Relations & Functions: Class 12 Previous Year Questions

Relations & Functions questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. The graph of a trigonometric function is as shown. Which of the following will represent graph of its inverse ? (A) (B) ··/2 ·/2 ·/2 ·/2 (C) (D) ·/2 -1 Assertion - Reason Based Questions Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) b…
   Board 20251 markAssertion-ReasonRepeated: 2025,2026
2. { } 32. (a) A relation R is defined on Z, the set of integers, as 5 R = {(x, y) : |x – y| is divisible by a prime number ‘p’, x, y  Z} check whether R is an equivalence relation or not. OR (b) A function f : R –     3 5  R –     3 5 is d…
   Board 20265 markslong answer
3. A relation R on set A = {1, 2, 3} defined as R = {(1, 1), (2, 2), (1, 2)} is 1 (A) Reflexive only (B) Reflexive and Transitive (C) Symmetric and Transitive (D) Transitive only
   Board 20261 markMCQ
4. (a) Check whether f : R – {3}  R defined as f(x) = 3 2 –  x x is onto or not. 2 OR (b) Check whether f : Z  Z  Z  Z (where Z is the set of integers) defined as f(x, y) = (2y, 3x) is injective or not. 2 d
   Board 20262 marksshort answer
5. { } 38. Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by C1 ; x2 + y2 = 64. There is a circular pond with a fountain in the middle of the ro…
   Board 20264 marksshort answer
6. { } 37. A racing track is build around an elliptical ground whose equation is given by 9x2 + 16y2 = 144. The width of the track is 3 m as shown below : 22 { }          : (i)        y  x     …
   Board 20264 marksshort answer
7. Let R be a relation defined over N, where N is set of natural numbers, defined as ·mRn if and only if m is a multiple of n, m, n e N." Find whether R is reflexive, symmetric and transitive or not.
   Board 20253 marksshort answer
8. A class-room teacher is keen to assess the learning of her students the concept of ·relations· taught to them. She writes the following five relations each defined on the set A = ({1, 2, 3) : R1 = (2, 3), (3, 2)) R² = ((1, 2), (1, 3), (3, 2) R, = ((1, 2), (2, …
   Board 20254 marksshort answer
9. A school is organizing a debate competition with participants as speakers S = {S1, S2, S3, S4 and these are judged by judges J = {Ji, J2, Jg). Each speaker can be assigned one judge. Let R be a relation from set S to J defined as R = ((x, y) : speaker x is jud…
   Board 20254 marksshort answer
10. l4. If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the following depicts the correct relation between set A and B? (B) (C) (D)
    Board 20251 markMCQ
11. Assertion (A) : Let Z be the set of integers. A function f : Z · Z defined as f(x) = 3x - 5, Vx e Z is a bijective. Reason (R) : A function is a bijective if it is both surjective and injective. Page 11 of 24 3x-8, x·5 20. 3 (A) : f(x) : 2k· x>5 k= () = : lim.…
    Board 20251 markAssertion-Reason
12. Page 13 of 23 26. (a) A relation R on set A = {1, 2, 3, 4, 5} is defined as R = {(x, y) : |x2 – y2| < 8}. Check whether the relation R is reflexive, symmetric and transitive. OR (b) A function f is defined from R ® R as f(x) = ax + b, such that f(1) = 1 and f(…
    Board 20243 marksshort answer
13. A function f : R+ ® R (where R+ is the set of all non-negative real numbers) defined by f(x) = 4x + 3 is : (A) one-one but not onto (B) onto but not one-one (C) both one-one and onto (D) neither one-one nor onto
    Board 20241 markMCQ
14. A linear programming problem deals with the optimization of a/an : (A) logarithmic function (B) linear function (C) quadratic function (D) exponential function
    Board 20241 markMCQ
15. Page 4 of 23 5. \$bZ f(x) = x3 – 3x2 + 12x – 18 : (A) R na {Za§Va õmg_mZ h¡ (B) R na {Za§Va dY©_mZ h¡ (C) R na Z Vmo {Za§Va dY©_mZ h¡ Am¡a Z hr {Za§Va õmg_mZ h¡ (D) (– ¥, 0) na {Za§Va õmg_mZ h¡ 666 Page 5 of 23 2. Let f : R+ ® [– 5, ¥) be defined as f(x) = 9x2…
    Board 20241 markMCQ
16. A relation R is defined on a set of real numbers as R = {(x, y) : x . y is an irrational number}. Check whether R is reflexive, symmetric and transitive or not.$ 2 2 1 1 1
    Board 20235 markslong answer
17. (a) A function f : A B defined as f(x) = 2x is both one-one and onto. If A = {1, 2, 3, 4}, then find the set B. OR (b) Evaluate : sin 1 4 3 sin + cos 1 4 3 cos + tan 1 (1)
    Board 20232 marksshort answer
18. The use of electric vehicles will curb air pollution in the long run. The use of electric vehicles is increasing every year and estimated electric vehicles in use at any time t is given by the function V : V(t) = t3 t2 + 25t - 2 where t represents the time and…
    Board 20234 marksshort answer
19. A function f: [- 4, 4] · [0, 4] is given by f(·) = 16 - x2. Show that f is an onto function but not a one-one function. Further, find all possible values of'a' for which f(a) = V7. Page 17 4 1 Aluminium cylinder head Combustion chamber Cylinder head surface th…
    Board 20235 markslong answer
20. Consider   : 5, f R given by  2 9 6 5 f x x x    where R is the set of all non- negative real numbers. Prove that f is one- one and onto function.
    CBSE practice 2023-245 markslong answer

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