Sets & Operations: JEE Questions & Solutions

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

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…

Let A = {1, 2, 3, …, 10} and B = { m/n: m, n ∈ A, m < n and gcd(m, n) = 1 }. Then n(B) is equal to:

Let A = {(x, y) ∈ ℝ × ℝ: |x + y| ≥ 3} and B = {(x, y) ∈ ℝ × ℝ: |x| + |y| ≤ 3}. If C = {(x, y) ∈ A ∩ B: x = 0 or y = 0}, then Σ_((x, y) ∈ C)…

Let S = {p₁, p₂, …, p₁₀} be the set of the first ten prime numbers. Let A = S ∪ P, where P is the set of all possible products of distinct…

Let A = { x ∈ (0, π) - { π/2 }: log_(2/π) |sin x| + log_(2/π) |cos x| = 2 } and B = { x ≥ 0: √x(√x - 4) - 3|√x - 2| + 6 = 0 }. Then n(A ∪…

Let M denote the set of all real matrices of order 3 × 3 and let S = {-3, -2, -1, 1, 2}. Let S₁ = {A = [a_ij] ∈ M: A = A^T and a_ij ∈ S, ∀…

Let the set C = {(x, y) | x² - 2^y = 2023, x, y ∈ N}. Then Σ_((x, y)∈ C)(x + y) is equal to:

A group of 40 students appeared in an examination of 3 subjects — Mathematics, Physics and Chemistry. It was found that all students passed…

Let A = {n ∈ [100, 700] ∩ N: n is neither a multiple of 3 nor a multiple of 4}. Then the number of elements in A is:

Let A = {x ∈ ℝ: [x+3] + [x+4] ≤ 3} and B = {x ∈ ℝ: 3^x(Σ_(r=1)^∞3/10^r)^(x-3) < 3^(-3x)}, where [t] denotes the greatest integer function.…

Let the sets A and B denote the domain and range respectively of the function f(x) = 1/√([x] - x), where [x] denotes the smallest integer…

Negation of ((p → q) → (q → p)) is:

The number of elements in the set {n ∈ ℤ: |n² - 10n + 19| < 6} is:

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only 5 men…

The number of elements in the set { n∈ℕ: 10≤ n≤ 100 and 3ⁿ-3 is a multiple of 7 } is