Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
Let $\mathrm{f}(\mathrm{x})$ be a polynomial with integer coefficients satisfying $\mathrm{f}(1)=5$ and $\mathrm{f}(2)=7$. The smallest possible positive value of $\mathrm{f}(12)$ is
MathematicsLinear ProgrammingKVPYKVPY 2017 (19 Nov SB/SX)
Options:
  • A 5
  • B 7
  • C 27
  • D 15
Solution:
2223 Upvotes Verified Answer
The correct answer is: 27
$\mathrm{f}(\mathrm{x})=\mathrm{ax}+\mathrm{b}$
$5=\mathrm{a}+\mathrm{b}$
$7=2 \mathrm{a}+\mathrm{b}$
solve $\quad \mathrm{a}=2$
$\quad \mathrm{~b}=3$
$\quad \mathrm{f}(\mathrm{x})=2 \mathrm{x}+3$
$\mathrm{f}(12)=24+3$
$\mathrm{f}(12)=27$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.