Mathematical Reasoning Test

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Mathematical Reasoning Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

If p: Every equilateral triangle is an isosceles and q: Every square is a rectangle, then which of following is equivalent to ~
$$\, ( p \Rightarrow q )$$?

A
The negation of "Every equilateral triangle is not isosceles or every square is a rectangle".

B
"Every equilateral triangle is not isosceles, then every square is not a rectangle".

C
Every equilateral triangle is isosceles, then every square is a rectangle".

D
None of these
Question 2
1 / -0

The contrapositive of $$(p \vee q) \Rightarrow r$$ is

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

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

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

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

Solution

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. $$\sim r\Rightarrow (\sim p\wedge\sim q)$$.
Question 3
1 / -0

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

A
Ag and Mg

B
Ag and Al

C
Mg and Al

D
Cu and Cr

Solution
Question 4
1 / -0

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

A
valid

B
invalid

C
a fallacy

D
none of these
Question 5
1 / -0

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

A
If a student get a seat in IIT then he was the student of NARAYANA college

B
If a student not joined in NARAYANA college then he does not get a seat in IIT

C
If a student does not a get a seat in IIT then he was not the student of NARAYANA college

D
A student get success if he joined in a NARAYANA college

Solution
Question 6
1 / -0

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.

A
$$\dfrac { 1 }{ 5 } $$

B
$$\dfrac { 2 }{ 5 } $$

C
$$\dfrac { 3 }{ 5 } $$

D
can't be determined by given information
Question 7
1 / -0

The converse of the statement "if $$p < q$$, then $$p-x < q-x$$" is :

A
If $$ p < q$$, then $$p-x > q-x$$

B
If $$ p > q$$, then $$p-x > q-x$$

C
If $$p-x > q-x$$, then $$p > q$$

D
If $$p-x < q-x$$, then $$p < q$$

Solution

$$\begin{array}{l} p<q,\, then\, \, p-x<q-x\, \, is \\ p-x<q-x \end{array}$$
adding n both sides
$$\begin{array}{l} p-x+x<q-x+x \\ p<q \end{array}$$
Question 8
1 / -0

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

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

B
$$\left(q\rightarrow r\right)\rightarrow\simp$$

C
$$\left(p\vee q\right)\rightarrow r$$

D
$$\left(p \rightarrow q\right)\rightarrow p$$
Question 9
1 / -0

- (The teacher will teach iff students are sincere )

A
the teacher will teach , if students are not sincere .

B
the teacher will teach but students are not sincere or the teacher will not teach but students are sincere .

C
the teacher will teach or students are not sincere , and the teacher will not teach or students are sincerer

D
the teacher will not teach iff students are not sincerer
Question 10
1 / -0

Consider the following statements. The number $$12375$$ is
(1) divisible by $$3$$
(2) divisible by $$11$$
(3) divisible by $$9$$
Of these statements:

A
1, 2 and 3 are correct

B
1 and 2 are correct

C
2 and 3 are correct

D
1 and 3 are correct

Solution

$$12375$$
$$1+2+3+7+5=18$$ 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 $$9$$.

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Re-Attempt Weekly Quiz Competition

Mathematical Reasoning Test - 32

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Mathematical Reasoning Test - 32

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SHARING IS CARING

Question 1

The negation of "Every equilateral triangle is not isosceles or every square is a rectangle".

"Every equilateral triangle is not isosceles, then every square is not a rectangle".

Every equilateral triangle is isosceles, then every square is a rectangle".

None of these

Question 2

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

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

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

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

Solution

Question 3

Ag and Mg

Ag and Al

Mg and Al

Cu and Cr

Solution

Question 4

valid

invalid

a fallacy

none of these

Question 5

If a student get a seat in IIT then he was the student of NARAYANA college

If a student not joined in NARAYANA college then he does not get a seat in IIT

If a student does not a get a seat in IIT then he was not the student of NARAYANA college

A student get success if he joined in a NARAYANA college

Solution

Question 6

$$\dfrac { 1 }{ 5 } $$

$$\dfrac { 2 }{ 5 } $$

$$\dfrac { 3 }{ 5 } $$

can't be determined by given information

Question 7

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

If $$ p > q$$, then $$p-x > q-x$$

If $$p-x > q-x$$, then $$p > q$$

If $$p-x < q-x$$, then $$p < q$$

Solution

Question 8

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

$$\left(q\rightarrow r\right)\rightarrow\simp$$

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

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

Question 9

the teacher will teach , if students are not sincere .

the teacher will teach but students are not sincere or the teacher will not teach but students are sincere .

the teacher will teach or students are not sincere , and the teacher will not teach or students are sincerer

the teacher will not teach iff students are not sincerer

Question 10

1, 2 and 3 are correct

1 and 2 are correct

2 and 3 are correct

1 and 3 are correct

Solution

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