JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q61

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MathematicsSingle correct+4 / -1Question 61 of 90

If $X=\{4^n-3n-1:n\in N\}$ and $Y=\{9(n-1):n\in N\}$ , where N is the set of natural numbers, then $X\cup Y$ is equal to :

Y-X

Answer and worked solution

Official answer: B

$4^n=(1+3)^n=1+3n+9\left[\binom n2+3\binom n3+\dots\right]$ , so $4^n-3n-1$ is always a multiple of 9 (and is 0 for $n=1$ ). Thus $X\subseteq Y=\{0,9,18,\dots\}$ , and $X\cup Y=Y$ .

Topics:Sets and operations Properties of binomial coefficients

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 61