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Mathematical Reasoning — JEE Main & Advanced Mathematics PYQs

204 previous year questions from Mathematical Reasoning with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

204 questionsMathematicsSolutions on every page
1

Negation of p ∧ q ∧ ~ p ∧ q is

JEE Main 2023 Solution View → 2

The statement ( p ∧ ( ~ q ) ) ∨ ( ( ~ p ) ∧ q ) ∨ ( ( ~ p ) ∧ ( ~ q ) ) is equivalent to _ _ _ _ _

JEE Main 2023 Solution View → 3

The negation of the statement ( ( A ∧ ( B ∨ C ) ) ⇒ ( A ∨ B ) ) ⇒ A is

JEE Main 2023 Solution View → 4

Among the two statements S 1 : p ⇒ q ∧ p ∧ ~ q is a contradiction and S 2 : p ∧ q ∨ ~ p ∧ q ∨ p ∧ ~ q ∨ ~ p ∧ ~ q is a t

JEE Main 2023 Solution View → 5

The converse of ~ p ∧ q ⇒ r is

JEE Main 2023 Solution View → 6

The number of ordered triplets of the truth values of p , q and r such that the truth value of the statement p ∨ q ∧ p ∨ r ⇒ q ∨ r is True, is equal t

JEE Main 2023 Solution View → 7

The statement ~ p ∨ ~ p ∧ q is equivalent to

JEE Main 2023 Solution View → 8

The negation of the statement p ∨ q ∧ q ∨ ~ r is

JEE Main 2023 Solution View → 9

The negation of ( p ∧ ( - q ) ) ∨ ( - p ) is equivalent to

JEE Main 2023 Solution View → 10

Negation of p → q → q → p is

JEE Main 2023 Solution View → 11

Among the statements S 1 : p ⇒ q ∨ ~ p ∧ q is a tautology S 2 : q ⇒ p ⇒ ~ p ∧ q is a contradiction

JEE Main 2023 Solution View → 12

Statement ( P ⇒ Q ) ∧ ( R ⇒ Q ) is logically equivalent to

JEE Main 2023 Solution View → 13

Which of the following statements is a tautology?

JEE Main 2023 Solution View → 14

The negation of the expression q ∨ ( ( ~ q ) ∧ p ) is equivalent to

JEE Main 2023 Solution View → 15

The number of values of r ∈ p , q , ~ p , ~ q for which p ∧ q ⇒ r ∨ q ∧ ( p ∧ r ⇒ q is a tautology, is :

JEE Main 2023 Solution View → 16

Consider: S 1 : p ⇒ q ∨ p ∧ ~ q is a tautology. S 2 : ~ p ⇒ ~ q ∧ ~ p ∨ q is a contradiction. Then

JEE Main 2023 Solution View → 17

Consider the following statements: P : I have fever Q : I will not take medicine R : I will take rest The statement "If I have fever, then I will take medicine and I will take rest

JEE Main 2023 Solution View → 18

Among the statements: S 1 : p ∨ q ⇒ r ⇔ p ⇒ r S 2 : p ∨ q ⇒ r ⇔ p ⇒ r ∨ q ⇒ r

JEE Main 2023 Solution View → 19

The statement B ⇒ ~ A ∨ B is not equivalent to :

JEE Main 2023 Solution View → 20

If p , q and r are three propositions, then which of the following combination of truth values of p , q and r makes the logical expression ( p ∨ q ) ∧ ( ( ~ p ) ∨

JEE Main 2023 Solution View → 21

Let △ , ∇ ∈ ∧ , ∨ be such that ( p → q ) △ ( p ∇ q ) is a tautology. Then

JEE Main 2023 Solution View → 22

The statement p ∧ ~ q ⇒ p ⇒ ~ q is

JEE Main 2023 Solution View → 23

Let p and q be two statements. Then ~ ( p ∧ ( p → ~ q ) is equivalent to

JEE Main 2023 Solution View → 24

The compound statement ( ~ ( P ∧ Q ) ) ∨ ( ( ~ P ) ∧ Q ) ⇒ ( ( ~ P ) ∧ ( ~ Q ) ) is equivalent to

JEE Main 2023 Solution View → 25

The statement p ⇒ q ∨ p ⇒ r is NOT equivalent to:

JEE Main 2022 Solution View → 26

The statement p ∧ q ⇒ p ∧ r is equivalent to

JEE Main 2022 Solution View → 27

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 village and i

JEE Main 2022 Solution View → 28

Let the operations * , ⊙ ∈ ∧ , ∨ . If p * q ⊙ p ⊙ ~ q is a tautology, then the ordered pair * , ⊙ is

JEE Main 2022 Solution View → 29

If the truth value of the statement P ∧ ~ R → ~ R ∧ Q is F , then the truth value of which of the following is F ?

JEE Main 2022 Solution View → 30

p ∧ r ⇔ p ∧ ~ q is equivalent to ~ p when r is

JEE Main 2022 Solution View → 31

Negation of the Boolean expression p ↔ q → p is

JEE Main 2022 Solution View → 32

The statement ~ p ⇔ ~ q ∧ q is:

JEE Main 2022 Solution View → 33

Consider the following statements: P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not honest. The negation of the statement "Ramu is intelligent and honest if and only if R

JEE Main 2022 Solution View → 34

Which of the following statements is a tautology?

JEE Main 2022 Solution View → 35

Negation of the Boolean statement p ∨ q ⇒ ~ r ∨ p is equivalent to:

JEE Main 2022 Solution View → 36

Let Δ ∈ ∧ , ∨ , ⇒ , ⇔ be such that p ∧ q Δ p ∨ q ⇒ q is a tautology. Then Δ is equal to

JEE Main 2022 Solution View → 37

The maximum number of compound propositions, out of p ∨ r ∨ s , p ∨ r ∨ ~ s , p ∨ ~ q ∨ s , ~ p ∨ ~ r ∨ s , ~ p ∨ ~ r ∨

JEE Main 2022 Solution View → 38

Let p , q , r be three logical statements. Consider the compound statements S 1 : ~ p ∨ q ∨ ~ p ∨ r and S 2 : p → q ∨ r Then, which of the following i

JEE Main 2022 Solution View → 39

Which of the following statement is a tautology?

JEE Main 2022 Solution View → 40

The boolean expression ~ p ∧ q ∨ q is equivalent to

JEE Main 2022 Solution View → 41

Let r ∈ P , q , ~ p , ~ q be such that the logical statement r ∨ ~ p ⇒ p ∧ q ∨ r is a tautology. Then r is equal to

JEE Main 2022 Solution View → 42

Let Δ , ∇ ∈ ∧ , ∨ be such that p ∇ q → p Δ q ∇ r is a tautology. Then p ∇ q ∆ r is logically equivalent to

JEE Main 2022 Solution View → 43

The negation of the Boolean expression ~ q ∧ p ⇒ ~ p ∨ q is logically equivalent to

JEE Main 2022 Solution View → 44

Consider the following two propositions : P 1 : ~ p → ~ q P 2 : p ∧ ~ q ∧ ~ p ∨ q If the proposition p → ~ p ∨ q is evaluated as FALSE, then

JEE Main 2022 Solution View → 45

Consider the following statements: A : Rishi is a judge. B : Rishi is honest. C : Rishi is not arrogant. The negation of the statement "if Rishi is a judge and he is not arrogant,

JEE Main 2022 Solution View → 46

The number of choices for Δ ∈ ∧ , ∨ , ⇒ , ⇔ , such that p Δ q ⇒ p Δ ~ q ∨ ~ p Δ q is a tautology, is

JEE Main 2022 Solution View → 47

Which of the following is equivalent to the Boolean expression p ∧ ~ q ?

JEE Main 2021 Solution View → 48

Negation of the statement ( p ∨ r ) ⇒ ( q ∨ r ) is :

JEE Main 2021 Solution View → 49

Let * , □ ∈ ∧ , ∨ be such that the Boolean expression ( p * ~ q ) ⇒ ( p □ q ) is a tautology. Then :

JEE Main 2021 Solution View → 50

The Boolean expression ( p ∧ q ) ⇒ r ∧ q ∧ p is equivalent to:

JEE Main 2021 Solution View → 51

The statement ( p ∧ ( p → q ) ∧ ( q → r ) ) → r is

JEE Main 2021 Solution View → 52

Consider the two statements : S 1 : ( p → q ) ∨ ( ~ q → p ) is a tautology. S 2 : ( p ∧ ~ q ) ∧ ( ~ p ∨ q ) is a fallacy. Then :

JEE Main 2021 Solution View → 53

If the truth value of the Boolean expression ( ( p ∨ q ) ∧ ( q → r ) ∧ ( ~ r ) ) → ( p ∧ q ) is false, then the truth values of the statements p

JEE Main 2021 Solution View → 54

Which of the following is the negation of the statement "for all M > 0 , there exists x ∈ S such that x ≥ M ' ' ?

JEE Main 2021 Solution View → 55

The compound statement P ∨ Q ∧ ~ P ⇒ Q equivalent to:

JEE Main 2021 Solution View → 56

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:

JEE Main 2021 Solution View → 57

The Boolean expression ( p ⇒ q ) ∧ ( q ⇒ ~ p ) is equivalent to :

JEE Main 2021 Solution View → 58

Which of the following Boolean expressions is not a tautology?

JEE Main 2021 Solution View → 59

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

JEE Main 2021 Solution View → 60

The Boolean expression p ∧ ~ q ⇒ q ∨ ~ p is equivalent to:

JEE Main 2021 Solution View → 61

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

JEE Main 2021 Solution View → 62

The missing value in the following figure is

JEE Main 2021 Solution View → 63

If the Boolean expression ( p ∧ q ) ⊛ ( p ⊗ q ) is a tautology, then ⊛ and ⊗ are respectively given by

JEE Main 2021 Solution View → 64

If the Boolean expression ( p ⇒ q ) ⇔ ( q * ( ~ p ) ) is a tautology, then the Boolean expression p * ( ~ q ) is equivalent to:

JEE Main 2021 Solution View → 65

Which of the following Boolean expression is a tautology ?

JEE Main 2021 Solution View → 66

Let F 1 A , B , C = A ∧ ~ B ∨ ~ C ∧ A ∨ B ∨ ~ A and F 2 A , B = A ∨ B ∨ B → ~ A be two logical expressions. Then :

JEE Main 2021 Solution View → 67

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

JEE Main 2021 Solution View → 68

The statement A → B → A is equivalent to :

JEE Main 2021 Solution View → 69

The negation of the statement ~ p ∧ p ∨ q is:

JEE Main 2021 Solution View → 70

For the statements p and q , consider the following compound statements: a   ~ q ∧ p → q → ~ p b   p ∨ q ∧ ~ p → q Then which of the f

JEE Main 2021 Solution View → 71

The statement among the following that is a tautology is:

JEE Main 2021 Solution View → 72

Consider the statement: "For an integer n , if n 3 - 1 is even, then n is odd". The contrapositive statement of this statement is:

JEE Main 2020 Solution View → 73

The negation of the Boolean expression p ∨ ( ~ p ∧ q ) is equivalent to :

JEE Main 2020 Solution View → 74

The statement p → q → p → p → p ∨ q is :

JEE Main 2020 Solution View → 75

The negation of the Boolean expression x ↔ ~ y is equivalent to:

JEE Main 2020 Solution View → 76

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

JEE Main 2020 Solution View → 77

Given the following two statements: S 1 : q ∨ p → p ↔ ~ q is a tautology S 2 : ~ q ∧ ~ p ↔ q is a fallacy. Then :

JEE Main 2020 Solution View → 78

Let p , q , r be three statements such that the truth value of p ∧ q → ~ q ∨ r is F . Then the truth values of p , q , r are respectively :

JEE Main 2020 Solution View → 79

The proposition p → ~ p ∧ ~ q is equivalent to :

JEE Main 2020 Solution View → 80

Which of the following is a tautology?

JEE Main 2020 Solution View → 81

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

JEE Main 2020 Solution View → 82

If p → p ∧ ~ q is false, then the truth values of p and q are respectively

JEE Main 2020 Solution View → 83

Negation of the statement: 5 is an integer or 5 is irrational is:

JEE Main 2020 Solution View → 84

Which of the following statement is a tautology?

JEE Main 2020 Solution View → 85

Which one of the following is a tautology?

JEE Main 2020 Solution View → 86

Let A , B , C and D be four non-empty sets. The contrapositive statement of “If A ⊆ B and B ⊆ D , then A ⊆ C ” is

JEE Main 2020 Solution View → 87

For two statements p and q , the logical statement p → q ∧ q → ~ p is equivalent to

JEE Main 2020 Solution View → 88

The logically equivalent proposition of p ⇔ q is

NTA Abhyas JEE Main 2020 Solution View → 89

The negation of p ∧ ( q → ∼ r ) is

NTA Abhyas JEE Main 2020 Solution View → 90

The contrapositive of the statement "If two triangles are identical, then they are similar" is

NTA Abhyas JEE Main 2020 Solution View → 91

If p ⇒ ~ p ∨ q is false, then the truth values of p and q are respectively

NTA Abhyas JEE Main 2020 Solution View → 92

If p : A man is happy and q : A man is rich are two statements, then the statement, "If a man is not happy, then he is not rich" can be written using logical operators as

NTA Abhyas JEE Main 2020 Solution View → 93

If p ⇒ q ∨ r is F a l s e , then the truth values of p ,   q ,   r are respectively (where T is T r u e and F is F a l s e )

NTA Abhyas JEE Main 2020 Solution View → 94

If p and q are two statements, then p ∨ ∼ p ⇒   ∼ q is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 95

For two statements p and q , the logical statement p ⇒ q ∧ q ⇒ ~ p is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 96

The contrapositive of ( p ∨ q ) ⇒ r is

NTA Abhyas JEE Main 2020 Solution View → 97

Which of the following is logically equivalent to ~ ( ~ p ⇒ q ) ?

NTA Abhyas JEE Main 2020 Solution View → 98

Consider three statements p : Suyash will come today evening q : Shalini will be at his home r : They will go to party. Then the statement ~ q ∧ ~ r ⇒ p is logically eq

NTA Abhyas JEE Main 2020 Solution View → 99

The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic." is

NTA Abhyas JEE Main 2020 Solution View → 100

Which of the following statement is equivalent to the statement "If 2 + 2 = 4 then India is a country"?

NTA Abhyas JEE Main 2020 Solution View → 101

Consider three statements p : Person ‘ A ’ passed in mathematics exam q : Person ‘ A ’ passed in physics exam r : Person ‘ A ’ passed in chemistry exam Then, the statement ~ ~ p ⇒

NTA Abhyas JEE Main 2020 Solution View → 102

Let p , q and r be three statements, then p → q → r is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 103

Let p , q and r be three statements. Consider two compound statements S 1 : p ⇒ q ⇒ r ≡ p ⇒ q ⇒ r S 2 : p ⇔ q ⇔ r ≡ p ⇔ q ⇔ r State in order, whether S 1 , S 2 are true or false. (

NTA Abhyas JEE Main 2020 Solution View → 104

If p and q are two statements, then which of the following statement is a tautology

NTA Abhyas JEE Main 2020 Solution View → 105

If p and q are two statements, then which of the following statements is not equivalent to p ⇔ p ⇒ q ?

NTA Abhyas JEE Main 2020 Solution View → 106

If p ⇒ q ∨ r is false, then the truth values of p ,   q and r respectively are (here, T is true and F is false)

NTA Abhyas JEE Main 2020 Solution View → 107

Let ⊕ and ⊗ are two mathematical operators. If p ⊕ q ⊗ r is equivalent to p ∧ q ⇒ r , then ⊕ and ⊗

NTA Abhyas JEE Main 2020 Solution View → 108

If p : " 4 is an odd number" and q : " 4 3 is an even number" are two statements, then which of the following statements is equivalent to ∼ p ⇒ q ?

NTA Abhyas JEE Main 2020 Solution View → 109

Let ⊕ and ⊗ are two mathematical operators. If p ⊕ p ⊗ q is not a tautology, then ⊕ and ⊗ can be

NTA Abhyas JEE Main 2020 Solution View → 110

Which of the following statements is not a fallacy?

NTA Abhyas JEE Main 2020 Solution View → 111

Let p : Maths is interesting and q : Maths is easy, then p ⇒ ~ p ∨ q is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 112

If p and q are two logical statements, then p ⇒ q ⇒ p is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 113

Which of the following is incorrect?

NTA Abhyas JEE Main 2020 Solution View → 114

The statement ~ p ⇔ q is not equivalent to

NTA Abhyas JEE Main 2020 Solution View → 115

If p ,   q and r are 3 statements, then the truth value of ~ p ∨ q ∧ ~ r ⇒ p is

NTA Abhyas JEE Main 2020 Solution View → 116

The statement p ⇔ q is not equivalent to

NTA Abhyas JEE Main 2020 Solution View → 117

Which of the following statements is false when p is true and q is false?

NTA Abhyas JEE Main 2020 Solution View → 118

The negation of ~ p ∧ q ∨ p ∧ ~ q is

NTA Abhyas JEE Main 2020 Solution View → 119

The converse of p ⇒ q ⇒ r is

NTA Abhyas JEE Main 2020 Solution View → 120

The statement ~ p ⇔ q ∧ p is equivalent to

NTA Abhyas JEE Main 2020 Solution View →
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