MCQ Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 10

Let

$A=\left\{ 2, 3, 5, 7\right\}$ . Examine whether the statements given below are true or false.

$\forall x \ in A, x$ is prime.

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True
0%
False

State whether the statements are true (T) or false (F).
There are countless rational numbers between

$\dfrac{5}{6}$ and

$\dfrac{8}{9}.$

0%
True
0%
False

The contrapositive of

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

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

Explanation

Contrapositive of

$p \rightarrow q$ is

$\sim q \rightarrow \sim p$ .

$\therefore$ Contrapositive of

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

$\sim r\Rightarrow\sim(p \vee q)$ i.e.

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

If p: Every equilateral triangle is an isosceles and q: Every square is a rectangle, then which of following is equivalent to ~

$\, ( p \Rightarrow q )$ ?

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The negation of "Every equilateral triangle is not isosceles or every square is a rectangle".
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"Every equilateral triangle is not isosceles, then every square is not a rectangle".
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Every equilateral triangle is isosceles, then every square is a rectangle".
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None of these

An electrical circuit for a set of 4 lights depends on a system of switches A, B, C and D. When these switches work they have the following effect on the lights: They each toggle the state of two lights (i.e. on becomes off and off becomes on). The lights that each switch controls are as follows.

A	B	C	D
1 and 2	2 and 4	1 and 3	3 and 4

In configuration I shown below, switches C-B-D-A are asserted in order, resulting in configurationOne switch did not work and had no effect at all. Which was that switch?

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A
0%
B
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C
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D

Let P(n) denote the statement that

$n^2+n$ is odd. It is seen that

$P(n)\Rightarrow P(n+1), P(n)$ is true for all.

0%
$n > 1$
0%
n
0%
$n > 2$
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None of these

Explanation

$P(n)=n^2+n$ . It is always odd (by statement) but square of any odd and

also, sum of two odd number is always even. So, for no any 'n' for which its statement is true.

The converse of

$\sim p \rightarrow q$ is equivalent to

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$p\rightarrow \sim q$
0%
$p\rightarrow q$
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$\sim q\rightarrow p$
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$q\rightarrow \sim p$

Of the following metals that cannot be obtained by electrolysis of the aqueous solution of their salts are

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Ag and Mg
0%
Ag and Al
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Mg and Al
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Cu and Cr

Consider statement " If I do not work, I will sleep. If I am worried, I will not sleep. Therefore if I am worried, I will work". This statement is

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valid
0%
invalid
0%
a fallacy
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none of these

The inverse of the statement "If a student join in NARAYANA collage then he get a seat in IIT" is

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If a student get a seat in IIT then he was the student of NARAYANA college
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If a student not joined in NARAYANA college then he does not get a seat in IIT
0%
If a student does not a get a seat in IIT then he was not the student of NARAYANA college
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A student get success if he joined in a NARAYANA college

Rohith makes a statements p,q about future.If it is Known that p

$\rightarrow$ q and probability of occurance of p is

$\frac { 3 }{ 5 }$ . what is the probability that q doesn't happen.

0%
$\dfrac { 1 }{ 5 }$
0%
$\dfrac { 2 }{ 5 }$
0%
$\dfrac { 3 }{ 5 }$
0%
can't be determined by given information

While simplifying

$\sqrt { \frac { 1-cosx }{ 1+cosx } }$ , two students got the following two answers A & B.
A) cosec x - cot x (B)

$\frac { 1 }{ cosecx+cotx }$ What can you say about answers ?

0%
Both A & B are wrong
0%
Both A & B are right
0%
A is right B is wrong
0%
B is right A is wrong

- (The teacher will teach iff students are sincere )

0%
the teacher will teach , if students are not sincere .
0%
the teacher will teach but students are not sincere or the teacher will not teach but students are sincere .
0%
the teacher will teach or students are not sincere , and the teacher will not teach or students are sincerer
0%
the teacher will not teach iff students are not sincerer

Consider the following statements. The number

$12375$ is

(1) divisible by

$3$

(2) divisible by

$11$

(3) divisible by

$9$

Of these statements:

0%
1, 2 and 3 are correct
0%
1 and 2 are correct
0%
2 and 3 are correct
0%
1 and 3 are correct

Explanation

$12375$

$1+2+3+7+5=18$ which is divisible by 3.

Therefore, the number 12375 is divisible by 3.

$12375$

$1+3+5=9$

$2+7=9$

$9-9=0$ if it is 0 or 11, then it is divisible by 11.

Therefore, the number 12375 is divisible by 11.

$12375$

$1+2+3+7+5=18$ which is divisible by 9.

$\therefore$ The number

$12375$ is divisible by

$9$ .

Select and write the most appropriate answer from the given alternatives in each of the following questions:
Contrapositive of

$p\rightarrow\left(q\rightarrow r\right)$ is logically equivalent to

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$p\rightarrow\left(q\rightarrow r\right)$
0%
$\left(q\rightarrow r\right)\rightarrow\simp$
0%
$\left(p\vee q\right)\rightarrow r$
0%
$\left(p \rightarrow q\right)\rightarrow p$

The converse of the statement "if

$p < q$ , then

$p-x < q-x$ " is :

0%
If $p < q$ , then $p-x > q-x$
0%
If $p > q$ , then $p-x > q-x$
0%
If $p-x > q-x$ , then $p > q$
0%
If $p-x < q-x$ , then $p < q$

Explanation

$\begin{array}{l} p<q,\, then\, \, p-x<q-x\, \, is \\ p-x<q-x \end{array}$

adding n both sides

$\begin{array}{l} p-x+x<q-x+x \\ p<q \end{array}$

The logically equivalent proportion of

$p \leftrightarrow q$ is

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$(p \wedge q) \vee (p \vee q)$
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$(p \rightarrow q) \wedge (p \rightarrow q)$
0%
$(p \rightarrow q) \vee (p \rightarrow q)$
0%
$(p \wedge q) \rightarrow (p \vee q)$

Which of the following proportional is a tautology?

0%
$\sim (p \rightarrow q) \vee (p \sim \wedge q)$
0%
$(p \rightarrow p) \vee (p \sim \wedge q)$
0%
$(p \rightarrow q) \vee (p \sim \wedge q)$
0%
$(p \rightarrow q) \wedge (p \wedge \sim q)$

If p, q, r are statements with truth values false, true and false respectively. then truth value of

$(\sim pv \sim q) v r$ is

0%
True
0%
False
0%
False, if r is true
0%
False, if q is false

The converse of the contra positive of

$\sim p \rightarrow q$ is ........(1)

0%
$q \rightarrow p$
0%
$\sim p \rightarrow p$
0%
$p \rightarrow \sim q$
0%
$\sim q \rightarrow \sim p$

The contrapositive of

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

0%
$\sim r \Rightarrow ( p \vee q )$
0%
$r \Rightarrow ( p \vee q )$
0%
$- r \Rightarrow ( - p \vee - q )$
0%
$p \Rightarrow ( q \vee r)$

Consider the statement :

$"P\left( n \right) :{ n }^{ 2 }-n+41$ is prime." Then which one of the following is true?

0%
P(3) is false but P(3) is true.
0%
P(3)is false but P(5) is true.
0%
Both P(3) and P(5) are true.
0%
Both P(3) and P(5) are false.

Two pairs of statement are:
p: If a quadrilateral is a rectangle, then its opposite sides are equal.
q: If opposite sides of a quadrilateral are equal, then the quadrilateral is a rectangle.
The combined statement of these pairs using If and only if is:

0%
A quadrilateral is a rectangle if and only if its all sides are equal.
0%
A quadrilateral is a rectangle if and only if its opposite sides are equal.
0%
A quadrilateral is a square if and only if its opposite sides are equal.
0%
A quadrilateral is not a rectangle if and only if its opposite sides are equal.

Let A and B denote the statements
A:

$\cos { \alpha } +\cos { \beta } +\cos { \gamma } =0$ & B:

$\sin { \alpha } +\sin { \beta } +\sin { \gamma } =0$
If

$\cos { (\beta -\gamma ) } +\cos { (\gamma -\alpha ) } +\cos { (\alpha -\beta ) } =-\frac { 3 }{ 2 }$ then

0%
A is true and Bis false
0%
A is false and B is true
0%
Both A and B are true
0%
Both A and B are false

Explanation

Given ,

$A:\cos\alpha+\cos\beta+\cos\gamma=0$ ..........(1)

$A:\sin\alpha+\sin\beta+\sin\gamma=0$ ..........(2)

Now,

on squaring both sides of equation (1) and (2)

we get,

$(\cos\alpha+\cos\beta+\cos\gamma)^2=0$ ........(3)

and

$(\sin\alpha+\sin\beta+\sin\gamma)^2=0$ ..........(4)

on adding equation (3) and (4) we get,

$\cos^2\alpha+\cos^2\beta+\cos^2\gamma+2(\cos\alpha\cos\beta+\cos\beta\cos\gamma+\cos\gamma\cos\alpha)+$

$\sin^2\alpha+\sin^2\beta+\sin^2\gamma+2(\sin\alpha\sin\beta+\sin\beta\sin\gamma+\sin\gamma\\sin\alpha)=0$

$\therefore (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac$

$\Rightarrow (\cos^2\alpha+\sin^2\alpha)+(\cos^2\beta+\sin^2\beta)+(\cos^2\gamma+\sin^2\gamma)+2[(\cos\alpha\cos\beta+\sin\alpha\sin\beta)+$

$(\cos\beta\cos\gamma+\sin\beta\sin\gamma)+(\cos\gamma\cos\alpha+\sin\gamma\sin\alpha)]=0$

$\Rightarrow 1+1+1+2[\cos(\alpha-\beta)+\cos(\beta-\gamma)+\cos(\gamma-\alpha)]=0$

$\because$ we know that

$\cos(\alpha-\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$

Also,

$\cos^2x+\sin^2x=1$

$\Rightarrow 3+2[\cos(\alpha-\beta)+\cos(\beta-\gamma)+\cos(\gamma-\alpha)]=0$

$\Rightarrow 2[\cos(\alpha-\beta)+\cos(\beta-\gamma)+\cos(\gamma-\alpha)]=-3$

$\Rightarrow \cos(\alpha-\beta)+\cos(\beta-\gamma)+\cos(\gamma-\alpha)=\dfrac{-3}{2}$

Thus, A and B both statement are true.

$x = 5$ and

$y = - 2$ then

$x - 2 y = 9 .$ The contrapositive of this statement is

0%
If $x - 2 y = 9$ then $x = 5$ and $y = - 2$
0%
If $x - 2 y \neq 9$ then $x \neq 5$ and $y \neq - 2$
0%
If $x - 2 y \neq 9$ then $x \neq 5$ or $y \neq - 2$
0%
If $x - 2 y \neq 9$ then either $x \neq 5$ or $y = - 2$

Choose the incorrect statements

0%
Digit at the units place of $3^{51}$ is $9$
0%
If $i-f=(9-\sqrt{82})^{11}$ and $< f < 1$ , then $'i'$ is an even integers
0%
If $7^{80}$ is divided by $13$ , then the remainder is $9$
0%
If only $6^{th}$ term in the expression of $\left(\dfrac{x}{5}+\dfrac{2}{5}\right)^{n}$ ahs numerically greatest coefficient, then $n=7$

State whether the statements are true (T) or false (F).
There are 200 natural numbers between

$100^2$ and

$101^2$ .

0%
True
0%
False

State whether the statements are true (T) or false (F).
For every rational numbers

$x, y$ and

$z, x + (y \times z) = (x + y) \times (x + z).$

0%
True
0%
False

Let

$A=\left\{ 2, 3, 5, 7\right\}$ . Examine whether the statements given below are true or false.

$\forall x \ in A, x+4\ge 11$

0%
True
0%
False

Let

$A=\left\{ 2, 3, 5, 7\right\}$ . Examine whether the statements given below are true or false.

$\exists \ x\in A$ such that

$x+3>9$ .

0%
True
0%
False

CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 10 - 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 10 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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