NIELIT 2016 MAR Scientist C - Section C: 18

Question

Two alternative package $A$ and $B$ are available for processing a database having $10^{k}$ records. Package $A$ requires $0.0001 n^{2}$ time units and package $B$ requires $10n\log _{10}n$ time units to process $n$ records. What is the smallest value of $k$ for which package $B$ will be preferred over $A$?

• A. $12$
• B. $10$
• C. $6$
• D. $5$

Answer 1

This can be solved using substitution.

Substituting the value of 6 in k we get that A takes more time (10^8) than B (6 * 10^7). making B more preferable than A.

Answer 2

I think answer should be D

Answer 3

https://gateoverflow.in/2185/Gate-cse-2010-question-12

 

//asked in gate 2010.