isi-entrance 2026 QB1

isi-entrance · India · UGA Number Theory Irrationality and Transcendence Proofs

Let $x$ be an irrational number. If $a , b , c$ and $d$ are rational numbers such that $\frac { a x + b } { c x + d }$ is a rational number, which of the following must be true?
(A) $a d = b c$
(B) $a c = b d$.
(C) $a b = c d$.
(D) $a = d = 0$

Let $x$ be an irrational number. If $a , b , c$ and $d$ are rational numbers such that $\frac { a x + b } { c x + d }$ is a rational number, which of the following must be true?\\
(A) $a d = b c$\\
(B) $a c = b d$.\\
(C) $a b = c d$.\\
(D) $a = d = 0$

Paper Questions

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