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CBSE CLASS XII

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Functions and Relations (1 Mark)

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  1. Is the function f: N → N, defined by f(x) = 3x, onto? Give reasons.
  2. If f(x) = [ x ] and g (x) = │x │, then evaluate (f o g) (1/2) – (g o f) (-1/2).
  3. If tan-11 + tan-1(1/2) = tan-1α, find α.
  4. 1If A and B are two sets such that n (A) = m and n (B) = n then write number of function from A → B.
  5. Let f : R – { - 4/3} → R be a function defined as f(x) = 4x / 3x+4. Find the inverse of f.
  6. Find the value of tan-1(1) + cos-1(-1/2) + sin -1 (-1/2).
  7. Evaluate Sin [ π– sin-1 (-1)].
  8. Let set A contains 3 elements. Write the total number of binary operation possible.
  9. Let ‘*’ be a binary operation defined on the set of integers as a*b=a+b+1 for a, b € I. Find the identity element.
  10. Prove that cos2(tan-12)+sin2(cot-13) = 3/10.
  11. What is the principal value of cos-1(cos 2 π/3)+sin-13(sin 2 π/3).
  12. If f(x) = 8x3 and g(x) = x1/3 , find g o f.
  13. Find the value of sin-1(sin 3π/5).
  14. Show that the signum function f : R → R given by f(x) = 1, if x is greater than 0, if x = 0, - 1, if x is less than 0 is neither one-to-one nor onto.
  15. If , find f o g.
  16. N → N, defined by f(x) = 3x onto?Give Reasons.
  17. If a binary operation * is defined on the set Z of integers as a*b = 3a –b, then find the value of (2*3)*4.
  18. Prove that sec2 (tan -1 2) + cosec2 (cot -1 3) = 15.
  19. How many relations can be defined from a non-empty set A to non-empty set B , if n(A) = 2 and n(B)=3.
  20. Find the principal value of tan-1[sin(sin-1x+cos-1x)] , x ε [ -1,1] .

 

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Submitted By Mrs. E.Praveen
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