Relations and Functions

CBSE Class 12 Mathematics · 70 board questions from this chapter; 69 listed below, 2023–2026

• A relation R on set A={1,2,3} defined as R={(1,1),(2,2),(1,2)} is2026
• A relation R on set A={1,2,3} is defined as R={(1,3),(3,3),(1,1),(2,2), (3,1)} is2026
• For f(x)=x+1/x(x ≠ 0)2026
• A relation R on set A={1,2,3} defined as R={(1,2),(2,1),(2,2)} is2026
• Assertion: A relation R on the set {1,2,3} defined as R={(1,1),(1,2),(2,1),(2,2),(3,3)} is an equivalence relation. Reason (R): A…2026
• Assertion: A function f: N → N given by f(x)=x^3+2, ∀ x ∈ N is one-one but not onto. Reason (R): Since ∀ y ∈ N (Codomain), there…2026
• Check whether f: R-{3} → R defined as f(x)=(x-2)/(x-3) is onto or not. OR Check whether f: Z × Z → Z × Z (where Z is the set of…2026
• Let A=R-{3} and B=R-{1}. A function f: A → B is defined by f(x)=((x-2)/(x-3)). Find whether f is one-one and onto. OR Let n be a…2026
• A relation R is defined on Z, the set of integers, as R={(x, y):|x-y| is divisible by a prime number ' p ', x, y ∈ Z} check…2026
• Show that f: R → R defined as f(x)=x/(√(1+x^2)) is one-one but not onto.2026
• Show that a function f: R_+ → A ⊂ N, defined as f(x)=4 x^2+12 x+15 is one-one. Find set A so that f is onto where R_+=[0, ∞).…2026
• Show that f: R_+ →[-5, ∞) given by f(x)=4 x^2+4 x-5 is both one-one and onto where R_+=[0, ∞). Also, find p ∈ R_+ such that…2026
• A school wants the students of class XII to do a project on 'Sustainability' keeping the world environment in mind. They select…2026
• For real x, let f(x)=x^3+5 x+1. Then:2025
• If f(x)=|x|+|x-1|, then which of the following is correct?2025
• If f: N → W is defined as f(n)= {n/2, if n is even; 0, if n is odd}, then f is:2025
• If f(x)=-2 x^8, then the correct statement is:2025
• If f(x)={[x], x ∈ R} is the greatest integer function, then the correct statement is:2025
• Let f(x)=|x|, x ∈ R. Then, which of the following statements is incorrect?2025
• Let f(x)=x^2, x ∈ R. Then, which of the following statements is incorrect?2025
• If R be a relation defined as a R b iff |a-b|>0 a, b ∈ R then R is:2025
• If f: R → R is defined as f(x)=2 x- sin x, then f is:2025
• For a function f(x), which of the following holds true?2025
• If f(x)=2 x+ cos x, then f(x):2025
• Assertion: Let Z be the set of integers. A function f: Z → Z defined as f(x)=3 x-5, ∀ x ∈ Z is a bijective. Reason (R): A…2025
• Assertion: Let f(x)=e^x and g(x)= log x. Then (f+g) x=e^x+ log x where domain of ( f+g ) is R. Reason (R): Dom(f+g)=Dom(f) ∩…2025
• Assertion: Let A={x ∈ R:-1 ≤ x ≤ 1}. If f: A → A be defined as f(x)=x^2, then f is not an onto function. Reason (R): If y=-1 ∈ A,…2025
• Let f: A → B be defined by f(x)=(x-2)/(x-3), where A=R-{3} and B=R-{1}. Discuss the bijectivity of the function.2025
• If f: R^+ → R is defined as f(x)= log_a x(a>0 and a ≠ 1), prove that f is a bijection. ( R^+ is a set of all positive real…2025
• Show that the function f: R → R defined by f(x)=4 x^3-5, ∀ x ∈ R is one-one and onto. OR Let R be a relation defined on a set N…2025
• Let R be a relation on set of real numbers R defined as {(x, y): x-y+√3 is an irrational number, x, y ∈ R} Verify R for…2025
• Let R be a relation defined over N, where N is set of natural numbers, defined as" m R n if and only if m is a multiple of n, m,…2025
• Prove that f: N → N defined as f(x)=a x+b(a, b ∈ N) is one-one but not onto.2025
• A student wants to pair up natural numbers in such a way that they satisfy the equation 2 x+y=41, x, y ∈ N. Find the domain and…2025
• A school is organizing a debate competition with participants as speakers S={S_1, S_2, S_3, S_4} and these are judged by judges…2025
• A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the…2025
• Let A be the set of 30 students of class XII in a school. Let f: A → N, N is a set of natural numbers such that function f(x)=…2025
• A function f: R_+ → R (where R_+ is the set of all non-negative real numbers) defined by f(x)=4 x+3 is:2024
• A function f: R → R defined as f(x)=x^2-4 x+5 is:2024
• Let f: R_+ →[-5, ∞) be defined as f(x)=9 x^2+6 x-5, where R_+ is the set of all non-negative real numbers. Then, f is:2024
• Let R_+ denote the set of all non-negative real numbers. Then the function f: R_+ → R_+ defined as f(x)=x^2+1 is:2024
• A function f(x)=|1-x+|x|| is:2024
• A relation R defined on a set of human beings as R={(x, y): x is 5 cm shorter than y } is:2024
• A function f: R → A defined as f(x)=x^2+1 is onto, if A is:2024
• Let Z denote the set of integers, then function f: Z → Z defined as f(x)=x^3-1 is:2024
• A relation R defined on set A={x: x ∈ Z and 0 ≤ x ≤ 10} as R={(x, y): x=y} is given to be an equivalence relation. The number of…2024
• Which of the following statements is not true about equivalence classes A_i(i=1,2, …. n) formed by an equivalence relation R…2024
• Assertion: The relation R={(x, y):(x+y) is a prime number and x, y ∈ N} is not a reflexive relation. Reason (R): The number ' 2 n…2024
• A relation R on set A={1,2,3,4,5} is defined as R={(x, y):|x^2-y^2|<8}. Check whether the relation R is reflexive, symmetric and…2024
• Show that a function f: R → R defined by f(x)=(2 x)/(1+x^2) is neither one-one nor onto. Further, find set A so that the given…2024
• Let A=R-{5} and B=R-{1}. Consider the function f: A → B, defined by f(x)=(x-3)/(x-5). Show that f is one-one and onto. OR Check…2024
• Show that a function f: R → R defined as f(x)=x^2+x+1 is neither one-one nor onto. Also, find all the values of x for which…2024
• Let A=R-{3} and B=R-{a}. Find the value of 'a' such that the function f: A → B defined by f(x)=(x-2)/(x-3) is onto. Also, check…2024
• A relation R on set A={x:-10 ≤ x ≤ 10, x ∈ Z} is defined as R={(x, y):(x-y) is divisible by 5 }. Show that R is an equivalence…2024
• Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum…2024
• Let R be a relation in the set N given by R={(a, b): a=b-2, b>6}. Then2023
• Let A={3,5}. Then number of reflexive relations on A is2023
• If f(x)=| cos x|, then f((3 π)/4) is2023
• The function f(x)=x|x| is2023
• Assertion: The number of onto functions from a set P containing 5 elements to a set Q containing 2 elements is 30. Reason (R):…2023
• A function f: A → B defined as f(x)=2 x is both one-one and onto. If A={1,2,3,4}, then find the set B. OR Evaluate: sin^-1( sin…2023
• A relation R is defined on a set of real numbers R as R={(x, y): x · y is an irrational number }. Check whether R is reflexive,…2023
• Show that a function f: R → R defined as f(x)=(5 x-3)/4 is both one-one and onto.2023
• Check whether a function f: R →[-1/2, 1/2] defined as f(x)=x/(1+x^2) is one-one and onto or not.2023
• Prove that a function f:[0, ∞) →[-5, ∞) defined as f(x)=4 x^2+4 x-5 is both one-one and onto.2023
• If N denotes the set of all natural numbers and R is the relation on N × N defined by (a, b) R(c, d), if ad(b+c)=bc(a+d). Show…2023
• A function f:[-4,4] →[0,4] is given by f(x)=√(16-x^2). Show that f is an onto function but not a one-one function. Further, find…2023
• A function f:[-4,4] →[0,4] is given by f(x)=√(16-x^2). Show that f is an onto function but not a one-one function. Further, find…2023
• An organization conducted bike race under two different categories - Boys and Girls. There were 28 participants in all. Among all…2023

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