Mathematical Reasoning PYQs - Last 5 Years

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MathematicsAlgebra2019-2023

All Mathematical Reasoning PYQs Last 10 Years Create chapter test

Practice 103 JEE Main Mathematics questions from Mathematical Reasoning. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

103

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2019-2023

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103

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2019-2023

103

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103PYQs

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Last 5 Years Mathematical Reasoning Questions

Showing 50 of 103 filtered questions.

1Mathematical Reasoning

Which of the following is the negation of the statement "for all M > 0, there exists x\(\in\)S such that x \(\ge\) M" ?

2Mathematical Reasoning

The statement (p \(\wedge\) (p \(\to\) q) \(\wedge\) (q \(\to\) r)) \(\to\) r is :

3Mathematical Reasoning

The Boolean expression (p \(\wedge\) q) \(\Rightarrow\) ((r \(\wedge\) q) \(\wedge\) p) is equivalent to :

4Mathematical Reasoning

Let F1(A, B, C) = (A \(\wedge\) \(\sim\) B) \(\vee\) [\(\sim\)C \(\wedge\) (A \(\vee\) B)] \(\vee\) \(\sim\) A and F2(A, B) = (A \(\vee\) B) \(\vee\) (B \(\to\) \(\sim\)A) be two logical expressions. Then :

5Mathematical Reasoning

If the truth value of the Boolean expression \(\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right)} \right) \to \left( {p \wedge q} \right)\) is false, then the truth values of the statements p,...

6Mathematical Reasoning

Consider the two statements :(S1) : (p \(\to\) q) \(\vee\) (\(\sim\) q \(\to\) p) is a tautology .(S2) : (p \(\wedge\) \(\sim\) q) \(\wedge\) (\(\sim\) p \(\wedge\) q) is a fallacy.Then :

7Mathematical Reasoning

The Boolean expression \((p \Rightarrow q) \wedge (q \Rightarrow \sim p)\) is equivalent to :

8Mathematical Reasoning

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :

9Mathematical Reasoning

The statement A \(\to\) (B \(\to\) A) is equivalent to :

10Mathematical Reasoning

The contrapositive of the statement "If you will work, you will earn money" is :

11Mathematical Reasoning

The statement among the following that is a tautology is :

12Mathematical Reasoning

The negation of the statement \(\sim p \wedge (p \vee q)\) is :

13Mathematical Reasoning

For the statements p and q, consider the following compound statements :(a) \(( \sim q \wedge (p \to q)) \to \sim p\)(b) \(((p \vee q) \wedge \sim p) \to q\)Then which of the following statements is correct?

14Mathematical Reasoning

Which of the following Boolean expressions is not a tautology?

15Mathematical Reasoning

The Boolean expression \((p \wedge \sim q) \Rightarrow (q \vee \sim p)\) is equivalent to :

16Mathematical Reasoning

Consider the following three statements :(A) If 3 + 3 = 7 then 4 + 3 = 8(B) If 5 + 3 = 8 then earth is flat.(C) If both (A) and (B) are true then 5 + 6 = 17.Then, which of the following statements is correct?

17Mathematical Reasoning

Which of the following is equivalent to the Boolean expression p \(\wedge\) \(\sim\) q ?

18Mathematical Reasoning

If P and Q are two statements, then which of the following compound statement is a tautology?

19Mathematical Reasoning

If the Boolean expression (p \(\Rightarrow\) q) \(\Leftrightarrow\) (q * (\(\sim\)p) is a tautology, then the boolean expression (p * (\(\sim\)q)) is equivalent to :

20Mathematical Reasoning

If the Boolean expression \((p \wedge q) \odot (p \otimes q)\) is a tautology, then \(\odot\) and \(\otimes\) are respectively given by :

21Mathematical Reasoning

Which of the following Boolean expression is a tautology?

22Mathematical Reasoning

Negation of the statement :
\(\sqrt 5\) is an integer or 5 is an irrational is :

23Mathematical Reasoning

If p \(\to\) (p \(\wedge\) ~q) is false, then the truth values
of p and q are respectively :

24Mathematical Reasoning

Which one of the following is a tautology?

25Mathematical Reasoning

Which of the following statements is a tautology?

26Mathematical Reasoning

The logical statement (p \(\Rightarrow\) q) \(\Lambda\) ( q \(\Rightarrow\) ~p) is equivalent to :

27Mathematical Reasoning

Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A \(\subseteq\) B and B \(\subseteq\) D,
then A \(\subseteq\) C" is :

28Mathematical Reasoning

The negation of the Boolean expression p \(\vee\) (~p \(\wedge\) q) is equivalent to :

29Mathematical Reasoning

Consider the statement : ‘‘For an integer n, if n3 – 1 is even, then n is odd.’’ The contrapositive statement of this statement is :

30Mathematical Reasoning

The negation of the Boolean expression x \(\leftrightarrow\) ~ y is equivalent to :

31Mathematical Reasoning

The statement
\(\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)\) is :

32Mathematical Reasoning

Given the following two statements:
\(\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \sim q} \right)\) is a tautology
\(\left( {{S_2}} \right): \,\,\sim q \wedge \left( { \sim p \leftrightarrow q} \right)\)...

33Mathematical Reasoning

Contrapositive of the statement :
‘If a function f is differentiable at a, then it is also continuous at a’, is:

34Mathematical Reasoning

The proposition p
\(\to\) ~ (p
\(\wedge\) ~q) is equivalent
to :

35Mathematical Reasoning

Let p, q, r be three statements such that the
truth value of (p \(\wedge\) q) \(\to\) (\(\sim\)q \(\vee\) r) is F. Then the
truth values of p, q, r are respectively :

36Mathematical Reasoning

The contrapositive of the statement "If I reach the
station in time, then I will catch the train" is :

37Mathematical Reasoning

Which of the following is a tautology ?

38Mathematical Reasoning

If the Boolean expression
(p \(\oplus\) q) \(\wedge\) (~ p \(\odot\) q) is equivalent
to p \(\wedge\) q, where \(\oplus , \odot \in \left\{ { \wedge , \vee } \right\}\), then the
ordered pair \(\left( { \oplus , \odot } \right)\)...

39Mathematical Reasoning

The logical statement
[ \(\sim\) ( \(\sim\) p \(\vee\) q) \(\vee\) (p \(\wedge\) r)] \(\wedge\) (\(\sim\) q \(\wedge\) r) is equivalent to :

40Mathematical Reasoning

For any two statements p and q, the negation of
the expression
p \(\vee\) (~p \(\wedge\) q) is :

41Mathematical Reasoning

If p \(\Rightarrow\) (q \(\vee\) r) is false, then the truth values of p,
q, r are respectively :-

42Mathematical Reasoning

The contrapositive of the statement "If you are
born in India, then you are a citizen of India", is :

43Mathematical Reasoning

Which one of the following statements is not a
tautology?

44Mathematical Reasoning

The Boolean expression ((p \(\wedge\) q) \(\vee\) (p \(\vee\) \(\sim\) q)) \(\wedge\) (\(\sim\) p \(\wedge\) \(\sim\) q) is equivalent to :

45Mathematical Reasoning

The expression \(\sim\) (\(\sim\) p \(\to\) q) is logically equivalent to :

46Mathematical Reasoning

If the truth value of the statement p \(\to\) (~q \(\vee\) r) is false (F), then the truth values of the statements p, q, r are
respectively :

47Mathematical Reasoning

The Boolean expression ~(p \(\Rightarrow\) (~q)) is equivalent to :

48Mathematical Reasoning

If q is false and p \(\wedge\) q \(\leftrightarrow\) r is true, then which one of the following statements is a tautology ?

49Mathematical Reasoning

Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

50Mathematical Reasoning

Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ?