Important Questions

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]