QJEEAdv18Mac024: JEE Advanced 2018 Mathematics - Class 11 JEEAdv18Mac024 Solution: Let X be the set consisting of the first 2018 terms of the…

Here, X = {1, 6, 11, ....., 10086}

[$$\because$$ a_n = a + (n $$-$$ 1)d]

and Y = {9, 16, 23, ..., 14128}

X $$\cap$$ Y = {16, 51, 86, ...}

t_n of X $$\cap$$ Y is less than or equal to 10086

$$\therefore$$ t_n = 16 + (n $$-$$ 1) 35 $$\le$$ 10086

$$\Rightarrow$$ n $$\le$$ 288.7

$$\therefore$$ n = 288

$$\because$$ n(X $$\cap$$ Y) = n(X) + n(Y) $$-$$ n(X $$\cap$$ Y)

$$\therefore$$ n(X $$\cap$$ Y) = 2018 + 2018 $$-$$ 288 = 3748