Relations and Functions

CBSE Class 12 Mathematics · every board question from this chapter, 2023–2026 · 40 of them repeated across years

• 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)2026asked 3×
• 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…2026asked 3×
• 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 does…2026asked 3×
• 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…2026asked 3×
• 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…2026asked 3×
• 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 whether…2026asked 3×
• 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, ∞). Also,…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…2026asked 3×
• For real x, let f(x)=x^3+5 x+1. Then:2025asked 3×
• If f(x)= x + x-1, then which of the following is correct?2025asked 3×
• If f: N → W is defined as f(n)=,. then f is:2025asked 3×
• If f(x)=-2 x^8, then the correct statement is:2025asked 3×
• If f(x)= [x], x ∈ R is the greatest integer function, then the correct statement is:2025asked 3×
• 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:2025asked 3×
• For a function f(x), which of the following holds true?2025asked 3×
• If f(x)=2 x+ cos x, then f(x):2025asked 2×
• 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 function…2025asked 3×
• 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) Dom(g).2025asked 3×
• 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,…2025asked 3×
• 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.2025asked 3×
• 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…2025asked 3×
• 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 of…2025asked 3×
• 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…2025asked 3×
• 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 J=…2025asked 3×
• A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the…2025asked 3×
• 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)=…2025asked 3×
• 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:2024asked 3×
• 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:2024asked 2×
• 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:2024asked 3×
• 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…2024asked 3×
• 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…2024asked 3×
• 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…2024asked 2×
• 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 whether…2024asked 3×
• 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…2024asked 3×
• 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 is2023asked 2×
• If f(x)= cos x, then f((3 π)/4) is2023
• The function f(x)=x x is2023asked 3×
• 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 (3…2023asked 3×
• 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,…2023asked 3×
• 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…2023asked 3×
• 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…2023asked 2×
• 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…2023asked 3×

Answers come from CBSE’s own marking schemes. How we source them.