Number of positive integral solutions of the equation $x y z = 90$ is

120

No worries! We‘ve got your back. Try BYJU‘S free classes today!

54

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

108

No worries! We‘ve got your back. Try BYJU‘S free classes today!

60

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $54$
As $x y z = 90 \Rightarrow x y z = 2^{1} \times 3^{2} \times 5^{1}$ $Let x = 2^{a_{1}} \times 3^{b_{1}} \times 5^{c_{1}} y = 2^{a_{2}} \times 3^{b_{2}} \times 5^{c_{2}} z = 2^{a_{3}} \times 3^{b_{3}} \times 5^{c_{3}} So, a_{1} + a_{2} + a_{3} = 1, Total Solutions will be =^{1 + 3 - 1} C_{3 - 1} = 3 b_{1} + b_{2} + b_{3} = 2, Total Solutions will be =^{2 + 3 - 1} C_{3 - 1} = 6 c_{1} + c_{2} + c_{3} = 1 Total Solutions will be =^{1 + 3 - 1} C_{3 - 1} = 3 ∴ Total number of solutions are = 3 \times 6 \times 3 = 54.$

Suggest Corrections

Similar questions

x y z = 60

x y z = 90

x y z = 21600

x y z = 30

(x, y, z)

x y z = 24

Join BYJU'S Learning Program