List of top Mathematics Questions on mathematical reasoning

The number of different permutations of all the letters of the word "PERMUTATION" such that any two consecutive letters in the arrangement are neither both vowels nor both identical is:
Which of the following statements is a tautology?

The number of values of $r \in\{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is :

Among the statements : 
\((S1)\) \((( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )\)
\((S2)\)\((( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))\)

Consider the following statements: 
P : I have fever 
Q: I will not take medicine 
R : I will take rest 
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:
The compound statement $(-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))$ is equivalent to

Equivalent statement to (p\(\to\)q) \(\vee\) (r\(\to\)q) will be

If gcd \( (m, n) = 1 \) and \[ 1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2022)^2 - (2023)^2 = 1012 \, m^2 n \] then \( m^2 - n^2 \) is equal to:

The number of seven-digit positive integers formed using the digits 1, 2, 3, and 4 only, and whose sum of the digits is 12, is         

The fractional part of the number \(\tfrac{4^{2022}}{15}\) is equal to:

The largest natural number \(n\) such that \(3^n\) divides \(66!\) is:
Maximum value n such that (66)! is divisible by 3n
Let 𝛂 be the remainder (22)\(^{2022}\) + (2022)\(^{22}\) is divided by 3 and ꞵ be the remainder when the same is divided by 7 then 𝛂\(^2\) + ꞵ\(^2\) is?
The statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent to
Let $p$ and $q$ be two statements Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to
The statement B⇒((∼A) ∨ B) is equivalent to :
The converse of ((~ p) ∧ q) ⇒ r is
Let \(p, q, r \)be three logical statements. Consider the compound statements
\(S_1 : ((~p) ∨q) ∨ ((~p) ∨r)\) and
\(S_2 :p→ (q∨r)\)
Then, which of the following is NOT true?
Which of the following statements is a tautology?
Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :
Consider the following two propositions:
\(P_1 : ~ (p → ~ q)\)
\(P_2: (p ∧ ~q) ∧ ((-~p) ∨ q)\)
If the proposition \(p → ((~p) ∨ q)\) is evaluated as FALSE, then:
Which of the following statements is a tautology?

Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to

\(\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}\)is equivalent to (~ p) when r is
Let r ∈ {p, q, ~p, ~q} be such that the logical statement r ∨ (~p) ⇒ (p ∧ q) ∨ r is a tautology. Then r is equal to :