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Important Questions

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=,
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. Show that binary operation a * b =   " a,b ò N is commutative but not associative.
Q. 7. Show that  ƒ: N N defined by  ƒ (x) = , if n is odd
, if n is even is many-one onto function.

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) = x-1,for every x > 2 is  onto but not one-one.

Prepared By Anil Kumar Tondak
M.Sc.(Maths), M.Ed., M.A.(Eco),M.B.A.(Mkt)
Mob No. 9811363962

Maths
  1. Application of Derivatives
  2. Inverse Trigonometric Functions
  3. Matrices
  4. Determinants
  5. Integrals
  6. Differential Equations
  7. Application of Integrals
  8. Continuity & Differentiation
  9. Vector Algebra
  10. Three Dimensional Geometry
  11. Probability
  12. Linear Programming
  13. Relations & Functions