Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Relations and Functions

Short Answer Type

211. Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric.

170 Views

212. Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b²] is neither reflexive nor symmetric nor transitive.

160 Views

213. Check whether the relation R in R defined by R = {(a,b) : a ≤ b³} is refleive, symmetric or transitive.

157 Views

214. If R and R’ arc reflexive relations on a set then so are R ∪ R’ and R ∩ R’.

135 Views

215. If R and R’ are symmetric relations on a set A, then R ∩ R’ is also a sysmetric relation on A.

214 Views

216. Show that the union of two symmetric relations on a set is again a symmetric relation on that set.

404 Views

217. Let A = {1. 2. 3}. Then show that the number of relations containing (1,2) and (2. 3) which are reflexive and transitive but not symmetric is four.

170 Views

218. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R₁ be a relation in X given by R₁ = {(x, y) : x – y is divisible by 3} and R₂ be another relation on X given by R₂ = {(x, y) : {x, y} ⊂ {1,4, 7 }} or ⊂ {2, 5, 8} or {x, y,}⊂ {3, 6, 9}}. Show that R₁ = R₂.

167 Views

219.

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}.
Choose the correct answer.
(A) (2. 4) ∈ R (B) (3, 8) ∈ R (C) (6,8) ∈ R (D)(8,7) ∈ R

158 Views

220.
Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is

(A) 1 (B) 2 (C) 3 (D) 4

A = {1, 2, 3}
R₁ = {(1,2), (1,3), (1, 1), (2, 2), (3, 3), (2, 1), (3, 1)} is the only relation on {1, 2, 3} which is reflexive, symmetric but not transitive and is such that (1, 2), (1, 3) ∈ R₁.
∴ (A) is correct answer.

374 Views