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CBSE CLASS XII

Functions and Relations (4/6 Mark)

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21. Prove that tan ^-1 (1/5) + tan ^-1 (1/7) + tan ^-1 (1/3) + tan ^-1 (1/8) = 1.
22. Prove that .
23. Prove that .
24. Prove that .
25. Write in simplest form: .
26. Prove that tan ^-1 3/4 + tan ^-1 3/5 – tan ^-1 8/15 = π/4.
27. Show that the binary operation * defined by a*b = a – b, on Z is not commutative and associative..
28. Let f : x → y and g : y → z be two invertible functions. Then gof is also with (gof)-1 = f^-1 o g^-1.
29. Show that the function f: Z → Z given by f(x) = x² is not injective.
30. Evaluate : .
31. Solve for .
32. If .
33. Check whether the operator define by a b=a+b -ab is commutative or aasociative.
34. if .
35. Proved that .
36. Let A =NxN and Let * be a binary operation on A defined by (a,b)*(c,d) = (ad+bc,bd) for all (a,b),(c,d) € NxN.Determine if * is commutative, associative,
37. Solve for .
38. Prove that: .
39. If the function f : R→R defined by ,Prove that f is one-one and onto function. Also find the inverse of the function f and f^-1(23) .
40. Solve for .

 

Submitted By Mrs. E.Praveen
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