Let \( n \) and \( m \) be two positive integers such that there are exactly 41 integers greater than \( 8^m \) and less than \( 8^n \), which can be expressed as powers of 2. Then, the smallest possible value of \( n + m \) is:
CAT 2026Papers & G StrategyQuantX maro (Modern Maths)
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Suppose \( f(x, y) \) is a real-valued function such that \( f(3x + 2y, 2x - 5y) = 19x \) for all real numbers \( x \) and \( y \). The value of \( x \) for which \( f(x, 2x) = 27 \), is: