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 = 
given by R=
, is an equivalence relation.
Q. 2. Show that the relation R in R defined by R=
, is reflexive and transitive but not symmetric.
Q. 3. Let A= R ─{3} and B = R─{1} , Consider the function ƒ: A ® B defined by ƒ (x) =
. Show that ƒ is one–one and onto
Q. 4. If ƒ: R ® R be given by ƒ (x) = (3-x3)
, find the value of ƒoƒ (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. Let f: N 
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 .
Q. 7. Show that binary operation a * b = 
" a,b ò N is commutative but not associative.
Q. 8. Show that ƒ: N 
N defined by ƒ (x) = 
, if n is odd
, if n is even
is many-one onto function.
Q. 9. Show that ƒ : R –{0} R–{0} given by ƒ (x) = 3/x is invertible and it is inverse of itself.
Q. 10.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. 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 R defined by ƒ (x) = 3x3 + 5 for x 
R is a bijection.
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
Email Id : [email protected]
