PrepWiser › Learn › Mathematics › Relations & Functions (Basic)Relations & Functions (Basic) — JEE Main PYQs & Practice Questions Relations & Functions (Basic) is a Mathematics chapter in the JEE Main syllabus. This page brings together 148 previous-year and practice questions on Relations & Functions (Basic), organised into 6 topics: Cartesian Product, Types of Relations, Types of Functions, Even, Odd and Periodic Functions, Greatest Integer and Fractional Part and Composition of Functions. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Cartesian Product Let R be a relation defined on the set {1,2,3,4}× {1,2,3,4} by… Let A={1,4,7} and B={2,3,8}. Then the number of elements, in the relation… Let A={2,3,4,5,6}. Let R be a relation on the set A× A given by (x,y)R(z,w) if and only… The number of elements in the relation R={(x,y):4x²+y²<52,x,y∈ Z} is Let f:R → R be a function such that f(x) = (x² + 2x + 1)/(x² + 1). Then Types of Relations Let A={0,1,2,…,9}. Let R be a relation on A defined by (x,y)∈ R if and only if |x-y| is… Let A = 2, 3, 4, 5, ....., 30 and '≃' be an equivalence relation on A × A, defined by… Let X=R × R. Define a relation R on X as : (a₁, b₁) R(a₂, b₂) ⇔ b₁=b₂ Statement I: R is… The number of symmetric relations defined on the set {1,2,3,4} which are not reflexive… The number of relations, on the set {1,2,3} containing (1,2) and (2,3), which are… Let A={-2,-1,0,1,2,3,4}. Let R be a relation on A defined by xRy if and only if 2x+y≤ 2… Let R = (P, Q) | P and Q are at the same distance from the origin be a relation, then… The number of equivalence relations on a set with 3 elements is x. Let S=N ∪{0}. Define a relation R from S to R by : R={(x, y): log ₑ y=x log ₑ(2/5), x ∈… A relation that is symmetric and transitive must also be reflexive. If R = (x, y) : x, y ∈ Z, x² + 3y² ≤ 8 is a relation on the set of integers Z, then the… Let R₁ and R₂ be relations on the set 1, 2, ......., 50 such that R₁ = (p, pⁿ) : p is a… Consider the relations R₁ and R₂ defined as a R₁ b ⇔ a²+b²=1 for all a, b ∈ R and (a, b)… Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only… Let R be a relation on ℝ, given by R={(a, b): 3 a-3 b+√7 is an irrational number }. Then… Let A={-2,-1,0,1,2,3}. Let R be a relation on A defined by x R y if and only if y=max… A relation R on set {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2)}. R is: Let A={1,2,3,4, … ., 10} and B={0,1,2,3,4}. The number of elements in the relation… The minimum number of elements that must be added to the relation R={(a, b),(b, c)} on… Let A={1,2,3, … … … …, 100}. Let R be a relation on A defined by (x, y) ∈ R if and only… Types of Functions Let f:(0,1)→ℝ be a function defined f(x) = 1/(1 - e⁻ˣ), and g(x) = ( f( - x) - f(x) )… Consider two sets A={x∈ Z:|(|x-3|-3)|≤ 1} and B={x∈… Let A={1,2,3,4} and B={1,4,9,16}. Then the number of many-one functions f: A → B such… The function f: N-{1} → N; defined by f(n)= the highest prime factor of n, is : The number of one-one functions f : a, b, c, d → 0, 1, 2, ......, 10 such that 2f(a) -… Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime… Which of the following is a one-one (injective) function from ℝ to ℝ? Every bijective function has an inverse. The number of functions f, from the set A={x ∈ N: x²-10 x+9 ≤ 0} to the set B={n²: n ∈… Let f, g: ℕ-{1} → ℕ be functions defined by f(a)=α, where α is the maximum of the powers… Let a function f : N → N be defined by f(n) = [ 2n,, n = 2,4,6,8,......; n - 1,, n =… The function f(x)=(x²+2 x-15)/(x²-4 x+9), x ∈ ℝ is If f(f(x)) = x for all x in domain, and f is one-one, then f(f(x)) = x. (Find the… Given below are two statements : Statement I : The function f:ℝ→ ℝ defined by… Let A={(x, y): 2 x+3 y=23, x, y ∈ ℕ} and B={x:(x, y) ∈ A}. Then the number of one-one… Let S = 1, 2, 3, 4. Then the number of elements in the set f : S × S → S : f is onto and… Let A={1,2,3,4,5,6}. The number of one-one functions f:A→ A such that f(1)≥ 3,f(3)≤ 4… Let f, g : N → N such that f(n + 1) = f(n) + f(1) ∀ n∈N and g be any arbitrary function… A function f: ℝ → ℝ is defined by f(x) = x². It is: Let R={a, b, c, d, e} and S={1,2,3,4}. Total number of onto functions f: R → S such that… Even, Odd and Periodic Functions Greatest Integer and Fractional Part Fractional part of the number 4²⁰²²/15 is equal to If [x] be the greatest integer less than or equal to x, then Σₙ₌₈¹⁰⁰ [ ( - 1)ⁿn/2 ] is… Let [ • ] denote the greatest integer function. If the domain of the function… If the domain of the function f(x)=[x]/(1+x²), where [x] is greatest integer ≤ x, is… Let [x] denote the greatest integer less than or equal to x. Then, the values of x∈R… Let [ x ] denote the greatest integer ≤ x, where x ∈ R. If the domain of the real valued… Let f(x)=[x]²-[x+3]-3,x∈ R, where [.] is the greatest integer funtion. Then The absolute minimum value, of the function f(x)=|x²-x+1|+[x²-x+1], where [t] denotes… The sum of the maximum and minimum values of the function f(x)=|5 x-7|+[x²+2 x] in the… Let [•] denote the greatest integer function. If the domain of the function… Let [t] denote the greatest integer ≤ t. Then the equation in x, [x]² + 2[x+2] - 7 = 0… If S={a ∈ R:|2 a-1|=3[a]+2{a }}, where [t] denotes the greatest integer less than or… The domain of the function f(x)=1/√([x]²-3[x]-10) is : ( where [x] denotes the greatest… The equation x² - 4x + [x] + 3 = x[x], where [x] denotes the greatest integer function… Let ƒ : (1, 3) → R be a function defined by f(x) = x[ x ]/(1 + x²) , where [x] denotes… The real valued function f(x) = (cos ec⁻¹x)/√(x - [x]), where [x] denotes the greatest… Let the sets A and B denote the domain and range respectively of the function f(x)=1/√(⌈… Let [α] denote the greatest integer ≤ α. Then [√1]+[√2]+[√3]+…+[√120] is equal to… Composition of Functions If g(x)=3x²+2x-3,f(0)=-3 and 4g(f(x))=3x²-32x+72, then f(g(2)) is equal to: Let f(x) = sin ⁻¹x and g(x) = (x² - x - 2)/(2x² - x - 6). If g(2) = lim _(x → 2) g(x)… For some a, b, c ∈ℕ, let f(x) = ax - 3 and g(x)=xᵇ+c,x∈ℝ. If (fog)⁻¹(x) = ( (x - 7)/2… Let f(x) = (x - 1)/(x + 1), x ∈ R - { 0, - 1,1}. If fⁿ⁺¹(x) = f(fⁿ(x)) for all n ∈ N… Let f¹(x)=(3 x+2)/(2 x+3), x ∈ R-{-3/2} For n ≥ 2, define fⁿ(x)=f¹ o fⁿ⁻¹(x). If… If g(x) = x² + x - 1 and (goƒ) (x) = 4x² - 10x + 5, then ƒ( 5/4 ) is equal to: Composition of functions is commutative: f∘g = g∘f for all f, g. Let f : R → R be defined as f (x) = 2x – 1 and g : R - 1 → R be defined as g(x) = (x -… Let f : R → R be defined as f (x) = x - 1 and g : R - 1, -1 → R be defined as g(x) =… Consider function f : A → B and g : B → C (A, B, C ⊆ R) such that (gof)⁻¹ exists, then : Consider the function f: ℝ → ℝ defined by f(x)=(2 x)/√(1+9 x²). If the composition of f… Let f: R → R and g: R → R be defined as f(x)={log ₑ x,, x>0; e⁻ˣ,, x ≤ 0 and g(x)={x,, x… Let f, g:(1, ∞) → ℝ be defined as f(x)=(2 x+3)/(5 x+2) and g(x)=(2-3 x)/(1-x). If the… If f(x)=(4 x+3)/(6 x-4), x ≠ 2/3 and (f ° f)(x)=g(x), where g: ℝ-{2/3} → ℝ-{2/3}, then… Let f, g: R → R be defined as : f(x)=|x-1| and g(x)= eˣ, x ≥ 0 ; x+1, x ≤ 0 . Then the… Let A = { 1,2,3,....,10} and f:A → A be defined as f(k) = { k + 1, if k is odd; k, if k… If f and g are both one-one functions, then fog is x (one-one/onto/bijective). Let f(x)=log ₑ x and g(x)=(x⁴-2 x³+3 x²-2 x+2)/(2 x²-2 x+1). Then the domain of f ° g is For x ∈ ℝ, two real valued functions f(x) and g(x) are such that, g(x)=√x+1 and f °… Let f:R - { α/6 } → R be defined by f(x) = (5x + 3)/(6x - α). Then the value of α for… More Mathematics chapters Frequently asked questions How many Relations & Functions (Basic) questions are there for JEE Main? PrepWiser has 148 Relations & Functions (Basic) questions for JEE Main, grouped into 6 topics such as Cartesian Product, Types of Relations and Types of Functions.
Are these Relations & Functions (Basic) questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Relations & Functions (Basic) questions? Open any Relations & Functions (Basic) question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.