Sets · Question 4

JEE Main 2025 (Online) 4th April Morning ShiftMCQMedium📈 Topic in 3% papers+4−1

Let A = \1, 6, 11, 16, \ and B = \9, 16, 23, 30, \ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A B) is

Answer

(4) 3761

A: an = 1 + (n-1)5 = 5n - 4; last term = 5(2025) - 4 = 10121

B: bm = 9 + (m-1)7 = 7m + 2; last term = 7(2025) + 2 = 14177

Common terms form an A.P. with first term 16 and common difference LCM(5, 7) = 35:

16, 51, 86, …, and they must not exceed 10121.

⇒ 16 + (k - 1)35 10121

⇒ k - 1 288.7 ⇒ k = 289

∴ n(A B) = 289

n(A B) = n(A) + n(B) - n(A B)

= 2025 + 2025 - 289 = 3761

Answer: (4)

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