List of top Mathematics Questions on validating statements asked in KEAM

Consider the following statements :
(i) For every positive real number $x$, $x - 10$ is positive.
(ii) Let $n$ be a natural number. If $n^2$ is even, then $n$ is even.
(iii) If a natural number is odd, then its square is also odd.
Then

Find minimum value of \( \sin x \sin \left( x + \frac{\pi}{3} \right) \)

The truth values of \( p, q \) and \( r \) for which \( (p \wedge q) \vee (\sim r) \) has truth value F are respectively:

The truth values of \( p, q \) and \( r \) for which \( (p \wedge q) \vee (\sim r) \) has truth value F are respectively:

The truth values of \( p, q \) and \( r \) for which \( (p \wedge q) \vee (\sim r) \) has truth value F are respectively: