Mathematical Reasoning MCQ Quiz in मल्याळम - Objective Question with Answer for Mathematical Reasoning - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Apr 9, 2025
Latest Mathematical Reasoning MCQ Objective Questions
Top Mathematical Reasoning MCQ Objective Questions
Mathematical Reasoning Question 1:
Which of the following is the inverse of the proposition: "If a number is a prime then it is odd."
Answer (Detailed Solution Below)
Mathematical Reasoning Question 1 Detailed Solution
Explanation:
p: A number is a prime. q: It is odd. We have, p ⇒ q
The inverse of p ⇒ q is ∼ p ⇒ ∼ q
i.e., If a number is not a prime then it is not odd.
Mathematical Reasoning Question 2:
DIRECTIONS: The pie chart, given here, represents the number of valid votes obtained by four students who confested election for school leadership. The total number of valid votes polled was 720. Observe the chart and answer the question based on it.
By how many votes did the winner defeat his nearest rival?
Answer (Detailed Solution Below)
Mathematical Reasoning Question 2 Detailed Solution
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)".
Mathematical Reasoning Question 3:
The price of item A increases by 50 paise every year while the price of item B increases by 25 paise every year. If in 2008, the price of item A was Rs. 3.20 and that of B was Rs. 5.30, in which year item A will cost 40 paise more than the item B?
Answer (Detailed Solution Below)
Mathematical Reasoning Question 3 Detailed Solution
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
Mathematical Reasoning Question 4:
The negation of the compound proposition p ∨ (~ p ∨ q) is
Answer (Detailed Solution Below)
Mathematical Reasoning Question 4 Detailed Solution
Mathematical Reasoning Question 5:
Negation of the statement p → (q ∧ r) is
Answer (Detailed Solution Below)
Mathematical Reasoning Question 5 Detailed Solution
p ∧ (~ (q ∧ r))
= p ∧ (~ q ∨ ~ r)Mathematical Reasoning Question 6:
p ⇒ q is false, if
Answer (Detailed Solution Below)
Mathematical Reasoning Question 6 Detailed Solution
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
Mathematical Reasoning Question 7:
Find the principal if the compound interest is charged on the principal at the rate of \(16\frac{2}{3}\%\) per annum for two years and the sum becomes Rs. 196.
Answer (Detailed Solution Below)
Mathematical Reasoning Question 7 Detailed Solution
Given:
The principal if the compound interest is charged on the principal at the rate of \(16\frac{2}{3}\%\) per annum for two years.
Formula Used:
A = P x (1 + r/100)n,
where A is the final amount,
P is the principal amount,
r is the interest rate,
and n is the number of compounding periods.
Calculation:
In this case, n = 2 and
r = \(16\frac{2}{3}\%\) .
So,
196 = P * (1 + \(16\frac{2}{3}\) /100)2
⇒ P = 196 / (1 + \(16\frac{2}{3}\) /100)2
⇒ P = 196 / (1 + 0.166)2
⇒ P = 196 / 1.34996
⇒ P ≈ 144
So, the principal amount is approximately Rs. 144.
Mathematical Reasoning Question 8:
What is negation of the compound proposition? If the examination is difficult, then I shall pass if I study hard.
Answer (Detailed Solution Below)
Mathematical Reasoning Question 8 Detailed Solution
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.
Mathematical Reasoning Question 9:
De-Morgan'w theorem is
Answer (Detailed Solution Below)
Mathematical Reasoning Question 9 Detailed Solution
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.
Inputs |
Truth Table Outputs For Each Term |
||||||
A |
B |
A.B |
A̅B̅ |
A̅ |
B̅ |
A̅ + B̅ |
|
0 |
0 |
0 |
1 |
1 |
1 |
1 |
|
0 |
1 |
0 |
1 |
0 |
1 |
1 |
|
1 |
0 |
0 |
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
0 |
0 |
0 |
0 |
So, A̅B̅ = A̅ + B̅
Hence, option (2) is correct.
Mathematical Reasoning Question 10:
The statement p ∨ q has the truth value F (False)
Answer (Detailed Solution Below)
Mathematical Reasoning Question 10 Detailed Solution
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.
p |
q |
p ∨ q |
T |
T |
T |
T |
F |
T |
F |
T |
T |
F |
F |
F |
∴ Option 4 is correct.