1.

The coefficient of `x^2 y^5 z^3` in the expansion of `(2x + y + 3z)^10` isA. `(10!)/(2!3!5!)`B. `(10!)/(2!3!5!)xx2^(2) xx3^(3)`C. `(10!)/(2!3!5!)xx2^(3) xx3^(2)`D. `10! xx2^(2) xx3^(3)`

Answer» Correct Answer - b
We have,
`(2x +y +3z)^(10) = sum_(r_(1)+r_(2)+r_(3) = 10) (10!)/(r_(1)!r_(2)!r_(3)!)(2x)^(r_(1)) (y)^(r_(2)) (3z)^(r_(3))`
The general term in the above expansion is
(10!)/(r_(1)!r_(2)!r_(3)!)(2x)^(r_(1)) (y)^(r_(2)) (3z)^(r_(3))=(10!)/(r_(1)!r_(2)!r_(3)!)2^(r_(1))3^(r_(3))x^(r_(1))y^(r_(2)) z^(r_(3)`
For the coefficient of `x^(2) `y^(5) z^(3)`, we must have
`r_(1) = 2 , r_(2) = 5 and r_(3) = 3.`
So, coefficient of `x^(2) y^(5) z^(3) = (10!)/(2!5!3!) 2^(2) xx3^(3)` .


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