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Sets · Question 1

JEE Main 2026 (Online) 22nd January Evening ShiftNumericalEasy📈 Topic in 6% papers+4
1

Let S be the set of the first 11 natural numbers. Then the number of elements in A = \B S : n(B) 2 and the product of all elements of B is even\ is .

Answer

1979

Solution

S = \1, 2, , 11\ has 5 even and 6 odd numbers.

The product of the elements of B is even B contains at least one even number.

Non-empty subsets with at least one even number = 211 - 26 = 2048 - 64 = 1984

(all subsets minus the subsets made of odd numbers only, including )

Of these, subsets with only one element are \2\, \4\, \6\, \8\, \10\, i.e. 5.

n(A) = 1984 - 5 = 1979

Answer: 1979

JEE Main 2026 (Online) 22nd January Evening Shift

Keep practising — Sets

2

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]
JEE Main 2026 (Online) 21st January Evening Shift
3

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
4

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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Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)