Mathematical Reasoning MCQ Quiz in मल्याळम - Objective Question with Answer for Mathematical Reasoning - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Total number of valid votes polled = 720

360º = 720

1º = 720/360 = 2

               1º = 2

Valid votes obtained by Tejas = 80º = 80 × 2 = 160

Valid votes obtained by Shivam = 120º = 120 × 2 = 240

Valid votes obtained by Pratham = 100º = 100 × 2 = 200

Valid votes obtained by Harsheet =80º = 80 × 2 = 160

from the above data it is clear Shivam won the election and Pratham is his nearest rival.

The difference of vote between Shivam and Pratham = 240 - 200 = 40 votes

Hence, the correct answer is "option(3)".

Given

In 2008 A = Rs. 3.2, B = Rs. 5.3

each year A is increased by Rs. 0.5 and B is increased by Rs. 0.25

Calculation

let after n year A will be Rs. 0.4 more than B

=> A + n(0.5) = B + n(0.25) + 0.4

=> 3.2 + 0.5n = 5.3 + 0.25n + 0.4

=> 0.5n - 0.25n = 5.7 - 3.2

=> 0.25n = 2.5

=> n = 2.5/0.25 = 10 years

so after 10 years from 2008 the year will be 2018

p ∧ (~ (q ∧ r))

Explanation:

p ⇒ q means i"if p then q"

p ⇒ q is false only when p is true and q is false.

(2) is correct

Concept:

Let p and q are any two statements.

 \(\rm \sim (p \rightarrow q) = p \wedge q\)

Calculations:

Let p: The examination is difficult.

q: I shall pass.

r: I study hard.

Symbolic form of "If the examination is difficult, then I shall pass if I study hard." is \(\rm p \rightarrow (r \rightarrow q)\)

Symbolic form of Negation of "If the examination is difficult, then I shall pass if I study hard." = \(\rm \sim (\rm p \rightarrow (r \rightarrow q))\)

we know, 

⇒ \(\rm \sim (\rm p \rightarrow (r \rightarrow q))\) = \(\rm p \wedge (r \wedge \sim q)\)

Hence, the examination is difficult and I study hard but I shall not pass.

Explanation:

DeMorgan’s Theorem is mainly used to solve the various Boolean algebra expressions. When two (or more) input variables are AND’ed and negated, they are equivalent to the OR of the complements of the individual variables.

So, A̅B̅ = A̅ + B̅

Hence, option (2) is correct.

Concept:

• Disjunction: If two simple statements p and q are connected by the word ‘or’, then the resulting compound statement “p or q” is called disjunction of p and q and is written in symbolic form as “p ∨ q”.
• The statement p ∨ q has the truth value F whenever both p and q have the truth value F.
• The statement p ∨ q has the truth value T whenever either p or q or both have the truth value T.

Now, “If you are born in India” is p

“you are a citizen of India" is q

It is known that contrapositive of p ⇒ q is ~q ⇒ ~p 

“if you are not a citizen of India” is ~q

“then you are not born in India” is ~p 

Thus, ~q ⇒ ~p is “If you are not a citizen of India, then you are not born in India”

Explanation:

From the question, we can understand that we need to find the symbols ⨁ and ⊙ to get the expression equivalent to p ∧ q.

Take ∨ ≈ ∪ and ∧ ≈ ∩

Option (a):

Consider, ⨁ = ∨ and ⊙ = ∧

In that case, we get

⇒ (p ∨ q) ∧ (~ p ∧ q) ≡ (~ p ∧ q)

Option (b):

Consider, ⨁ = ∨ and ⊙ = ∨

In that case, we get

⇒ (p ∨ q) ∧ (~ p ∨ q) ≡ q

Option (c):

Consider, ⨁ = ∧ and ⊙ = ∨

In that case,

⇒ (p ∧ q) ∧ (~ p ∨ q) ≡ (p ∧ q)

Option (d):

Consider, ⨁ = ∧ and ⊙ = ∧

In that case,

⇒ (p ∧ q) ∧ (~ p ∧ q) ≡ null set

In option (c), when ⊕ and ⊙ is equal to ∧ and ∨.

The expression become,

(p ∧ q) ∧ (~ p ∨ q) ≡ (p ∧ q)

And the condition given in the question is satisfied.