CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Anil Kumar Tondak CBSE CLASS XII Relations & Functions Q. 1. Show that the relation R in the set A = Q. 2. Show that the relation R in R defined by R= Q. 3. Let A= R ─{3} and B = R─{1} , Consider the function ƒ: A ® B defined by ƒ (x) = Q. 4. If ƒ: R ® R be given by ƒ (x) = (3-x3) Q. 5. Consider ƒ : R ® R given by f(x) = 4x+3, show that ƒ is invertible . Find the inverse of ƒ. Q. 6. Let f: N Q. 7. Show that binary operation a * b =
Q. 9. Show that ƒ : R –{0} Q. 10.On the set M = A (x) = Q. 11. Let ƒ (x) = [x] and g(x) = êx ê find goƒ (-5/3) – ƒog (-5/3) Q. 12. Show that the function ƒ: R Q. 13. Show that the relation R on the set R of all real numbers, defined as R = { (a, b): a £ b 2 } is neither reflexive nor symmetric nor transitive. Q. 14. Show that the function ƒ:N ® Ngiven by ƒ (1) = ƒ (2) =1 and ƒ (x) = x-1,for every x > 2 is onto but not one-one. Q. 15. If is a binary operation on R defined by a b = a/4 + b/7 for a, b  R, find the value of ( 2 5 ) 7
Paper By Mr. Anil Kumar Tondak |
given by R=
, is an equivalence relation. 
, is reflexive and transitive but not symmetric.
. Show that ƒ is one–one and onto
, find the value of ƒoƒ (x)
be a function defined as f ( x ) = 4x2 + 12x + 15 .Show that f: N 
where S is the range of f, is invertible .Find the inverse of f .
" a,b ò N is commutative but not associative.
N defined by ƒ (x) = 
, if n is odd
, if n is even
is many-one onto function.
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.