CUET PG 2026 — DSA PYQ

Analysis of Assertion (A):

• Binary Search always operates on the entire array of size $N$, taking $O(\log N)$ time regardless of where the element is located.

• Exponential Search bounds the search range exponentially ($1,2,4,8,\dots$) first, taking $O(\log i)$ time where $i$ is the target index.

• When $i\ll N$ (element is near the beginning), $O(\log i)$ is significantly smaller than $O(\log N)$, making Exponential Search much faster.

• Therefore, Assertion (A) is True.

Analysis of Reason (R):

• Exponential search first identifies a range $[2^{k-1},2^k]$ containing index $i$ in $O(\log i)$ steps, avoiding the need to operate over the entire array size $N$.

• Therefore, Reason (R) is True.

Relationship between (A) and (R):

• The reason Exponential Search outperforms Binary Search near the beginning of a massive array is precisely because its time complexity depends on $O(\log i)$ rather than $O(\log N)$.

• Hence, (A) Both (A) and (R) are true, and (R) is the correct explanation of (A).