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JEE Mathematical Reasoning PYQs with Solutions

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

204 questionsMathematics2008–2023Answers + solutions

About Mathematical Reasoning PYQs

Mathematical Reasoning has 204 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 204 questions in this list come from JEE Main (135) and NTA Abhyas JEE Main (69), spanning 2008 to 2023. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2023: 24
  • 2022: 22
  • 2021: 25
  • 2020: 85
  • 2019: 16
  • 2018: 4
  • 2017: 3
  • 2016: 3
  • 2015: 3
  • 2014: 5
  • 2013: 5
  • 2012: 5

Mathematical Reasoning questions with solutions

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 tautology

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 to

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 (S1): (p ⇒ q) ∨ ((~ p) ∧ q) is a tautology (S2): (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: (S1): (p ⇒ q) ∨ (p ∧ (~ q)) is a tautology. (S2): ((~ 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

JEE Main 2023 Solution View → 18

Among the statements: (S1): ((p ∨ q) ⇒ r) ⇔ (p ⇒ r) (S2): ((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 ) ∨ r ) → ( ( ~ q ) ∨

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

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

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 ∨ ~ s, ~ p ∨ q ∨ ~ s, q ∨ r ∨ ~ s, q ∨ ~ r ∨ ~ s, ~ p ∨ ~ q ∨ ~

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 is NOT true?

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 ) ∇ 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

JEE Main 2022 Solution View → 46

The number of choices for Δ ∈ \ ∧ , ∨ , ⇒ , ⇔\ , such that (p ) ⇒ ((pΔ ~ q) ∨ ((~ p) )) 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, q, r respectively can be:

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

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 following statements is correct?

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 False , then the truth values of p, q, r are respectively (where T is True and F is False)

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 equivalent

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 ⇒ q)) ⇒ r)

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

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 → 121

The negation of the statement "If I will become rich, then I will open a school", is

NTA Abhyas JEE Main 2020 Solution View → 122

The compound statement (p → q) ∨ (p ∧ q) is logically equivalent to

NTA Abhyas JEE Main 2020 Solution View → 123

Which of the following is not a statement?

NTA Abhyas JEE Main 2020 Solution View → 124

If p and q are two logical statements, then (p ∨ q)→ (p → q) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 125

The statement p ⇒ (q ∧ p) is negation of the statement

NTA Abhyas JEE Main 2020 Solution View → 126

If p, q and r are three logical statements then the truth value of the statement (p ∧ q) ∨ (q → r) , where p is true, is

NTA Abhyas JEE Main 2020 Solution View → 127

The statement p → (q → p) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 128

Which of the following is not a tautology?

NTA Abhyas JEE Main 2020 Solution View → 129

Which of the following statements is not a tautology?

NTA Abhyas JEE Main 2020 Solution View → 130

What are the truth values of (∼ p ⇒ ∼ q) and (∼ p ⇒ q) respectively, when p and q always speak the truth in any argument?

NTA Abhyas JEE Main 2020 Solution View → 131

Equivalent statement of the statement “If 9 > 10 then 3 ^ 2 = 5 ” will be

NTA Abhyas JEE Main 2020 Solution View → 132

∼ (p ∨ q) ∨ (∼ p ∧ q) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 133

If x = 6 and y = - 2 then x - 2y = 9. The contrapositive of this statement is

NTA Abhyas JEE Main 2020 Solution View → 134

The compound statement (p → ∼ q) ∨ (p ∧ q) is logically equivalent to

NTA Abhyas JEE Main 2020 Solution View → 135

If p and q are logical statements, then (p ∧ q)→ (p → q) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 136

If p, q, r are simple propositions, then the truth value of (∼ p ∨ q) ∧ ∼ r ⇒ p is

NTA Abhyas JEE Main 2020 Solution View → 137

The negation of the statement “If I will become famous then I will open a school” is

NTA Abhyas JEE Main 2020 Solution View → 138

Negation of “Monu is in class X or Anu is in class XII ” is

NTA Abhyas JEE Main 2020 Solution View → 139

The compound statement (p ↔ q) ∨ (p ↔ q) is logically equivalent to

NTA Abhyas JEE Main 2020 Solution View → 140

If p, q and r are three logical statements, then the truth value of the statement (p ∧ q) ∨ (∼ q → r) , where p is true, is

NTA Abhyas JEE Main 2020 Solution View → 141

If p and q are logical statements, then ( p)→ (p → q) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 142

Which of the statements is not a fallacy?

NTA Abhyas JEE Main 2020 Solution View → 143

The logical statement& [∼ (∼ p ∨ ∼ q) ∨ (p ∧ r)] ∧ (q ∧ r) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 144

Which of the following option is incorrect?

NTA Abhyas JEE Main 2020 Solution View → 145

Consider three statements p: Aman will come today~ q: Aditi will be at her home r: They will go to party. Then, the statement (q ∧ ∼ r) ⇒ p is logically equivalent to

NTA Abhyas JEE Main 2020 Solution View → 146

Let p, q ~and& r be three statements, then (~ p → q) → r is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 147

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

NTA Abhyas JEE Main 2020 Solution View → 148

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 ⇒ q)) ⇒ r)

NTA Abhyas JEE Main 2020 Solution View → 149

Let p, q and r are three statements in which p is true. Consider two compound statements S _ 1 : (p ⇒ q) ⇒ r ≡ p ⇒ (q ⇒ r) S _ 2 : (p ⟺ q) ⟺ r ≡ p ⟺ (q ⟺ r) State in order

NTA Abhyas JEE Main 2020 Solution View → 150

Consider the statement p: If slope of a straight line is 1 then it is equally inclined to both the axes. Then, the contrapositive of the statement p & is

NTA Abhyas JEE Main 2020 Solution View → 151

For two statements p and q , the statement ( p ∨ ( q ) ) is equivalent to

NTA Abhyas JEE Main 2020 Solution View → 152

Consider the statement p: If a hexagon is regular then all its sides and angles are equal. The contrapositive of statement p is

NTA Abhyas JEE Main 2020 Solution View → 153

Negation of the statement, “I will work hard and party” is

NTA Abhyas JEE Main 2020 Solution View → 154

Which of the following is true? (i) If p is a statement then p is not a statement (ii) If p is a statement then p is also a statement (iii) Negation of " p: x is a positive real

NTA Abhyas JEE Main 2020 Solution View → 155

Consider the statement p : If a cylinder is right circular cylinder then its volume is (1)/(3) ^ 2 h . Contrapositive of the statement p is

NTA Abhyas JEE Main 2020 Solution View → 156

Which of the following statement is converse of the statement “If it rains then we will party”?

NTA Abhyas JEE Main 2020 Solution View → 157

The Boolean expression ∼ (p ⇒ (∼ q)) is equivalent to

JEE Main 2019 Solution View → 158

If the truth value of the statement p → (~ q ∨ r) is false (F), then the truth values of the statementsp, q, r are respectively

JEE Main 2019 Solution View → 159

The negation of the Boolean expression ~ s ∨ (~ r ∧ s) is equivalent to

JEE Main 2019 Solution View → 160

Which one of the following Boolean expression is a tautology?

JEE Main 2019 Solution View → 161

If p ⇒ (q ∨ r) is False , then the truth values of p, q, r are respectively, (where T is True and F is False )

JEE Main 2019 Solution View → 162

For any two statement p and q, the negative of the expression p ∨ (~ p ∧ q) is

JEE Main 2019 Solution View → 163

Which one of the following statements is not a tautology?

JEE Main 2019 Solution View → 164

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

JEE Main 2019 Solution View → 165

The expression ~ (~ p → q) is logically equivalent to

JEE Main 2019 Solution View → 166

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

JEE Main 2019 Solution View → 167

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

JEE Main 2019 Solution View → 168

If q is false and p ∧ q rightarrow r is true, then which one of the following statements is a tautology?

JEE Main 2019 Solution View → 169

Consider the following three statements: P: 5 is a prime number Q: 7 is a factor of 192 R: LCM of 5 and 7 is 35 Then the truth value of which one of the following statements is

JEE Main 2019 Solution View → 170

Consider the statement: " P(n): n ^ 2 - n + 41 is prime". Then which one of the following is true?

JEE Main 2019 Solution View → 171

The logical statement [~ (~ p ∨ q) ∨ (p ∧ r)] ∧ (~ q ∧ r) is equivalent to

JEE Main 2019 Solution View → 172

If the Boolean expression (p ⊕ q) ∧ (~ p ⊙ q) is equivalent to p ∧ q, where ⊕ , ⊙ ∈ \ ∧ , ∨\ ,then the ordered pair (⊕ , ⊙) is

JEE Main 2019 Solution View → 173

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

JEE Main 2018 Solution View → 174

If (p ∧ ∼ q) ∧(p ∧ r) arrow ∼ p ∨ q is false, then the truth values of p, q and r are respectively

JEE Main 2018 Solution View → 175

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

JEE Main 2018 Solution View → 176

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

JEE Main 2018 Solution View → 177

The contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

JEE Main 2017 Solution View → 178

The proposition (~ p) ∨ (p ∧ ~ q) is equivalent to

JEE Main 2017 Solution View → 179

The statement (p → q) → [(~ p → q) → q] is

JEE Main 2017 Solution View → 180

The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is

JEE Main 2016 Solution View → 181

Consider the following two statements: P : If 7 is an odd number, then 7 is divisible by 2 . Q : If 7 is a prime number, then 7 is an odd number. If V _ 1 is the truth value of

JEE Main 2016 Solution View → 182

The Boolean Expression (p ∧ ∼ q) ∨ q ∨ (∼ p ∧ q) is equivalent to

JEE Main 2016 Solution View → 183

Consider the following statements: P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement, "Suman is brilliant and dishonest if and only if

JEE Main 2015 Solution View → 184

The contrapositive of the statement "If it is raining, then I will not come", is

JEE Main 2015 Solution View → 185

The negation of ∽ s ∨ (∽ r ∧ s) is equivalent to

JEE Main 2015 Solution View → 186

The contrapositive of the statement ''if I am not feeling well, then I will go to the doctor" is

JEE Main 2014 Solution View → 187

Let p, q, r denote arbitrary statements. Then the logically equivalent of the statement p ⇒(q ∨ r) is:

JEE Main 2014 Solution View → 188

The proposition ∼(p ∨ ∼ q) ∨ ∼(p ∨ q) is logically equivalent to:

JEE Main 2014 Solution View → 189

The contrapositive of the statement "I go to school if it does not rain" is

JEE Main 2014 Solution View → 190

The statement ∼(p ↔ ~ q) is

JEE Main 2014 Solution View → 191

Let p and q be any two logical statements and r: p arrow(∼ p ∨ q) . If r has a truth value F , then the truth values of p and q are respectively:

JEE Main 2013 Solution View → 192

For integers m and n , both greater than 1, consider the following three statements : P: m divides n Q: m divides n^2 R: m is prime, then

JEE Main 2013 Solution View → 193

The statement p arrow(q arrow p) is equivalent to :

JEE Main 2013 Solution View → 194

Statement-1: The statement A arrow(B arrow A) is equivalent to A arrow(A ∨ B) . Statement-2: The statement ∼[(A ∧ B) arrow (∼ A ∨ B)] is a Tautology.

JEE Main 2013 Solution View → 195

Consider : Statement - I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy. Statement - II : (p → q) ↔ (~ q → ~ p) is a tautology.

JEE Main 2013 Solution View → 196

Let p and q denote the following statements p : The sun is shining q : I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play

JEE Main 2012 Solution View → 197

Let p and q be two Statements. Amongst the following, the Statement that is equivalent to p arrow q is

JEE Main 2012 Solution View → 198

The logically equivalent preposition of p ⇔ q is

JEE Main 2012 Solution View → 199

The Statement that is TRUE among the following is

JEE Main 2012 Solution View → 200

The negation of the statement "If I become a teacher, then I will open a school" is

JEE Main 2012 Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Mathematical Reasoning in other exams

BITSAT Mathematical Reasoning (14)