CBSE Guess > Papers > Important Questions > Class XII > 2009 > Maths > Mathematics By Anil Kumar Tondak CBSE CLASS XII Relations & Functions Q. 1. Show that the relation R in the set A = given by R=, Q. 2. Show that the relation R in R defined by R=, is reflexive and transitive Q. 3. Let A= R ─{3} and B = R─{1} , Consider the function ƒ: A ® B defined by ƒ (x) =. Q. 5. Consider ƒ : R ® R given by f(x) = 4x+3, show that ƒ is invertible . Find the inverse of ƒ. Q. 6. Show that binary operation a * b = " a,b ò N is commutative but not associative. Q. 8. Show that ƒ : R –{0} R–{0} given by ƒ (x) = 3/x is invertible and it is inverse of itself. Q. 9. On the set M = A (x) = of 2 ´ 2 matrices, find the identity element for the multiplication of matrices as a binary operation. Also, find the inverse of an element of M. Q. 10. Let ƒ (x) = [x] and g(x) = êx ê find goƒ (5/3) – ƒog (5/3) Q. 10. Show that the function ƒ: R R defined by ƒ (x) = 3x3 + 5 for x R is a bijection. Q. 12. Show that the relation R on the set R of all real numbers, defined as R = { (a, b): a £ b2 } is neither reflexive nor symmetric nor transitive. Q. 13. Show that the function ƒ:N ® Ngiven by ƒ (1) = ƒ (2) =1 and ƒ (x) = x1,for every x > 2 is onto but not oneone. Prepared By Anil Kumar Tondak

