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JEE Advanced 2018Paper 1
Exam
JEE Advanced
Year
2018
Paper
Paper 1
Subject
Mathematics
Chapter
Sequences and Series

JEE Advanced 2018 · Paper 1 · Mathematics · Sequences and Series

Let X be the set consisting of the first 2018 terms of the...

Let XX be the set consisting of the first 20182018 terms of the arithmetic progression 1,6,11,…,1,6, 11, \ldots , and YY be the set consisting of the first 20182018 terms of the arithmetic progression 9,16,23,…9,16,23, \ldots . Then, the number of elements in the set X∪YX \cup Y is___.

Correct answer

0

Step-by-step solution

X:1,6,11,…,10086X: 1, 6, 11, \ldots , 10086
Y:9,16,23,….,14128Y: 9, 16, 23, \ldots . , 14128
X∩Y:16,51,86,…..X \cap Y: 16, 51, 86, \ldots . .
Let m=n(X∩Y)m = n\left(X \cap Y\right)
∴16+(m−1)×35≤10086∴ 16 + \left(m - 1\right) \times 35 \le 10086
⇒m≤288.71⇒ m \le 288.71
⇒m=288⇒ m = 288
∴n(X∪Y)=n(X)+n(Y)−n(X∩Y)∴ n\left(X \cup Y\right) = n\left(X\right) + n\left(Y\right) - n\left(X \cap Y\right)
=2018+2018−288=3748= 2018 + 2018 - 288 = 3748
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