A
— Multiply 2x by 2x^2.
Learn More →
Q. In probability theory, what does a probability of 0 indicate?
A.
An event is certain to occur.
B.
An event is impossible.
C.
An event is likely to occur.
D.
An event has an equal chance of occurring.
Show solution
Solution
A probability of 0 indicates that an event is impossible and cannot occur.
Correct Answer:
B
— An event is impossible.
Learn More →
Q. In probability theory, what does the term 'independent events' mean?
A.
Events that cannot occur at the same time.
B.
Events where the outcome of one does not affect the other.
C.
Events that are mutually exclusive.
D.
Events that have the same probability of occurring.
Show solution
Solution
Independent events are defined as events where the outcome of one does not affect the outcome of the other, a key concept in probability theory.
Correct Answer:
B
— Events where the outcome of one does not affect the other.
Learn More →
Q. In probability theory, what does the term 'independent events' refer to?
A.
Events that cannot occur at the same time
B.
Events where the outcome of one does not affect the other
C.
Events that are mutually exclusive
D.
Events that are guaranteed to happen
Show solution
Solution
Independent events are those where the occurrence of one event does not influence the occurrence of another, a key concept in probability.
Correct Answer:
B
— Events where the outcome of one does not affect the other
Learn More →
Q. In resource allocation, what does the term 'scarcity' imply?
A.
Resources are abundant and easily accessible.
B.
There is a limited availability of resources relative to demand.
C.
Resources can be allocated without any constraints.
D.
All resources are equally important.
Show solution
Solution
Scarcity implies that resources are limited compared to demand, making option 1 the correct answer.
Correct Answer:
B
— There is a limited availability of resources relative to demand.
Learn More →
Q. In resource allocation, what does the term 'trade-off' refer to?
A.
The process of allocating resources without any constraints.
B.
The balance between different resource needs and their availability.
C.
The elimination of all costs associated with resource use.
D.
The equal distribution of resources among all stakeholders.
Show solution
Solution
A trade-off in resource allocation refers to the balance between different resource needs and their availability, making option 1 the correct interpretation.
Correct Answer:
B
— The balance between different resource needs and their availability.
Learn More →
Q. In statistics, what does a 'normal distribution' imply?
A.
Data is uniformly distributed.
B.
Data is symmetrically distributed around the mean.
C.
Data has no outliers.
D.
Data is always positively skewed.
Show solution
Solution
A normal distribution implies that data is symmetrically distributed around the mean, forming a bell-shaped curve.
Correct Answer:
B
— Data is symmetrically distributed around the mean.
Learn More →
Q. In statistics, what does the term 'standard deviation' measure?
A.
The average of a data set
B.
The spread or dispersion of a data set
C.
The midpoint of a data set
D.
The maximum value in a data set
Show solution
Solution
Standard deviation measures the spread or dispersion of a data set, indicating how much the values deviate from the mean.
Correct Answer:
B
— The spread or dispersion of a data set
Learn More →
Q. In statistics, what does the term 'variance' measure?
A.
The average of a set of numbers
B.
The spread of a set of data points
C.
The median of a data set
D.
The mode of a data set
Show solution
Solution
Variance measures the spread of a set of data points, indicating how much the data points differ from the mean.
Correct Answer:
B
— The spread of a set of data points
Learn More →
Q. In team formation, what does the term 'groupthink' refer to?
A.
A collaborative decision-making process
B.
A phenomenon where the desire for harmony leads to poor decisions
C.
An effective brainstorming technique
D.
A method for conflict resolution
Show solution
Solution
'Groupthink' refers to a phenomenon where the desire for harmony and conformity in a group results in irrational or dysfunctional decision-making.
Correct Answer:
B
— A phenomenon where the desire for harmony leads to poor decisions
Learn More →
Q. In team formation, what does the term 'norming' refer to?
A.
Establishing team goals
B.
Resolving conflicts
C.
Developing team norms and standards
D.
Evaluating team performance
Show solution
Solution
Norming is the stage where team members establish norms and standards for how they will work together.
Correct Answer:
C
— Developing team norms and standards
Learn More →
Showing 3001 to 3030 of 5536 (185 Pages)
