List of top Mathematics Questions on Statements asked in MHT CET

If \(\sim p∨q\) is false then which of the following is correct?
The contrapositive of \(\sim q\rightarrow p\) is equivalent to
The statement having truth value 'T' from the following is
Consider the following statements.
\(p\): If \(3^4 > 4^3\), then \(3^3 > 4^4\)
\(q\): The roots of the equation \(x^2-2x+2 = 0\) are real if and only if Mumbai is in Maharashtra.
\(r\): Statement \(p\) is true or statement \(q\) is false.
Which of the following has truth value T (true)?
Which of the following is/are not true ?
I) If 1 is not a prime number, then 2 is not a prime number.
II) e is a vowel and \(12\times 3 = 36\)
III) It is not true that 14 is a composite number and 3 is even number.
IV) \(\sqrt{5}\) is an irrational number, but \(3+\sqrt{5}\) is a complex number.
The negation of the inverse of the statement \(\sim p∨\sim q\) is...
If \(\sim p\rightarrow q\) is false and \(q\leftrightarrow r\) is false, then the truth value of \((p,q,r)\) is...
If the truth value of \([(p∨q)∧(q\rightarrow r)∧(\sim r)]\rightarrow (p∧q)\) is false, then which of the following is NOT true?
If p, q, r are simple propositions with truth values T, F, T respectively, then which of the following is not a true statement?
The logical statement \((p∨q)∧[(\sim p∧q)∨(p∧\sim q)]∧\sim q\) is logically equivalent to ...
Which of the following logical statements is a tautology?
If \(sin^{-1}(x-2)+cos^{-1}(x)+tan^{-1}(x+2)+cot^{-1}(x+4) = sec^{-1}(\sqrt{k})-\frac{π}{2}\), then \(cos(2\,\text{cosec}^{-1}\sqrt{k-1}) = \ldots\)
If the statements
p: If voltage increases then current decreases.
q : If voltage does not increases then current does not decreases.
r : If current decreases then voltage increases.
s : If current does not decreases then voltage does not increases.
then which of the following pairs of statements having same meaning
If \(p\rightarrow (q∨\sim r)\) is false, then the truth values of \((p\leftrightarrow q)∧r\) and \(\sim p\rightarrow \sim q\) are :
If the truth value of the compound statement \([(p\leftrightarrow q)∧(q\rightarrow r)∧\sim r]\rightarrow (p∧\sim q)\) is false, then the truth values of the statement patterns \((p\rightarrow q)\leftrightarrow (q\rightarrow r)\) and \(\sim (p∨r)\rightarrow (q∧p)\) are, respectively ...
The negation of the contrapositive of the statement \((p∨\sim q)\rightarrow (p∧\sim q)\) is
Negation of the statement "If an integer is greater than 4 and less than 5, then it is a multiple of 3", is
The dual of the converse of the inverse of the logical statement \(p\rightarrow (q\rightarrow r)\) is equivalent to...
The statements p, q and r have truth values True, False and False respectively. The truth values of a logical statement \([\sim (p∧\sim q)∨(q∨\sim r)]\) and its dual are, respectively.....
Consider the following three statements:
(A) If $3 + 2 = 7$ then $4 + 3 = 8$.
(B) If $5 + 2 = 7$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 11$.
Which of the following statements is correct?
If p,q,r,s are statements, where: $p:A^{2}-B^{2}=(A-B)(A+B)$ for matrices $AB\ne BA$; $q:5\le5$; $r:{^{8}C_{1}+{}^{8}C_{2}+...+^{8}C_{8}=256}$; $s$: Max value of ${}^{8}C_{r}$ is 70. The statement with truth value true is:

Which of the following statements has the truth value \(T\)?
A. Cube roots of unity are in Geometric Progression and their sum is \(1\) 
B. \[ 4 + 7 > 10 \iff 2 + 8 < 10 \] 
C. \[ \exists x \in \mathbb{N} \text{ such that } x^2 - 3x + 2 = 0 \text{ and } \exists n \in \mathbb{N} \text{ such that } n \text{ is an odd number} \] 
D. \[ 3+i \text{ is a complex number } \; \text{or} \; \sqrt{2}+\sqrt{3}=\sqrt{5} \]

If \( x \neq 0 \), then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]
The negation of the statement "The number is an odd number if and only if it is divisible by 3."