A) 2032
B) 4032
C) 8066
D) 8064
Correct Answer: D
Solution :
\[xy=15!={{2}^{11}}{{.3}^{6}}{{5}^{3}}{{.7}^{2}}.11.13\] No. of positive integral solutions = No. of ways of fixing x = Number of factors \[=15!=(11+1)(6+1)(3+1)\]\[(2+1)\]\[{{(1+1)}^{2}}=4032\] \[\therefore \] Total number of integral solutions \[=24032=8064\] (As solution can be positive or negative) As \[HCF(\alpha ,\beta )=1\] So, \[\alpha \And \beta \] will not have common factor other than 1, so identical prime number should not be separated. So, the number of solutions \[={{2}^{6}}.\] (4)You need to login to perform this action.
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