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JEE Advanced Sets and Relations — practice questions

Explore 36 free Sets and Relations questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sets and Relations questions and exercises with answers

Showing questions 1–30 of 36.

Inverse of function f exists if and only if f is:Read the answer and worked solution →Composition of functions (g ∘ f)(x) =Read the answer and worked solution →If A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, find A ∩ B:Read the answer and worked solution →Number of subsets of {1, 2, 3, 4, 5} with exactly 3 elements:Read the answer and worked solution →For 3 sets A, B, C: n(A ∪ B ∪ C) =Read the answer and worked solution →100 students; 50 like math, 60 like physics, 30 like both. Find students who like neither:Read the answer and worked solution →Number of one-one functions from {1, 2, 3} to {a, b, c, d, e}:Read the answer and worked solution →Equivalence relation requires:Read the answer and worked solution →For sets A, B: A × B = B × A iff:Read the answer and worked solution →Range of f(x) = sin(x) from R to R:Read the answer and worked solution →|A| = 5, |B| = 3. Number of relations from A to B:Read the answer and worked solution →For f: A → B and g: B → C, (g ∘ f)⁻¹ =Read the answer and worked solution →Function f(x) = (x-1)/(x+2) on R - {-2}. f is bijection from R - {-2} to R - {?}:Read the answer and worked solution →Equivalence classes of 'congruent mod 3' on Z:Read the answer and worked solution →Number of one-one and onto (bijective) functions from {1,2,3} to {1,2,3}:Read the answer and worked solution →For function f(x) = ax + b (a ≠ 0), inverse is:Read the answer and worked solution →For f: R → R, f(x) = x³, f is:Read the answer and worked solution →Distributive law: A ∩ (B ∪ C) =Read the answer and worked solution →Inverse image f⁻¹(B) under f: X → Y for B ⊆ Y:Read the answer and worked solution →Number of equivalence relations on set {a, b, c}:Read the answer and worked solution →If $n(A)=3$ and $n(B)=2$, then $n(A\times B)$ equals:Read the answer and worked solution →The Cartesian product $A\times B$ is the set of all:Read the answer and worked solution →If $n(A)=2$ and $n(B)=3$, the number of relations from $A$ to $B$ is:Read the answer and worked solution →If $n(A)=2$ and $n(B)=3$, the number of functions from $A$ to $B$ is:Read the answer and worked solution →The domain of the function $f(x)=\dfrac{1}{x-2}$ is:Read the answer and worked solution →The range of the function $f(x)=x^2,\; x\in\mathbb{R}$ is:Read the answer and worked solution →The domain of $f(x)=\sqrt{x-1}$ is:Read the answer and worked solution →If $(x+1,\,y-2)=(3,\,1)$, then $(x,y)$ equals:Read the answer and worked solution →The domain of $f(x)=\sqrt{4-x^2}$ is:Read the answer and worked solution →If $f(x)=x^2+1$, then $f(2)$ equals:Read the answer and worked solution →

Worked practice questions

Inverse of function f exists if and only if f is:

  1. Even
  2. Continuous
  3. Bijective (one-one AND onto)
  4. Linear
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Correct answer: C. Bijective (one-one AND onto)

f⁻¹ exists iff f is bijection. We have (f⁻¹ ∘ f)(x) = x. So (f⁻¹ ∘ f)(x) = (f ∘ f⁻¹)(y). e.g., f(x) = x³ is bijective; f⁻¹(y) = y^(1/3). f(x) = x² is not.

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Composition of functions (g ∘ f)(x) =

  1. g(f(x)) — apply f first, then g
  2. f(x) × g(x)
  3. f(g(x))
  4. Random
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Correct answer: A. g(f(x)) — apply f first, then g

(g ∘ f)(x) = g(f(x)). Inner function applied first. **NOT commutative in general:** f ∘ g ≠ g ∘ f.

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If A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, find A ∩ B:

  1. {1,2}
  2. ∅
  3. {3, 4, 5}
  4. {3, 4, 5}
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Correct answer: C. {3, 4, 5}

Intersection = common elements = {3, 4, 5}. n(A ∩ B) = 3. By inclusion-exclusion: n(A ∪ B) = 5 + 5 - 3 = 7.

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