Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

Trigonometric Identities Quiz 1

August 19, 2025 by Muhammad Imdad Ullah

Test your understanding of Trigonometric Identities Quiz (Chapter 10, 1st Year Mathematics – Punjab Board) with this 20-MCQ quiz! Covers key concepts like distance formula, $cos(\alpha \pm \beta)$, $sin(\alpha\pm \beta)$, co-function identities, and angle transformations. Perfect for exam prep, admission tests, and job interviews, boost your problem-solving skills now! Let us start with the Trigonometric Identities Quiz now.

Trigonometric Identities Quiz with Answers First year Mathematics

Online Trigonometric Identities Quiz with Answers

Distance between the points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ is
The distance between the points $A(3, 8)$ and $(5, 6)$ is
Fundamental law of Trigonometry is $cos(\alpha – \beta) =$
$cos(\alpha – \beta)$ is equal to
$cos(\alpha + \beta)$ is equal to
$sin(\alpha – \beta)$ is equal to
$sin(\alpha + \beta)$ is equal to
$cos\left(\frac{\pi}{2} -\beta\right)$ is equal to
$cos\left(\beta + \frac{\pi}{2} \right)$ is equal to
$sin\left(\beta – \frac{\pi}{2}\right)$ is equal to
$cos(2\pi – \theta)$ is equal to
$sin(2\pi – \theta)$ is equal to
$tan(\alpha + \beta)$ is equal to
$tan(\alpha – \beta)$ is equal to
Angles associated with basic angles of measure $\theta$ to a right angle or its multiples are called
$sin\left(\frac{\pi}{2}-\theta\right)$ is equal to
$sin\left(\frac{\pi}{2} + \theta\right)$ is equal to
$cos\left(\frac{\pi}{2}-\theta\right)$ is equal to
$cos\left(\frac{\pi}{2} + \theta\right)$ is equal to
$tan\left(\frac{\pi}{2} – \theta\right)$ is equal to

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Logic and Critical Thinking MCQs 3

August 17, 2025 by Muhammad Imdad Ullah

Master Logic and Critical Thinking MCQs with 20 Important MCQs! Test your reasoning skills, strengthen argument analysis, and ace competitive exams. Perfect for students, psychologists, sociologists, and business professionals preparing for jobs and academic success. Boost your decision-making abilities today! Let us start with the Online Logic and Critical Thinking MCQs now.

Online Logic and Critical Thinking MCQs with Answers

———— is a set of statements, some of which attempt to provide a reason for thinking that some other is true.
————— is the fundamental principle of critical thinking.
————– is not a component of an argument.
————– are those which cannot be identified without understanding the concepts involved in the argument.
A ———— is simply a mistake in reasoning.
A ———— is just an argument with two premises and one conclusion, where every statement of the argument is a categorical statement.
A ———— is a valid argument that has all true premises.
A —————– is an argument whose conclusion cannot possibly be false, assuming that the premises are true.
The ————– is simply the argument whose premises indirectly support the main conclusion.
The ————— is the subject of the argument’s conclusion.
The predicate of the argument’s conclusion is called the —————-.
————— is the logic that deals with the logical relationship between categorical statements.
—————- is the truth-functional operator that switches the truth value of a proposition from false to true or from true to false.
This proposition is called a ———— because it contains the connective ‘and ‘ which connects two separate propositions.
A truth-functional proposition whose component statements are connected by the truth-functional operator ‘and’ is called
Fuzzy logic was introduced by ————–.
With a compound statement, the ability to determine its truth value can be a little more ————.
————— are the only kind that can lead to two conclusions from only one premise.
A false dilemma assumes that only ———- options exist.
A ————– is an illogical step in the formation of an argument.

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Logic Critical Thinking MCQs 2

August 15, 2025 by Muhammad Imdad Ullah

Master Logic Critical Thinking MCQS with 20 Key MCQs! Perfect for psychology, sociology, and business administration students—boost your exam prep, job readiness, and interview skills. Covering arguments, syllogisms, propositional logic, and more, this quiz sharpens analytical reasoning for academic and career success. Test your knowledge about Logic Critical Thinking MCQs now!

Online Logic Critical Thinking MCQs with Answers

The conclusion is guaranteed to be true in ———— an argument.
Critical thinking helps us to —————.
There are ————— types of arguments.
The supported statements of an argument are called —————.
The combination of simple statements using logical connectives is called ————–.
Necessity and possibility are the statements represented by —————.
Free logic is introduced by ————.
Model logic is the —————- system.
Logic is the study of correct ————–.
————– is essential for critical thinking.
Aristotle introduced a particular type of deductive argument called —————.
—————– the part of the premises about which we talk.
————- cause is the basic stuff out of which the thing is made.
————– arguments are general to specific.
———— in this syllogism, in which both premises and conclusions start with capital A.
———– is the branch of philosophy that seeks to organize reasoning.
In propositional logic, what is the negation of the statement “If it’s raining, then I’ll stay home”?
Argument is ————— if the conclusion follows from the premises.
Which of the following is NOT a valid form of categorical syllogism in classical logic is —————.
Who is known as the father of logic is —————-.

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