Mathematical Logic & Miscellaneous Algebra: JEE Main Mathematics Previous Year Questions

171 previous year questions from Mathematical Logic & Miscellaneous Algebra. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.If $A=(x\text{∈}R/\sqrt{x^2-8x+15}\text{∈}R)$ and $B=(x\text{∈}R/\frac{x-3}{2x-5}<\frac{x-6}{2x-11})$, then $A\text{∩}B=$
2. 2.The contrapositive statement of the statement "If $x$ is prime number, then $x$ is odd" is
3. 3.Contrapositive of statement : ‘If a function $f$ is differentiable at a, then it is also continuous at ‘a’ is:
4. 4.Boolean expression (p ⇒ q) ∧ (q ⇒∼ p) is equivalent to :
5. 5.The inverse of the proposition $\text{(}p\text{∧}\text{∼}q\text{)}\to r$ is
6. 6.Let $p\text{,}q\text{,}r$ be three statements such that the truth value of $\left(p\text{∧}q\right)\to \left(\text{∼}q\text{∨}r\right)$ is F. Then the truth values of…
7. 7.The proposition $p\to \text{∼}\left(p\text{∧}\text{∼}q\right)$ is equivalent to:
8. 8.The set of all real numbers satisfying the inequation $x^2-\text{|}x+2\text{|}+x>0$ is
9. 9.The contrapositive of the statement "If you will work, you will earn money" is:
10. 10.The negation of " $\text{∀}n\text{∈}N\text{,}n+7>6$ " is
11. 11.Let p : Ramesh listens to music. q : Ramesh is out of his village r : It is Sunday s : It is Saturday Then the statement "Ramesh listens to music only if he is in his vil…
12. 12.The negation of the statement "For all real numbers $x$ and $y\text{,}x+y=y+x^{\text{’}\text{’}}$ is
13. 13.If the Boolean expression $\text{(}p\text{∧}q\text{)}\text{⊛}\text{(}p\text{⊗}q\text{)}$ is a tautology, then $\text{⊛}$ and $\text{⊗}$ are respectively given by
14. 14.The compound statement…
15. 15.The negation of $p\to \text{(}\text{∼}p\text{∨}q\text{)}$ is
16. 16.The negation of the Boolean expression $x\text{↔}\text{∼}y$ is equivalent to:
17. 17.If the truth value of the statement (P $\wedge$(~R))$\to$ ((~R) $\wedge$Q) is F, then the truth value of which of the following is F?
18. 18.The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic."
19. 19.The statement $\text{[}\text{(}p\to q\text{)}\text{∧}\text{∼}q\text{]}\to r$ is a tautology, when $r$ is equivalent to
20. 20.The statement pattern $p\text{∧}\text{(}\text{∼}p\text{∧}q\text{)}$ is
21. 21.If $p\text{:}A$ man is happy, $q\text{:}$ A man is rich, then the symbolic form of $A$ man is neither happy nor rich is
22. 22.Given the following two statements: $\left(s_1\right)\text{:}\left(q\text{∨}p\right)\to \left(p\text{↔}\text{∼}q\right)$is a tautology:…
23. 23.If $p$ : Every square is a rectangle $q$ : Every rhombus is a kite then truth values of $p\to q$ and $p\text{↔}q$ are and respectively.
24. 24.The Boolean expression (p ∧ q) ⇒ ((r ∧ q) ∧ p) is equivalent to:
25. 25.The negation of the statement "If I become a teacher, then I will open a school", is