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Mere Teacher · Previous Year Questions
JEE Main Mathematics · Mathematical Logic & Miscellaneous Algebra · Set 1 (Q1-30)
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1.
If A=(x∈R/x2−8x+15∈R) and B=(x∈R/2x−5x−3<2x−11x−6), then A∩B=
(1)ϕ
(2)(25,3)∪(5,211)
(3)(25,421)
(4)(25,211)
2.
The contrapositive statement of the statement "If x is prime number, then x is odd" is
(1)If x is not a prime number, then x is odd
(2)If x is not a prime number, then x is not odd.
(3)If x is a prime number, then x is not odd
(4)If x is not odd, then x is not a prime number.
3.
Contrapositive of statement : ‘If a function f is differentiable at a, then it is also continuous at ‘a’ is:
(1)If a function f is continuous at a, then it is differentiable at a.
(2)If a function f is not continuous at a, then it is not differentiable at a.
(3)If a function f is not continuous at a, then it is differentiable at a.
(4)If a function f is continuous at a, then it is not differentiable at a.
4.
Boolean expression (p ⇒ q) ∧ (q ⇒∼ p) is equivalent to :
(1)∼ q
(2)q
(3)p∧q
(4)∼p
5.
The inverse of the proposition (p∧∼q)→r is
(1)(∼r)→(∼p)∨q
(2)(∼p)∨q→(∼r)
(3)r→p∧(∼q)
(4)(∼p)∨(∼q)→r
6.
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.
(1)T,F,T
(2)F,T,F
(3)T,T,T
(4)T,T,F
7.
The proposition p→∼(p∧∼q) is equivalent to:
(1)q
(2)(∼p)∧q
(3)(∼p)∨(∼q)
(4)(∼p)∨q
8.
The set of all real numbers satisfying the inequation x2−|x+2|+x>0 is
(1)[−2,−2)∪(2,∞)
(2)(−∞,−2)∪(2,∞)
(3)(−∞,−2)∪(2,∞)
(4)(−∞,−2)∪(2,∞)
9.
The contrapositive of the statement "If you will work, you will earn money" is:
(1)If you will not earn money, you will not work
(2)You will earn money, if you will not work
(3)If you will earn money, you will work
(4)To earn money, you need to work
10.
The negation of " ∀n∈N,n+7>6 " is
(1)∃n∈N, such that n+7≤6
(2)∃n∈N, such that n+7≥6
(3)∀n∈N,n+7≤6
(4)∃n∈N, such that n+7<6
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 village and it is Sunday or Saturday" can be expressed as
(1)((~q)∧ (r∨s))⇒ p
(2)(q∧(r∨s))⇒p
(3)p⇒(q∧(r∨s))
(4)p⇒((~q)∧(r∨s))
12.
The negation of the statement "For all real numbers x and y,x+y=y+x’’ is
(1)for some real numbers x and y, x+y=y+x
(2)for some real numbers x and y, x+y=y+x
(3)for some real numbers x and y, x−y=y−x
(4)for all real numbers x and y, x+y=y+x
13.
If the Boolean expression (p∧q)⊛(p⊗q) is a tautology, then ⊛ and ⊗ are respectively given by
(1)→,→
(2)∧,∨
(3)∨,→
(4)∧,→
14.
The compound statement ((P∧Q))∨((P)∧Q)⇒((P)∧(Q)) is equivalent to
(1)((P)∨Q)∧((Q)∨P)
(2)(Q)∨P
(3)((P)∨Q∧~Q
(4)(P)∨Q
15.
The negation of p→(∼p∨q) is
(1)p∨(p∨∼q)
(2)p→q
(3)p→∼(p∨q)
(4)p∧∼q
16.
The negation of the Boolean expression x↔∼y is equivalent to:
(1)(x∧∼y)∨(∼x∧y)
(2)(x∧y)∨(∼x∧∼y)
(3)(x∧y)∧(x∨∼y)
(4)(∼x∧y)∨(∼x∧∼y)
17.
If the truth value of the statement (P ∧(~R))→ ((~R) ∧Q) is F, then the truth value of which of the following is F?
(1)P ∨Q →~ R
(2)R ∨ Q →~ P
(3)~(P∨Q)→ ~R
(4)~(R∨Q)→ ~P
18.
The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic."
(1)The weather is fine but my friends will not come or we do not go for a picnic
(2)If my friends do not come or we do not go for picnic then weather will not be fine
(3)If the weather is not fine then my friends will not come or we do not go for a picnic
(4)The weather is not fine but my friends will come and we go for a picnic
19.
The statement [(p→q)∧∼q]→r is a tautology, when r is equivalent to
(1)p∧∼q
(2)q∨p
(3)p∧q
(4)∼q
20.
The statement pattern p∧(∼p∧q) is
(1)a tautology
(2)a contradiction
(3)equivalent to p∧q
(4)equivalent to p∨q
21.
If p:A man is happy, q: A man is rich, then the symbolic form of A man is neither happy nor rich is
(1)∼(p∨q)
(2)p∧q
(3)∼p∨∼q
(4)∼p∧q
22.
Given the following two statements: (s1):(q∨p)→(p↔∼q)is a tautology: (s2):∼q∧(∼p↔q)is a fallacy. Then :
(1)only(S1)is correct.
(2)boths1 and (s2) are correct.
(3)only(S2) is correct.
(4)bothS1 and (S2) are not correct.
23.
If p : Every square is a rectangle q : Every rhombus is a kite then truth values of p→q and p↔q are and respectively.
(1)F, F
(2)T, F
(3)F, T
(4)T,T
24.
The Boolean expression (p ∧ q) ⇒ ((r ∧ q) ∧ p) is equivalent to:
(1)(p ∧ q) ⇒ (r ∧ q)
(2)(q ∧ r) ⇒ (p ∧ q)
(3)(p ∧ q) ⇒ (r ∨ q)
(4)(p ∧ r) ⇒ (p ∧ q)
25.
The negation of the statement "If I become a teacher, then I will open a school", is
(1)Neither I will become a teacher nor I will open a school.
(2)I will not become a teacher or I will open a school.
(3)I will become a teacher and I will not open a school.
(4)Either I will not become a teacher or I will not open a school.
26.
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:
(1)The match will not be played and weather is not good and ground is wet.
(2)If the match will not be played, then either weather is not good or ground is wet.
(3)The match will be played and weather is not good or ground is wet.
(4)The match will not be played or weather is good and ground is not wet.
27.
Which of the following statement is a tautology?
(1)∼(p∨∼q)→p∨q
(2)p∨(∼q)→p∨q
(3)∼(p∧∼q)→p∨q
(4)∼(p∨∼q)→p∧q
28.
The equivalent form of the statement ∼(p→∼q) is
(1)p∧q
(2)p∧∼q
(3)p∨∼q
(4)∼p∨q
29.
Let A and B denote the statements A : cos α + cos β + cos γ = 0 B : sin α + sin β + sin γ = 0 If cos (β – γ) + cos (γ – α) + cos (α – β) = – 23 , then :
(1)A is false and B is true
(2)both A and B are true
(3)both A and B are false
(4)A is true and B is false
30.
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” is equivalent to
