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CBSE CLASS XII

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Functions and Relations (1 Mark)

Page 2 of 5

  1. Evaluate sin{ 1/2 cos -1(4/5) }.
  2. Find gof(-5/2) and fog(3/2) if f is identity function and g is signum function .
  3. Evaluate the value of cos -1(-1/2) + Sin -1(-√3/2).
  4. If : R → R ,a,b,c,d є R such that (a,b) *(c,d) = (ac, b + ad) Find the identity element of the function.
  5. Let * be a binary operation defined by a * b =2ab-7. Is * associative?
  6. Write the range of one branch of sin -1 x, other than the Principal Branch.
  7. If f(x) = x-1 / x+1;, then find f -1(x ).
  8. Find the value of cosec (sec -1 ө+cosec -1 ө).
  9. Evaluate : Cos (π/3- sin-1(-√3/2)).
  10. Show that the function f: R → R such that f(x) = x2 is neither one –one nor onto.
  11. If f(x) = x + 7 and g(x) = x – 7, x є R, find (fog) (7).
  12. Let * be a binary operation on N given by a * b = H.C.F. ( a , b ) , a, b є N. Find 12 * 4.
  13. if f(x)=x2-1 and g(x)=2x+3 find fog(2).
  14. if sin(sin-1 1/5 + cos-1 x) = 1, then find the value of x.
  15. Evaluate: sin [ π/3 - sin-1(-1/2) ].
  16. Which of the following graph represent a function .
  17. Write the range of one branch of cos x, other than the principal branch.
  18. Which one of the following graphs represents an identity function? Why?
  19. Let A = {1, 2, 3) and B = {4, 5, 6}, f: A → B is a function defined on f(1) = 4, f(2)=5and f(3) = 6. Write the inverse as set of ordered pairs.
  20. Let * be the binary operation on N defined by a*b = a+b+10 for all a, b є N and if 3*p=15 then find p.
  21. Find the value of the parameter for which the function is the inverse of itself.
  22. If f(x) = ex and g(x) = logex , find fog and gof. Is fog = gof ?

 

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Submitted By Mrs. E.Praveen
Email Id : [email protected]