JEE Main Mathematics - Mathematical Reasoning
Exam Duration: 60 Mins Total Questions : 30
Which among the following is a conjunction?
- (a)
12+12=24 or 12 is greater than 10
- (b)
India is in Asia Lucknow is in UP
- (c)
2+2=4 and 12 is greater than 10
- (d)
None of the above
The negation of '12>4' is
- (a)
\(12\le4\)
- (b)
13>5
- (c)
12>3
- (d)
\(12\ge 4\)
If \(p\leftrightarrow q\) is true, then which of the following is true?
- (a)
p is true and q is false
- (b)
p is false and q is true
- (c)
p is true and q is true
- (d)
None of the above
Which among the following is not a negation of 'The Sun is a star'?
- (a)
The Sun is not a star.
- (b)
It is not the case that Sun is a star.
- (c)
It is false that the Sun is a star.
- (d)
It is true that the Sun is a star.
The value of ~(~p) is
- (a)
~p
- (b)
p~
- (c)
p
- (d)
q
Which of the following is wrong form of If p, then q' ?
- (a)
p is sufficient condition for q
- (b)
p only if q
- (c)
q is necessary condition for p
- (d)
\(\sim q\rightarrow p\)
Which among the following is equivalent to \(r\leftrightarrow s\) ?
- (a)
\(\left( r\wedge s \right) \vee \left( r\vee s \right) \)
- (b)
\(\left( r\vee s \right) \vee \left( r\vee \sim s \right) \)
- (c)
\(\left( \sim r\vee s \right) \vee \left( r\vee s \right) \)
- (d)
\(\left( r\wedge s \right) \vee \left( -r\wedge \sim s \right) \)
If \(p\rightarrow \left( \sim p\vee q \right) \) is false, then the truth value of p and q are respectively
- (a)
F,F
- (b)
T,T
- (c)
T,F
- (d)
F,T
Which of the following proposition is true?
- (a)
\(\sim (p\leftrightarrow q)\equiv \sim (p\rightarrow q)\wedge \sim (q\rightarrow p)\)
- (b)
\(\sim (p\rightarrow \sim q)\equiv \sim p\wedge q\)
- (c)
\(\sim (\sim p\rightarrow \sim q)\equiv \sim p\wedge q\)
- (d)
\((p\rightarrow \sim q)\equiv (\sim p\Rightarrow \sim q)\)
Which of the following sentences is not a statement?
- (a)
Two plus three is ten
- (b)
Every square is a triangle
- (c)
Sun rises in the East
- (d)
Everyone in this room is bold
Which of the following is not logically equivalent to the following proposition?
"A real number is either rational or irrational".
- (a)
If a number is neither rational nor irrational, then it is not real
- (b)
If a number is not a rational or not an irrational, then it is real
- (c)
If a number is not real, then it is neither rational nor irrational
- (d)
If a number is real, then it is rational or irrational
The sentence "There are 35 days in a month" is
- (a)
a statement
- (b)
not a statement
- (c)
may be a statement or not
- (d)
None of the above
Which of the following is a statement?
- (a)
Please help me
- (b)
Hurrah! India has won the match
- (c)
Good night to all
- (d)
17 is a prime number
Which of the following compound statements is true after writing the component statements of each compound statement?
- (a)
A line is straight and extends indefinitely in both directions
- (b)
0 is greater than every positive integer and less than every negative integer
- (c)
All living things have two legs and two eyes
- (d)
42 is divisible by 4 and 5
If p: It is snowing, q : I am cold, then the compound statement "It is snowing and it is not that I am cold" is given by
- (a)
p\(\wedge \)(~q)
- (b)
p \(\wedge \) q
- (c)
(~p)\(\wedge \)q
- (d)
(~p)\(\wedge \)(~q)
Which of the following statements is "inclusive or" statement?
- (a)
Sun rises or moon sets
- (b)
All integers are positive or negative
- (c)
Two lines intersect at a point or are parallel
- (d)
The school is closed if it is holiday or a Sunday
The contrapositive and converse of the statement : "If the two lines are parallel, then they do not interest in the same plane" is
- (a)
If the two straight lines intersect in a plane, the the lines are not parallel.
If the two lines do not intersect in the same plane, then the two lines are parallel - (b)
If the two straight lines do not intersect in a plane, then the lines are parallel.
If the two lines do not intersect in the same plane, then the two lines are parallel - (c)
If the two straight lines intersect in a plane, then the lines are not parallel.
If the two lines do not intersect in the same plane, then the two lines are not parallel. - (d)
None of these
Which of the following is the converse of the statement? "If Billu secure good marks, then he will get a bicycle
- (a)
If Billu will not get bicycle, then he will not
secure good marks - (b)
If Billu will get a bicycle, then he will secure
good marks - (c)
If Billu will get a bicycle, then he will not secure good marks
- (d)
If Billu will not get a bicycle, then he will secure good marks
The contrapositive and converse of the statement "I go to beach whenever it is a sunny day" is
- (a)
(i) If it is not a sunny day, then I do not go to beach.
(ii) If it is a sunny day, then I go to beach. - (b)
(i) If it is a sunny day, then I do not go to beach.
(ii) If it is a sunny day, then I go to beach - (c)
(i) If it is not a sunny day, then I go to beach.
(ii) If it is not a sunny day, then I go to beach - (d)
None of these
If P : The unit digit of an integer is zero and q : It is divisble by 5, then the biconditional statement p⇔ q is
- (a)
The unit digit of an integer is zero, if and only if it is divisible by 5
- (b)
If the unit digit of an integer is zero, then it is
divisible by 5 - (c)
The unit digit of an integer is zero or it is divisible by 5
- (d)
None of these
The conditional statement of "You will get a sweet dish after the dinner" is
- (a)
If you take the dinner, then you will get a sweet dish
- (b)
If you take the dinner, you will get a sweet dish
- (c)
You get a sweet dish if and only ifyou take the dinner
- (d)
None of these
Which of the following is not true?
- (a)
~(P ∧ q) = (~p) v (~q)
- (b)
~ (p v q) = (~ p) ∧ (~ q)
- (c)
p ⟶ q = ~ p v q
- (d)
~ (p v q) = ~ p v ~ q
Which of the following is true?
- (a)
~(p ∧ q) = ~P ∧ ~q
- (b)
~(p v q) = ~p ∧ ~q
- (c)
~(p⟶q) = pv ~q
- (d)
None of these
Consider the following statements:
(i) If price increases, then demand falls.
(ii) If price does not increase, then demand does not fall.
(iii)If demand falls, then price does not increase.
(iv) If demand does not fall, then price does not increase. Identify the pair of statement having the same meaning.
- (a)
(i) and (iv)
- (b)
(i) and (ii)
- (c)
(ii) and (iii)
- (d)
None of these
The negation of the statement "Rajesh or Rajni lived in Bangalore" is
- (a)
Rajesh did not live in Bangalore or Rajni lives in Bangalore
- (b)
Rajesh lives in Bangalore and Rajni did not live in Bangalore.
- (c)
Rajesh did not live in Bagalore and Rajni did not live in Bangalore
- (d)
Rajesh did not live in Bangalore or Rajni did not live in Bangalor
The converse of the statement
"If x > y, then x + a > y + a" is
- (a)
If x < y, then x + a < y + a
- (b)
If x + a > y + a, then x > y
- (c)
If x < y, then x + a > y + a
- (d)
If x > y, then x + a < y + a
The converse of the statement
"If sun is not shining, then sky is filled with clouds" is
- (a)
If sky is filled with clouds, then the sun is not shining
- (b)
If sun is shining, then sky is filled with clouds.
- (c)
If sky is clear, then sun is shining
- (d)
If sun is not shining, then sky is not filled with clouds
The contrapositive of statement
'If Chandigarth is capital of punjab, then Chandigarth is in India' is
- (a)
If Chandigarth not in India, then Chandigarh is not the capital of punjab
- (b)
If Chandigarth not in India, then Chandigarh is the capital of punjab
- (c)
If Chandigarth not the capital Punjab, then Chandigarh is not the capital of India
- (d)
If Chandigarth is the capital of Punkab, then Changigarth is not in India
Let p be the statement, "Mr. A passed the examination", q be the statement. " Mr. A is sad" and r be the statement " It is not true that Mr. A passed therefore he is sad.
Statement-I: r≡p ⇒ q
Statement-II: The logical equivalent of p ⇒ q is ~ p v q.
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement-I
- (b)
If both Statement-I and Statement-II are true and Statement-II is not the correct explanation of Statement-I
- (c)
If Statement-I is true but Statement-II is false
- (d)
If Statement-I is true but Statement-II is true.
Let q: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Statement-I: The contrapositive of the above statements is "If the diagonnals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram."
Statement-II: p⟶q ≡ ~q⟶ ~p
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement-I
- (b)
If both Statement-I and Statement-II are true and Statement-II is not the correct explanation of Statement-I
- (c)
If Statement-I is true but Statement-II is false
- (d)
If Statement-I is true but Statement-II is true.