Mathematical Reasoning Test

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Mathematical Reasoning Test - 28

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Question 1
1 / -0

The moment of inertia of the plate about the $$x-$$axis is

A
$$\dfrac{{M{L^2}}}{8}$$

B
$$\dfrac{{M{L^2}}}{32}$$

C
$$\dfrac{{M{L^2}}}{24}$$

D
$$\dfrac{{M{L^2}}}{6}$$

Solution
Question 2
1 / -0

Negation of $$p \rightarrow ( p \vee \sim q )$$ is

A
$$\sim p \rightarrow ( \sim p \vee q )$$

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

C
$$\sim p \vee ( \sim p \vee \sim q )$$

D
$$\sim p \leftarrow ( \sim p \rightarrow q )$$

Solution
Question 3
1 / -0

The negation of $$q\vee \sim (p\wedge r)$$ is?

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

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

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

D
$$\sim r\vee(p\wedge r)$$

Solution

$$q \vee \sim (p \wedge r)\,\,\,\,\,\,\,\,\,\,\left[ {\because \sim ( \sim p) = p} \right]$$
$$ \sim q \wedge \sim (p \wedge r)\,\,\,\,\,\left[ {\because \sim \left( {p \vee q} \right) = \sim p \wedge \sim q} \right]$$ [by De Morgans law]
Question 4
1 / -0

Dual of $$( p \rightarrow q ) \rightarrow r$$ is _________________.

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

B
$$p\vee q\wedge r$$

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

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

Solution
Question 5
1 / -0

Consider the following two statements :
P: If 7 is odd number, then is divisible by $$2$$.
Q: If 7 is a prime number, Then is an odd number.
If $${ V }_{ 1 }$$ is the value of the contra-positive of $$p$$ and $${ V }_{ 2 }$$ Is the truth value of contra-positive of Q, then the orders pair $$({ V }_{ 1 },{ V }_{ 2 })$$ equals :

A
$$(T,T)$$

B
$$(T,F)$$

C
$$(F,T)$$

D
$$(F,F)$$

Solution

P= odd number cannot be divisible by 2,
$${V_1}$$ is contra positive value of P
$${V_1} = T$$
Q=Every prime number is an odd number but not every odd number . is a prime number $${V_2}$$ is the contra positive value of Q
$$\left( {{V_1},{V_2}} \right) = \left( {T,F} \right)$$
Question 6
1 / -0

P: he studies hard, q: he will get good marks. The symbolic form of " If he studies hard then he will get good marks "is_____

A
$$\sim q\Rightarrow p$$

B
$$p\Rightarrow q$$

C
$$\sim p\vee q$$

D
$$p\Leftrightarrow q$$

Solution
Question 7
1 / -0

Negation of compound proposition : If the examination is difficult, then I shall pass if I study hard

A
The examination is difficult and I study hard and I shall pass

B
The examination is difficult and I study hard but I shall not pass

C
The examination is not difficult and I study hard and I shall pass

D
All of these

Solution
Question 8
1 / -0

The cost of an article including the sales tax is $$Rs\ .616$$. The rate of sales tax is $$10\%$$,if the shopkeeper has made a profit of $$12\%$$ , then the cost price of the article is?

A
$$Rs\ .350$$

B
$$Rs\ .400$$

C
$$Rs\ .500$$

D
$$Rs\ .800$$

Solution

Let the cost price $$=Rs100$$

Then, including tax $$=100+\dfrac{11}{100}=110\%$$

So,

$$110\%$$ of S.P $$=Rs\,616$$

Then,

$$ S.P=\dfrac{616}{110}\times 100 $$

$$ S.P=Rs\,560 $$

Now, Cost price of $$12\%$$ $$=\dfrac{100\times560}{100+12}=\dfrac{100\times 560}{112}$$

$$=Rs\,500$$
Hence, this is the answer.
Question 9
1 / -0

Consider the following statement
p:you want to success
q:you will find a away,
then the negation of $$\sim \left( p\ \nu\ q \right) $$

A
you want success or you will find a way

B
you want of success and you do not find a way

C
if you want of success then you cannot find a way

D
if you do not want to succeed then you will not find a way

Solution
Question 10
1 / -0

If $$p, q, r$$ are three propositions, then the negation of $$p\rightarrow (q\wedge r)$$ is logically equivalent to

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

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

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

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

Solution