Page 1 CBSE TEST PAPER-02 CLASS - XII MATHEMATICS (Relations and Functions) Topic:- Relation and function 1. Prove that the function f: R R, given by f(x) = 2x, is one – one. [1] 2. State whether the function is one – one, onto or bijective f: R R defined by f(x) = 1+ x 2 [1] 3. Let S = {1, 2, 3} [1] Determine whether the function f: S S defined as below have inverse. f = {(1, 2), (2, 1), (3, 1)} 4. Find gof f(x) = |x|, g(x) = |5x + 1| [1] 5. Let f, g and h be function from R to R show that (f + g) oh = foh = goh [1] 6. If a * b = a + 3b 2 , then find 2 * 4 [1] 7. Show that the relation in the set R of real no. defined R = {(a, b) : a = b 3 }, is neither reflexive nor symmetric nor transitive. [4] 8. Let A = N× N and * be the binary operation on A define by (a, b) * (c, d) = (a + c, b + d) [4] Show that * is commutative and associative. 9. Show that if f: 7 3 5 5 R R ? ? ? ? - ? - ? ? ? ? ? ? ? ? is defining by f(x) = 3 4 5 7 x x + - and g: 3 7 5 5 R R ? ? ? ? - ? - ? ? ? ? ? ? ? ? is define by g(x) = 7 4 , 5 3 x x + - then fog = I A and gof = I B when 3 7 , 5 5 A R B R ? ? ? ? = - = - ? ? ? ? ? ? ? ? ; I A (x) = x, for all x?A, I B(x) = x, for all x?B are called identify function on set A and B respectively. [4] 10. Let f: N N be defined by f(x) = 1 , all n 2 2 n if n is odd for N n if n is even + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Examine wether the function f is onto, one – one or bijective [4]Read More

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