Answer:
I ... 3
II ... 4
III ... 2
IV ... 1
Step-by-step explanation:
Recall binomial theorem as
(x+y)^n = x^n+nCr x^(n-1)Y+....+y^n
Using the above we find that
(x+y)^4 = x^4+4x^3+6x^2+4x+1
Hence 4 matches with 1.
Next option 27,54,36,8
are from (3x+2y)^3 because
(3x+2y)^3 = 27x^3+8y^3+18xy(3x+2y)
Option 2 for question 3.
Next is (2x+y)^3 will have 4 terms with coefficients as
8, 12,6,1
So I question for option 4.
The last question 2 = (2x+3y)^4
= (2x)^4+4(2x)^3(3y) + 6(2x)^2(3y)^2+4(2x)(3y)^3+(3y)^4
Hence coefficients are 16,96, 216,216 and 81
I ... 3
II ... 4
III ... 2
IV ... 1