Which of the following asymptotic relations correctly expresses that grows strictly slower than ?

Explanation: Little-o notation ( ): Represents a strictly upper bound . It denotes that grows strictly slower than . Mathematically, . Big-O notation ( ): Represents an upper bound, meaning grows at most as fast as ( ). It includes equal growth rates as well. Big-Omega notation ( ): Represents a lower bound, meaning grows at least as fast as . Big-Theta notation ( ): Represents a tight bound, meaning and have the same rate of growth. Therefore, correctly represents that grows strictly slower than . Correct Answer: (B)

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CUET PG 2026 — DSA PYQ

CUET PG | DSA | 2026

Which of the following asymptotic relations correctly expresses that $f (n)$ grows strictly slower than $g (n)$ ?

Choose the correct answer:

(Correct Answer)

C.
$f (n) = Ω (g (n))$

D.
$f (n) = Θ (g (n))$

Explanation

Little-o notation ( $o$ ): Represents a strictly upper bound. It denotes that $f (n)$ grows strictly slower than $g (n)$ . Mathematically, $lim_{n \to \infty} \frac{f ( n )}{g ( n )} = 0$ .
Big-O notation ( $O$ ): Represents an upper bound, meaning $f (n)$ grows at most as fast as $g (n)$ ( $f (n) \leq c \cdot g (n)$ ). It includes equal growth rates as well.
Big-Omega notation ( $Ω$ ): Represents a lower bound, meaning $f (n)$ grows at least as fast as $g (n)$ .
Big-Theta notation ( $Θ$ ): Represents a tight bound, meaning $f (n)$ and $g (n)$ have the same rate of growth.

Therefore, $f (n) = o (g (n))$ correctly represents that $f (n)$ grows strictly slower than $g (n)$ .

Correct Answer: (B) $f (n) = o (g (n))$

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