NIMCET 2020 Question Paper with solutions

let Xn=4n−3n−1,n∊N. then x1=4−3−1=0
And, for n≥2, we have [using Binomial Theorem]
Thus, Xn is some positive integral multiple of 9 for n≥2
Hence, X consists of all positive integral multiplies of 9 of the form
together with 0
Now, y={9(n−1):n∊N}. this shows that Y consists of all integral multiples of 9 together with 0.
In fact, we have
X={0,9,54,243,.....} and y={0,9,18,278,36,54,....}
Thus X ⊂ Y