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Recent questions and answers in Mathematical Reasoning
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JEEMAIN and NEET
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Class11
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Mathematical Reasoning
The statement $\sim(p \leftrightarrow \sim q)$ is
jeemain
math
class11
ch14
mathematical-reasoning
jeemain-2014
implications-(tautology-contradiction.)
q38
asked
Apr 6, 2014
by
balaji.thirumalai
0
answers
Statement-1: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy, and Statement-2 : $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology. Given these two statements, which of the following is true?
jeemain
math
class11
ch14
mathematical-reasoning
implications-(tautology-contradiction.)
medium
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
Which of the following is a logical statement?
jeemain
math
class11
ch14
mathematical-reasoning
logical-operations-(and-or)
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
Consider this statement "If the bank was robbed then I will not have any money".
jeemain
math
class11
ch14
mathematical-reasoning
statements
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
If the following statements are true: $ ~r$, $p \rightarrow q$ and $q \rightarrow r$, then:
jeemain
math
class11
ch14
mathematical-reasoning
statements
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
Let $S$ be a non empty subset of $R$. Consider the following statement: $P$: There is a rational number $x \in S$ such that $x\gt 0$. Then, which of the following statements is the negation of statement $P$:
jeemain
math
class11
ch14
mathematical-reasoning
statements
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
Which of the following are tautologies and which are contradictions?
jeemain
math
class11
ch14
mathematical-reasoning
implications-(tautology-contradiction.)
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
Choose the correct answer. The statement $p \rightarrow (q \rightarrow p)$ is equivalent to which of the following?
jeemain
math
class11
mathematical-reasoning
ch14
implications-(tautology-contradiction.)
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
The proposition $(P \vee Q) \vee (\sim P \wedge \sim Q)$ is a:
jeemain
math
class11
mathematical-reasoning
ch14
implications-(tautology-contradiction.)
medium
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
$^{\sim}(p \Rightarrow q)$ is equivalent to
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q30
answered
Jan 24, 2014
by
thanvigandhi_1
1
answer
Let f : $R \rightarrow R$ be a function defined by $f(x) = min \{ x+1, |x| + 1 \}$. Then which of the following statements is true?
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q29
answered
Jan 24, 2014
by
thanvigandhi_1
1
answer
For which of the sets of a, is the statement, “The difference between the roots of the equation $x^2+ax+1 = $ is less than $ \sqrt 5”$ true?
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q28
answered
Jan 24, 2014
by
thanvigandhi_1
1
answer
$ ^{\sim}(p V q)$ is equivalent to
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q27
answered
Jan 24, 2014
by
thanvigandhi_1
1
answer
$ ^{\sim}(p \wedge q)$ is equivalent to
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q26
answered
Jan 24, 2014
by
thanvigandhi_1
1
answer
$ ^{\sim}(p \leftrightarrow q)$ is equivalent to
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q25
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
$(p \wedge\: ^{\sim}q) \wedge (^{\sim}p V q)$ is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q24
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
$ ^{\sim}[(p \wedge q) \rightarrow (^{\sim}p V q)]$ is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q23
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
If p,q,r are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true, then
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q22
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
If p, q, r are simple propositions with truth values T,F,T then the truth value of $ [(^{\sim}p Vq) \wedge ^{\sim}r] \Rightarrow p$ is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q21
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
The statement $ p V q \Rightarrow \: p \wedge q$ is a
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q20
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
The contrapositive of $ (p V q) \Rightarrow r$ is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q19
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
If a,b,c are the sides of a triangle, then the statement, “$ \large\frac{1}{(b+c)},\: \large\frac{1}{(c+a)},\: \large\frac{1}{(a+b)}$ are also the sides of the triangle”, is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q18
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
A survey shows that 63% of the Americans like cheese whereas 76% like apples. The statement, “x% of Americans like both cheese and apples” is true for
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q17
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
If p : It rains today. q : I go to school. r : I shall meet my friends. s : I shall go for a movie. Then which of the following is the proportionate representation of the statement, If it does not rain or if I do not go to school, then I shall meet my friends and go for a movie.
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q16
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
Consider the statement $ \log \bigg(\large\frac{5c}{a} \bigg),\: \log \bigg(\large\frac{3b}{5c} \bigg)$ and $ \log \bigg(\large\frac{a}{3b} \bigg)$ are in AP, where a,b,c are in GP. The statement is true only if a,b,c are the lengths of sides of
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q15
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
The proposition $ (p \Rightarrow \: ^{\sim}p) \wedge (^{\sim}p \Rightarrow p)$ is a
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q14
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
Which one of the following is a fallacy?
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q13
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
If $ \phi(x) = f(x) + f(1-x), f’(x)<0 \: for\: 0 \leq x \leq 1$, then the tautology among the following is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q12
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
The proposition $ p \Rightarrow ^{\sim}(p \wedge\: ^{\sim}q)$ is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q11
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
S1 : The function $f(x)=|x|$ is not one-one.\[\] S2: The negative real numbers are not the images of any real numbers. \[\] If the statement S1 holds true then,
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q10
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
The first two terms of a geometric progression add up to 12. The terms of the G.P. are alternately positive and negative.The statement - The sum of the third and the fourth terms is 48 holds true for the first term being
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q9
answered
Jan 23, 2014
by
thanvigandhi_1
1
answer
Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number” and r be the statement “x is a rational number iff y is a transcendental number”. \[\] S1 : r is equivalent to either q or p \[\] S2 : r is equivalent to $ ^{\sim}(p \leftrightarrow \: ^{\sim}q)$
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q8
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
S1:$ ^{\sim} (p \leftrightarrow\: ^{\sim} q)$ is equivalent to $p \leftrightarrow q.$ \[\] S2 :$ ^{\sim} (p\leftrightarrow \: ^{\sim} q)$ is a tautology.
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q7
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
Given $ P(x)=x^4+ax^3+bx^2+cx+d$ such that $x=0 $ is the only real root of $P’(x)=0. \: If\: P(-1)<P(1)$, then in the interval $[-1,1]$, which of the following statements is true
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q6
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
Let A and B denote the statements \[ \] A: $ \cos \alpha + \cos \beta + \cos \gamma = 0$ \[\] B: $ \sin \alpha + \sin \beta + \sin \gamma = 0$ \[\] If $ \cos(\beta- \alpha) + \cos( \gamma- \alpha) + \cos( \alpha - \beta)= -\large\frac{3}{2}$, then
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q5
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q4
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
The inverse of the converse of a conditional statement is the _______________.
jeemain
math
mathematical-reasoning
class11
ch14
difficult
statements
q3
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
What is true about the statement "If two angles are right angles, the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?
jeemain
math
mathematical-reasoning
class11
ch14
difficult
implications-(tautology-contradiction.)
q2
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
In a class of 50 students, 18 take music, 26 take art, and 2 take both art and music. How many students in the class are not enrolled in either music or art?
jeemain
math
mathematical-reasoning
class11
ch14
difficult
logical-operations-(and-or)
q1
answered
Jan 22, 2014
by
thanvigandhi_1
1
answer
Given the following statement: All seats are hot. All belts are hot. Now, consider the claims: C1: Some seats are belts. C2: All hot are either seats or belts . Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.
jeemain
math
mathematical-reasoning
class11
unit14
easy
q30
asked
Jan 21, 2014
by
thanvigandhi_1
0
answers
Given the following statement: All doors are windows. Some windows are clips. Now, consider the claims: C1 :Some clips, if they are doors, they are also windows C2: All clips which are not widows are also not doors. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.
jeemain
math
mathematical-reasoning
class11
unit14
easy
q27
asked
Jan 21, 2014
by
thanvigandhi_1
0
answers
Given the following statement: Some paints are red. AIl red which are paints are yellow. Now, consider the claims: C1 :C1: Some paints are yellow. C2: Some yellow are red. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.
jeemain
math
mathematical-reasoning
class11
unit14
easy
q29
asked
Jan 21, 2014
by
thanvigandhi_1
0
answers
Given the following statement: Statements: No shoe is a chappal. Some chappals are sandals. Now, consider the claims: C1: Some sandals are not chappals.. C2: Sandals which are not chappals are shoes. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.
jeemain
math
mathematical-reasoning
class11
unit14
easy
q28
asked
Jan 21, 2014
by
thanvigandhi_1
0
answers
Given the following statement: All doors are windows. Some windows are dips. Now, consider the claims: C1: Some clips are doors. C2: Some windows are doors. Now, mark according to the rules - \[\] i) Mark A if C1 is true, ii) Mark B if C2 is true,iii) Mark C if neither C1 nor C2 is true and iv) Mark D if both C1 and C2 are true.
jeemain
math
mathematical-reasoning
class11
unit14
easy
q26
asked
Jan 21, 2014
by
thanvigandhi_1
0
answers
Which of the following is not a false statement?
jeemain
math
mathematical-reasoning
class11
ch14
medium
statements
q40
answered
Jan 21, 2014
by
thanvigandhi_1
1
answer
Which of the following is a true statement?
jeemain
math
mathematical-reasoning
class11
ch14
medium
statements
q39
answered
Jan 21, 2014
by
thanvigandhi_1
1
answer
Let A={2,3,5,7}. For which of the sets, truth value is true?
jeemain
math
mathematical-reasoning
class11
ch14
medium
implications-(tautology-contradiction.)
q38
answered
Jan 21, 2014
by
thanvigandhi_1
1
answer
What is the converse of the statement: n is divisible by 3, if the sum of digits of n is divisible by 3?
jeemain
math
mathematical-reasoning
class11
ch14
medium
implications-(tautology-contradiction.)
q37
answered
Jan 21, 2014
by
thanvigandhi_1
1
answer
What is the contrapositive of the statement: If $f(2)=0$, then $ f(x)$ is divisible by $(x-2)$?
jeemain
math
mathematical-reasoning
class11
ch14
medium
implications-(tautology-contradiction.)
q36
answered
Jan 20, 2014
by
thanvigandhi_1
1
answer
What is the converse of the statement: If $x-4 = 5$, then $x=9$?
jeemain
math
mathematical-reasoning
class11
ch14
medium
implications-(tautology-contradiction.)
q35
answered
Jan 20, 2014
by
thanvigandhi_1
1
answer
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