List of top Mathematics Questions on mathematical reasoning asked in KEAM

The contrapositive of the statement "If the number is not divisible by 3, then it is not divisible by 15" is

Consider the following statements:
(i) For every positive real number X, x-10 is positive.
(ii) Let n be a natural number. If n² is even, then n is even.
(iii) If a natural number is odd, then its square is also odd.
Then

If $p :$ The earth is round, $q : 3 + 4 = 7 $ then $\left(\sim p\right)\vee\left(\sim q\right)$ is

In a boolean algebra $B$ with respect to $' +' $ and $'.',$ $ x' $ denotes the negation of $ x\in B $ . Then

If $p :$ It is snowing, $q :$ I am cold, then the compound statement "It is snowing and it is not that I am cold" is given by

Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?

If $p : 2$ plus $3$ is five and $q $ : Delhi is the capital of India < are two statements, then the statement "Delhi is the capital of India and it is not that $2$ plus $3$ is five" is

Let $P$ be the statement Ravi races and let $Q$ be the statement Ravi wins. Then, the verbal translation of $ \tilde{\ }(p\vee (\tilde{\ }q)) $ is

For any two statements $p$ and $q$, the statement $\sim\left(p \vee q\right) \vee \left(\sim p \wedge q\right)$ the is equivalent to

The output of the circuit is

The statement $p \rightarrow \left(\sim q\right)$ is equivalent to

The boolean expression corresponding to the combinational circuit is

The negation of $\left(p\vee\sim q\right)\wedge q$ is

Let $p$ : roses are red and q : the sun is a star. Then, the verbal translation of $ (-\text{ }p) \vee q $ is

Which one of the following is not a statement?

Let $p, q, r$ be three statements. Then $\sim (p \vee \left(q \wedge r\right))$ is equal to