The constant term in the expansion of (2 x+(1/x7)+3 x2)5 is

Question

The constant term in the expansion of (2 x+(1/x7)+3 x2)5 is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

General term is ∑ (5 !(2 x)n1(x-7)n2(3 x2)n3/n1 ! n2 ! n3 !) For constant term, n 1+2 n 3=7 n 2 n 1+ n 2+ n 3=5 Only possibility n 1=1, n 2=1, n 3=3 ⇒ constant term =1080

Q. The constant term in the expansion of $(2 x + \frac{1}{x ^{7}} + 3 x^{2})^{5}$ is_____

General term is $\sum \frac{5 ! ( 2 x ) ^{n_{1}} ( x ^{- 7} ) ^{n_{2}} ( 3 x ^{2} ) ^{n_{3}}}{n _{1} ! n _{2} ! n _{3} !}$
For constant term,
$n_{1} + 2 n_{3} = 7 n_{2}$
$& n_{1} + n_{2} + n_{3} = 5$
Only possibility $n_{1} = 1, n_{2} = 1, n_{3} = 3$
$\Rightarrow$ constant term $= 1080$

Q. The constant term in the expansion of (2x+x71​+3x2)5 is_____

General term is ∑n1​!n2​!n3​!5!(2x)n1​(x−7)n2​(3x2)n3​​ For constant term, n1​+2n3​=7n2​ &n1​+n2​+n3​=5 Only possibility n1​=1,n2​=1,n3​=3 ⇒ constant term =1080

Q. The constant term in the expansion of $(2 x + \frac{1}{x ^{7}} + 3 x^{2})^{5}$ is_____

General term is $\sum \frac{5 ! ( 2 x ) ^{n_{1}} ( x ^{- 7} ) ^{n_{2}} ( 3 x ^{2} ) ^{n_{3}}}{n _{1} ! n _{2} ! n _{3} !}$
For constant term,
$n_{1} + 2 n_{3} = 7 n_{2}$
$& n_{1} + n_{2} + n_{3} = 5$
Only possibility $n_{1} = 1, n_{2} = 1, n_{3} = 3$
$\Rightarrow$ constant term $= 1080$