Assertion (A): Case 1 of the Master Theorem applies to the recurrence relation . Reason (R): For this recurrence, grows polynomially smaller than , satisfying the condition .

Both (A) and (R) are true, and (R) is the correct explanation of (A). Explanation: Master Theorem Formulation: For a recurrence relation of the form , where and : Here, , , and . Calculating Critical Term: Analysis of Assertion (A) & Reason (R): We compare with . for . Since is polynomially smaller than , Case 1 of the Master Theorem applies and gives . Therefore, Assertion (A) is True and Reason (R) is True . Relationship: Reason (R) states the exact condition and mathematical justification for why Case 1 applies to this recurrence relation. Hence, (R) is the correct explanation of (A) .

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CUET PG 2026 — DSA PYQ

CUET PG | DSA | 2026

Assertion (A): Case 1 of the Master Theorem applies to the recurrence relation $T (n) = 8 T (n /2) + n^{2}$ .

Reason (R): For this recurrence, $f (n) = n^{2}$ grows polynomially smaller than $n^{l o g_{b} a} = n^{3}$ , satisfying the condition $f (n) = O (n^{l o g_{b} a - ϵ})$ .

Choose the correct answer: