MCQ Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 6

Find the counter example of the .statement "Every natural number is either prime or composite''.

0%
5
0%
1
0%
6
0%
None of these

Explanation

$1$ is neither prime nor composite, it is a counter example to the statement, "Every natural number is either prime or composite ".

The statement "

$x>5$ or

$x<3$ " is true, if x equals

0%
$1$
0%
$3$
0%
$4$
0%
$5$

Explanation

For "or" to be true either (or both) of the conditions must be true.

The only value that makes either of the conditions true is when

$x=1$

For

$x>5$ i.e

$1>5$ is not true

but For

$x<3$ i.e

$1<3$ is true.

When

$x=3$

For

$x>5$ is not true

also For

$x<3$ is not true.

Both the conditions are False.

When

$x=4$

For

$x>5$ is not true

also For

$x<3$ is not true.

Both the conditions are False

When

$x=5$

For

$x>5$ is not true

also For

$x<3$ is not true.

Both the conditions are False

Option A is correct.

Which statement represents the inverse of the statement "If it is snowing then Skeeter wears a sweater"?

0%
If Skeeter wears a sweater then it is snowing
0%
If Skeeter does not wear a sweater then it is not snowing
0%
If it is not snowing then Skeeter does not wear a sweater
0%
If it is not snowing then Skeeter wears a sweater

Which of the following statements is the contrapositive of "If a polygon has four sides, then it is called a quadrilateral."?

0%
If a polygon is called a quadrilateral, then it has four sides.
0%
If a polygon is not called a quadrilateral, then it does not have four sides
0%
If a polygon does not have four sides, then it is not called a quadrilateral.
0%
None of these

Which of the following statements is the contrapositive of "If you understand logic, you will be a good consumer."?

0%
If you are a good consumer, then you do not understand logic.
0%
If you are not a good consumer, then you do not understand logic.
0%
If you do not understand logic, then you will not be a good consumer.
0%
None of these

Explanation

Contrapositive of

$p\rightarrow q$ is given by

$\sim q\rightarrow \sim p$

So contrapostive of given statement is given by,

"If you will not be a good consumer, then you don't understand logic"

Hence, option B is correct.

State the following statement is True or False

If Susan does not like spinach then the truth value of the statement "Susan likes ice cream and she like spinach" is True

0%
True
0%
False

I had Rs. 200 with me. I gave Rs. x to Anwar, Rs.

$\displaystyle \frac{x}{2}$ to Vidhu and I am left with Rs

$\displaystyle \frac{x}{2}$ . The amount I gave to vidhu is ..........

0%
Rs. 50
0%
Rs. 40
0%
Rs. 30
0%
Rs. 15

Explanation

Let us consider the problem:

$\dfrac{{x + x}}{2} + \dfrac{x}{2} = 200$
implies that,

$\dfrac{{\left( {2x + x + x} \right)}}{2} = 200$

implies that,

$\dfrac{{4x}}{2} = 200$

implies that,

$2x = 200$

implies that,

$x = 100$

Hence,the Vidhi got

$\dfrac{{100}}{2} = Rs50$ .

State the following statement is True or False

If Shelly does not like John, then the truth value of the statement "Shelly likes Mike and she likes John" is True

0%
True
0%
False

The statement "If x is divisible by 8 then it is divisible by 6" is false if x equals

0%
6
0%
14
0%
32
0%
48

Explanation

A sentence in "If....then..." form is called an implication. The only time when an implication is false is when the "If" part of the sentence is true and the "then" part of the sentence is false. The number

$32$ makes the first part of the statement true and the second part of the statement false.

"If Tom buys a red skateboard then Amanda buys green in-line skates". Which statement below is logically equivalent?

0%
If Amanda does not buy green in-line skates then Tom does not buy a red skateboard
0%
If Tom does not buy a red skateboard then Amanda does not buy green in-line skates
0%
If Amanda buys green in-line skates then Tom buys a red skateboard
0%
If Tom buys a red skateboard then Amanda does not buy green in-line skates

Which of the following is the negation of the statement, For all odd primes

$p < q$ there exists positive non-primes

$r < s$ such that

$p^2 + q^2 = r^2 + s^2$ .

0%
For all odd primes $p < q$ there exists positive non-primes $r < s$ such that $p^2 + q^2 = r^2 + s^2$ .
0%
There exists odd primes $p < q$ such that for all positive non-primes $r < s$ , $p^2 + q^2 = r^2 + s^2$ .
0%
There exists odd primes $p < q$ such that for all positive non-primes $r < s$ , $p^2 + q^2 \neq r^2 + s^2$ .
0%
For all odd primes $p < q$ and for all positive non-primes $r < s$ , $p^2 + q^2 \neq r^2 + s^2$ .

Explanation

For the inverse of a statement, "for all" and "there exists" are interchanged, and "

$=$ " changes to "

$\neq$ ".

Therefore, the negative of the given statement will be:

There exists odd primes

$p<q$ such that for all positive non-primes

$r<s$ ,

$p^2+q^2 \neq r^2+s^2$

Negation of "Ram is in class

$X$ or Rashmi is in class

$XII$ " is

0%
Ram is not in class $X$ but Rashmi is in class $XII$
0%
Ram is not in class $X$ and Rashmi is not in class $XII$
0%
Either Ram is not in class $X$ or Rashmi is not in class $XII$
0%
None of the above

Explanation

Let

$p:$ Ram is in class

$X$

$q:$ Rashmi is in class

$XII$

Given proposition is

$p\vee q$

Its negation is

$\sim (p\vee q)=-p\wedge \sim q$ , Ram is not in class

$X$ and Rashmi is not in class

$XII$

Consider the statement, if

$n$ is divisible by

$30$ then

$n$ is divisible by

$2, 3$ and by

$5$ . Which of the following statements is equivalent to this statement?

0%
If $n$ is not divisible by $30$ then $n$ is divisible by $2$ or divisible by $3$ or divisible by $5$ .
0%
If $n$ is not divisible by $30$ then $n$ is not divisible by $2$ or not divisible by $3$ or not divisible by $5$ .
0%
If $n$ is divisible by $2$ and divisible by $3$ and divisible by $5$ then $n$ is divisible by $30$ .
0%
If $n$ is not divisible by $2$ or not divisible by $3$ or not divisible by $5$ then $n$ is not divisible by $30$ .

Explanation

$n$ is not divisible by

$2$ or divisible by

$3$ or not divisible by

$5$ then

$n$ is divisible by

$30$ .

Let p : A triangle is equilateral, q : A triangle is equiangular then inverse of

$\displaystyle q\rightarrow p$ is

0%
If a triangle is not equilateral then it is not equiangular
0%
If a triangle is not equiangular then it is not equilateral
0%
If a triangle is equiangular then it is not equilateral
0%
If a triangle is equiangular then it is equilateral

Explanation

Here, p is A triangle is equilateral and q is A triangle is equiangular.

The inverse of

$q \rightarrow p$ is

$\sim q \rightarrow \sim p$

On the same lines, the inverse statement becomes If a triangle is not equiangular then it is not equilateral.

The statement form

$(p \Leftrightarrow r) \Rightarrow (q \Leftrightarrow r)$ is equivalent to

0%
$[(\sim p \vee r)\wedge (p \vee \sim r)] \vee \sim [(\sim q \vee r)\wedge (q \vee \sim r)]$
0%
$\sim [(\sim p\vee r)\wedge (p\vee \sim r)]\wedge [(\sim q\vee r) \vee(q\vee \sim r)]$
0%
$[(\sim p\vee r)\wedge (\sim p \vee \sim r)] \wedge [(\sim q\vee r)\wedge (q\vee \sim r)]$
0%
$\sim[(\sim p\vee r) \wedge (p\vee \sim r)]\wedge [(\sim q\vee r)\wedge (q \vee \sim r)]$

Explanation

$p$	$q$	$r$	$p\leftrightarrow r$	$q\leftrightarrow r$	$\left( p\leftrightarrow r \right) \rightarrow \left( q\leftrightarrow r \right)$
T	T	T	T	T	T
T	T	F	F	F	T
T	F	T	T	F	F
T	F	F	F	T	T
F	T	T	F	T	T
F	T	F	T	F	F
F	F	T	F	F	T
F	F	F	T	T	T

$p$

$q$

$r$

$\sim p$

$\sim q$

$\sim r$

$\sim p\vee r$

$\left( p\vee \sim r \right)$

$\left[ \left( \sim p\vee r \right) \wedge \left( p\vee \sim r \right) \right]=a$

$\sim q\vee r$

$q\vee \sim r$

$[\left( \sim q\vee r \right) \wedge \left( q\vee \sim r \right)]=b$

$a\wedge b$

$\sim \left( a\wedge b \right)$

The statement form,

$\left( p\leftrightarrow r \right) \rightarrow \left( q\leftrightarrow r \right)$

$\therefore$ The statement

$\left( p\leftrightarrow r \right) \rightarrow \left( q\leftrightarrow r \right)$ is not equivalent to

$\sim \left[ \left( \sim p\vee r \right) \wedge \left( p\vee \sim r \right) \right] \wedge \left[ \left( \sim q\vee r \right) \wedge \left( q\vee \sim r \right) \right]$

Consider the statement, Given that people who are in need of refuge and consolation are apt to do odd things, it is clear that people who are apt to do odd things are in need of refuge and consolation. This statement, of the form

$(P \Rightarrow Q) \Rightarrow (Q \Rightarrow P)$ , is logically equivalent to

0%
People who are in need of refuge and consolation are not apt to do odd things.
0%
People are apt to do odd things if and only if they are in need of refuge and consolation.
0%
People who are apt to do odd things are in need of refuge and consolation.
0%
People who are in need of refuge and consolation are apt to do odd things.

Explanation

Given statement is "people who are in need of refuge and consolation are apt to do odd things"

It is in the form of

$p\Rightarrow q$ , where

$p$ is "in need of refuge and consolation" and

$q$ is "apt to do odd things"

$q\Rightarrow p$ is equivalent to "people who are apt to do odd things are in need of refuge and consolation"

Therefore option

$C$ is correct

The metal that does not displace hydrogen from an acid is

0%
Ca
0%
Al
0%
Zn
0%
Hg

When electric current is passed through acidified water for 1930 s, 1120 mL, of $H_2$ gas is collected (at STP) at the cathode. What is the current passed in amperes?

0%
0.05
0%
0.50
0%
5.0
0%
50

Negation of "

$2+3=5$ and

$8<10$ " is

0%
$2+3\ne 5$ and $< 10$
0%
$2+3=5$ and $8\nless 10$
0%
$2+3\ne 5$ or $8\nless 10$
0%
None of the above

Explanation

Let

$p:2+3=5$
and

$q=8<10$
Given proposition is

$p\wedge q$
Its negatition is

$\sim (p\wedge q)=\sim p\wedge \sim q$

$\therefore$ We have

$2+3\ne 5$ or

$8\nless 10$

The inverse of the proposition

$(p\wedge \sim q)\Rightarrow r$ is

0%
$\sim r\Rightarrow( \sim p \vee q)$
0%
$(\sim p \vee q)\Rightarrow \sim r$
0%
$r\Rightarrow p (\wedge \sim q)$
0%
None of these

Explanation

Inverse of

$p\Rightarrow q$ is

$\sim p\Rightarrow \sim q$

$\therefore$ Inverse of

$(p\wedge \sim q)\Rightarrow r$ is

$\sim(p\wedge \sim q)\Rightarrow \sim r$

i.e,

$(\sim p\vee q)\Rightarrow \sim r$

Which of the following is the inverse of the proposition : 'If a number is a prime then it is odd"?

0%
If a number is not a prime then it is odd
0%
If a number is not a prime then it is not odd
0%
If a number is not odd then it is not prime
0%
If a number is odd then it is a prime

Explanation

Let

$p:$ Number is prime

and

$q:$ Number is odd

The given statement is

$p \rightarrow q$

Its inverse is

$\sim p \rightarrow \sim q$

Therefore, the inverse is "If a number is not a prime then it is not odd."

So, option B is correct.

Which of the following is not proposition?

0%
$3$ is prime.
0%
$\sqrt{2}$ is irrational.
0%
Mathematics is interesting.
0%
$5$ is an even integer.

Explanation

$\textbf{Step 1: Finding the options which are not a proposition}$

$\text{Looking at option A, 3 is prime}$

$\text{This can be classified as true unanimously, therefore it is a proposition}$

$\text{Looking at option B, }\sqrt2\text{ is irrational}$

$\text{This can be classified as true unanimously, therefore it is a proposition}$

$\text{Looking at option C, Mathematics is interesting}$

$\text{This can be classified as true or false unanimously, therefore it is not proposition}$

$\text{Looking at option D, 5 is an even integer}$

$\text{This can be classified as false unanimously, therefore it is a proposition}$

$\textbf{Hence Option C is correct}$

Given: All seniors are mature students. Which statement expresses a conclusion that logically follows from the given statement?

0%
All mature students are seniors
0%
If Bill is a mature student, then he is a senior
0%
If Bill is not a mature student, then he is not a senior
0%
If Bill is not a senior, then he is not a mature student
0%
All sophomores are not mature students.

Explanation

Given that all seniors are mature students (

$p\Longrightarrow q$ )

$p\Longrightarrow q$ is equivalent to

$\sim q\Longrightarrow \sim p$
So the correct answer is , If Bill is not a senior , then he is not a mature senior
So the correct option is

$C$

The inverse of statement " If a quadrilateral is a rectangle,then it has two pairs of parallel sides."

0%
If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides.
0%
If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
0%
If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle.
0%
None of these

STATEMENT: All cabbages are red.
Which of the following statements shows that the statement above is FALSE?

0%
David is eating a red apple
0%
Bill is eating a green apple
0%
Alice is not eating a red cabbage
0%
Ted is eating a red cabbage
0%
Keisha is eating green cabbage

"If p, then q" is logically equivalent to which of the following?
I. If q, then p
II. If not p, then not q.
III. If not q, then not p

0%
None of the above
0%
III Only
0%
I and II only
0%
I and III only
0%
I, II and III

Explanation

"If

$p$ , then

$q$ " means

$p \Rightarrow q$
The explanation for the given statement is if

$p$ happens then

$q$ will happen , which implies if

$q$ wont happen then

$p$ also wont happen

Therefore "If

$p$ , then

$q$ " implies "If not

$q$ , then not

$p$ "

Therefore the correct answer is option

$B$

The inverse of " If two angles are congruent, then they have the same measure" is

0%
If two angles have the same measure, then they are congruent.
0%
If two angles are not congruent, then they do not have the same measure.
0%
If two angles do not have the same measure, then they are not congruent.
0%
None of these

"If A is true, then B is false", is logically equivalent to which of the following?
I. If A is false, then B is true.
II. If B is false, then A is true.
III. If B is true, then A is false

0%
None of the above
0%
III only
0%
I and II only
0%
II and III only
0%
I, II and III

The inverse of statement is " If you grew in Alaska, then you have seen snow."

0%
"If you did not grow up in Alaska, then you have not seen snow."
0%
"If you grow up in Alaska, then you have not seen snow."
0%
"If you did not grow up in Alaska, then you have seen snow."
0%
None of these

Explanation

The inverse of a statement is when you write negative of statement without changing the actual meaning of statement.

The inverse of “If p then q” is "If

$\text{~p}$ then

$\text{~q}$ ." in the solution
In statement 'If you grew in Alaska ,then you have seen snow'.
Inverse :- 'If you did not grow up in Alaska, then you have not seen snow'.

The inverse of the statement " if Abbey is not injured, she will win the race." is

0%
If Abbey is injured, she will not win the race.
0%
If Abbey is not injured, she will not win the race."
0%
If Abbey is injured, she will win the race."
0%
None of these

CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 6 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 6 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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