Mathematical Reasoning PYQs - Last 10 Years

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Practice 163 MHT CET Mathematics questions from Mathematical Reasoning. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Mathematical Reasoning Questions

Showing 50 of 163 filtered questions.

1Mathematical Reasoning

The negation of the inverse of the statement $\sim p \vee \sim q$ is...

2Mathematical Reasoning

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 irrationa...

3Mathematical Reasoning

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 foll...

4Mathematical Reasoning

The contrapositive of $\sim q \rightarrow p$ is equivalent to

5Mathematical Reasoning

If $\sim p \vee q$ is false then which of the following is correct?

6Mathematical Reasoning

Which of the following logical statements is a tautology?

7Mathematical Reasoning

The logical statement $(p \vee q) \wedge [(\sim p \wedge q) \vee (p \wedge \sim q)] \wedge \sim q$ is logically equivalent to ...

8Mathematical Reasoning

The simplified switching circuit for the following circuit is

9Mathematical Reasoning

If $\sim p \to q$ is false and $q \leftrightarrow r$ is false, then the truth value of $(p, q, r)$ is...

10Mathematical Reasoning

If p, q, r are simple propositions with truth values T, F, T respectively, then which of the following is not a true statement?

11Mathematical Reasoning

If the truth value of $[(p \vee q) \wedge (q \to r) \wedge (\sim r)] \to (p \wedge q)$ is false, then which of the following is NOT true?

12Mathematical Reasoning

The negation of the converse of $p \vee q$ is

13Mathematical Reasoning

The contrapositive of the statement pattern $[p \vee (p \to q)] \to (p \wedge \sim q)$ is

14Mathematical Reasoning

The correct logical equivalence from the following is /are ___(I) $p \to (q \to r) \equiv (p \wedge q) \to r$(II) $(p \to q) \to r \equiv p \to (q \vee r)$(III) $(p \to q) \to r \equiv (p \to r) \wedge (\sim q \to r)$(IV) $p \to (q \to r) \...

15Mathematical Reasoning

The minimum number of switches in the simplified form of the following switching circuit is

16Mathematical Reasoning

If the truth value of the statement pattern $(\sim p \wedge q) \vee (\sim p \wedge \sim q) \vee (p \wedge \sim q)$ is $F$, then the truth values of $(p \vee \sim q)$ and $(p \to q)$ are $\ldots$ respectively.

17Mathematical Reasoning

In a switching circuit, if the combination $(S_1 \wedge S_2)$ is connected in parallel to the combination $(S_1' \wedge S_2')$, then the room is lit only when $\ldots$

18Mathematical Reasoning

If $p \to (q \vee \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \wedge r$ and $\sim p \to \sim q$ are :

19Mathematical Reasoning

If the statementsp: 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 increa...

20Mathematical Reasoning

The statement pattern $[(p \wedge q) \rightarrow (\sim p \vee r)] \vee [(\sim p \vee r) \rightarrow (p \wedge q)]$ is

21Mathematical Reasoning

The negation of $(p \wedge q) \rightarrow ((p \vee r) \rightarrow\, \sim q)$ is equivalent to ...

22Mathematical Reasoning

Which of the following statements is/are False?$S_1 : \exists\, n \in N$, such that $n^2 + n + 2$ is divisible by 4.$S_2 : \exists\, x \in N$, such that $x - 17 < 20$.$S_3 : \forall\, n \in N, \quad x^2 + 3x - 10 = 0$.$S_4 : \forall\, n \in...

23Mathematical Reasoning

Simplest form of the following switching circuit is

24Mathematical Reasoning

The negation of the contrapositive of the statement $(p \vee \sim q) \to (p \wedge \sim q)$ is

25Mathematical Reasoning

If the truth value of the compound statement $[(p \leftrightarrow q) \wedge (q \to r) \wedge \sim r] \to (p \wedge \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim(p \vee r) ...

26Mathematical Reasoning

The statements p, q and r have truth values True, False and False respectively. The truth values of a logical statement $[\sim(p \wedge \sim q) \vee (q \vee \sim r)]$ and its dual are, respectively.....

27Mathematical Reasoning

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

28Mathematical Reasoning

Negation of the statement "If an integer is greater than 4 and less than 5, then it is a multiple of 3", is

29Mathematical Reasoning

The dual of the statement pattern $(p \wedge \sim q) \longrightarrow (q \wedge \sim p)$ is equivalent to

30Mathematical Reasoning

The statement pattern $(p \wedge q) \rightarrow (r \vee \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively

31Mathematical Reasoning

Consider the statement patternsA. $(q \rightarrow p) \vee (p \rightarrow q)$B. $(\sim p \vee \sim q) \leftrightarrow \sim (p \wedge q)$C. $[(p \vee q) \wedge \sim p] \wedge \sim q$D. $(p \wedge q) \wedge (\sim p \vee \sim q)$then statement ...

32Mathematical Reasoning

Which of the following statements is logically equivalent to $\sim(p \leftrightarrow q)$ ?

33Mathematical Reasoning

If the truth value of the compound statement$[(p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)] \rightarrow (p \wedge q)$ is false, then the truth values of $p \rightarrow q$ and $q \rightarrow p$ are respectively...

34Mathematical Reasoning

The statement pattern $(p \vee q) \rightarrow \sim r$ is logically equivalent to

35Mathematical Reasoning

If the truth value of the compound statement $[(p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)] \rightarrow (p \wedge q)$ is False then the truth values of $p \rightarrow q$ and $q \rightarrow p$ are respectively......

36Mathematical Reasoning

If $A = \{1, 2, 3, 4, 5\}$, then which of the following statements is not true?

37Mathematical Reasoning

Consider the following statements$r$: If $p \rightarrow q$ is false then $p \vee q$ is false.$s$: If $p \leftrightarrow q$ is false then $p \vee q$ is false.The truth values of $r \rightarrow s$ and $s \rightarrow r$ are respectively ____

38Mathematical Reasoning

If $A = \{1, 2, 3, 4, 5, 6\}$ then which of the following is not true?

39Mathematical Reasoning

If p : switch $\mathrm{S}_1$ is closed, q : switch $\mathrm{S}_2$ is closed then correct interpretation from the following circuit is

40Mathematical Reasoning

The negation of statement pattern $(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow(\mathrm{p} \vee \sim \mathrm{q})$ is

41Mathematical Reasoning

Consider statements $\mathrm{p}: \mathrm{S}_1$ is closed; $\mathrm{q}: \mathrm{S}_2$ is closed; $\mathrm{r}: \mathrm{S}_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectiv...

42Mathematical Reasoning

If the truth value of the expression $[(p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)] \rightarrow(p \wedge q)$ is False, then truth values of $p, q, r$ are respectively.

43Mathematical Reasoning

Which of the following statement is a tautology?

44Mathematical Reasoning

If $p, q, r, s$ are statements, where, $\mathrm{p}: \mathrm{A}^2-\mathrm{B}^2=(\mathrm{A}-\mathrm{B})(\mathrm{A}+\mathrm{B}) ; \mathrm{A}, \mathrm{B}$ are matrices, $A B \neq B A$
q: $5 \leq 5$
r: ${ }^8 \mathrm{C}_1+{ }^8 \mathrm{C}_2+{ }^...

45Mathematical Reasoning

If the statements $p, q$ and $r$ are true, false and true statements respectively, then the truth value of the statement pattern $[\sim \mathrm{q} \wedge(\mathrm{p} \vee \sim \mathrm{q}) \wedge \sim \mathrm{r}] \vee \mathrm{p}$ and the trut...

46Mathematical Reasoning

The negation of the statement "The triangle is an equilateral or isosceles triangle and the triangle is not isosceles and it is right angled" is

47Mathematical Reasoning

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?

48Mathematical Reasoning

If $p \equiv$ The switch $S_1$ is closed, $q \equiv$ The switch $\mathrm{S}_2$ is closed, $\mathrm{r} \equiv$ switch $\mathrm{S}_3$ is closed, then symbolic form of following switching circuit is equivalent to

49Mathematical Reasoning

The contrapositive of the statement $\sim p \vee(q \wedge \sim r)$ is

50Mathematical Reasoning

Which of the following is the negation of the statement " For all M>0, there exist $x \in \mathrm{~s}$ such that $x \geqslant \mathrm{M}^{\prime \prime}$