MHT CET · Maths · Mathematical Reasoning
Consider the following three statements
\(P: 11\) is a prime number.
Q: 7 is a factor of 176 .
\(R\) : LCM of 3 and 7 is 21 .
Then, the truth value of which one of the following statement is true?
- A \(P \vee(\sim Q \wedge R)\)
- B \((\sim P) \wedge(\sim Q \wedge R)\)
- C \((P \wedge Q) \vee(\sim R)\)
- D \((\sim P) \vee(Q \wedge R)\)
Answer & Solution
Correct Answer
(A) \(P \vee(\sim Q \wedge R)\)
Step-by-step Solution
Detailed explanation
\(P: 11\) is a prime number \((\mathrm{T})\)
\(Q: 7\) is a factor of \(176(\mathrm{~F})\)
\(R\) : L.C.M of 3 and 7 is 21 (T)
Now, \(P \vee(\sim Q \wedge R) \equiv \mathrm{T} \vee(\mathrm{T} \wedge \mathrm{T}) \equiv \mathrm{T}\)
\(Q: 7\) is a factor of \(176(\mathrm{~F})\)
\(R\) : L.C.M of 3 and 7 is 21 (T)
Now, \(P \vee(\sim Q \wedge R) \equiv \mathrm{T} \vee(\mathrm{T} \wedge \mathrm{T}) \equiv \mathrm{T}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The perimeter a square whose two sides have equations \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}\) and \(\frac{x}{2}=\frac{y-1}{3}=\frac{z+1}{4}\) isMHT CET 2025 Hard
- If \(\bar{a}\) and \(\bar{b}\) are vectors such that \(|\bar{a}+\bar{b}|=\sqrt{29}\) and \(\bar{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \bar{b}\), then a possible value of \((\bar{a}+\bar{b}) \cdot(-7 \hat{i}+2 \hat{j}+3 \hat{k})\) isMHT CET 2022 Medium
- If \(y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]\), then \(\frac{d y}{d x}=\)MHT CET 2020 Easy
- If one end of the diameter is \((1,1)\) and the other end lies on the line \(x+y=3\), then locus of centre of circle isMHT CET 2008 Medium
- The differential equation of all circles which pass through the origin and whose centres lie on \(\mathrm{Y}\)-axis isMHT CET 2023 Medium
- If \(\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} < x < \frac{\pi}{2}\) and \(f(0)=0\), then \(f(1)\) isMHT CET 2023 Medium
More PYQs from MHT CET
- Identify neutral ligand from following?MHT CET 2025 Easy
- Argument of the complex number \(\mathrm{z}=\frac{13-5 \mathrm{i}}{4-9 \mathrm{i}}, i=\sqrt{-1}\) isMHT CET 2025 Medium
- 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: \(\exists x \in \mathbb{N}\) such that \(x^2-3 x+2=0\) and \(\exists \mathrm{n} \in \mathbb{N}\) such that n is an odd number
D : \(3+\mathrm{i}\) is a complex number or \(\sqrt{2}+\sqrt{3}=\sqrt{5}\)MHT CET 2025 Medium - Two cars of masses \(m_{1}\) and \(m_{2}\) are moving in circles of radii \(r_{1}\) and \(r_{2}\) respectively. Their speeds are such that they make complete circles in the same time \(\mathrm{t}\). The ratio of their centripetal force isMHT CET 2020 Easy
- A projectile is thrown with an initial velocity \((\hat{a}+b \hat{j}) \mathrm{m} / \mathrm{s}\), where \(\hat{i}\) and \(\hat{j}\) are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, thenMHT CET 2021 Medium
- A mass \(m\) is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass executes S.H.M. of time period T . If the mass is increased by \(\mathrm{m}_0\), the periodic time becomes \(\frac{5 \mathrm{~T}}{4}\). The ratio \(\frac{\mathrm{m}_0}{\mathrm{M}}\) isMHT CET 2025 Medium