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Sets · Question 2

JEE Main 2026 (Online) 21st January Evening ShiftMCQEasy📈 Topic in 3% papers+4−1
1

Let A = \x : |x2 - 10| 6\ and B = \x : |x - 2| > 1\. Then

  1. A B = (- , 1] (2, )
  2. B - A = (- , -4) (-2, 1) (4, )
  3. A - B = [2, 3)
  4. A B = [-4, -2] [3, 4]

Answer

(2) B - A = (- , -4) (-2, 1) (4, )

Solution

|x2 - 10| 6 ⇒ 4 x2 16

A = [-4, -2] [2, 4]

|x - 2| > 1 ⇒ x < 1 or x > 3

B = (- , 1) (3, )

A B = (- , 1) [2, ) ⇒ (1) false

B - A = (- , -4) (-2, 1) (4, ) ⇒ (2) true

A - B = [2, 3] ⇒ (3) false

A B = [-4, -2] (3, 4] ⇒ (4) false

Answer: (2)

JEE Main 2026 (Online) 21st January Evening Shift

Keep practising — Sets

2

Let A = \( , ) R R : | - 1| 4 and | - 5| 6\ and B = \( , ) R R : 16( - 2)2 + 9( - 6)2 144\. Then

  1. A B
  2. B A
  3. neither A B nor B A
  4. A B = \(x, y) : -4 x 4, -1 y 11\
JEE Main 2025 (Online) 7th April Evening Shift
3

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

  1. 3814
  2. 4003
  3. 4027
  4. 3761
JEE Main 2025 (Online) 4th April Morning Shift

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