Q63 / 120 · VITEEE 2007 · Mathematics
The number of positive integral solutions of the equation $x_{1} x_{2} x_{3} x_{4} x_{5}=1050$ is
- A1870
- Correct answerB1875
- C1865
- D1880
Solution
Given, $x_{1} x_{2} x_{3} x_{4} x_{5}=1050$
$\Rightarrow x_{1} x_{2} x_{3} x_{4} x_{5}=2 \times 3 \times 5^{2} \times 7$
Each of 2,3 or 7 can take 5 places and $5^{2}$ can be disposed in 15 ways.
Hence, number of positive integral solution $=5^{3} \times 15=1875$
Hence, the correct answer is option: 'B'.