Pick one box and pick only one ball from it and then correctly label all the three boxes ?

Pick one ball from the box labeled "mixture" (this box should contains only red ones or only blue ones), if the ball is red then the box contains only blue ones, if the ball is blue then it contains only red ones (the labels always lie).
The other two boxes are labeled "red" and "blue". If the picked ball is red then the box labeled "red" contains blue ones or a mixture. Since the "blue" box can not contain only blue ones, it contains a mixture. As a result, the "red" box contains a mixture. Similarly if the picked ball is blue.
Lini

what abt answer?

Pick a ball from the box labeled as mixed.
If the ball is red then do following
1. Label this box as red.
2. Change the label of other box from red to blue
3. Change the label of last box from blue to mixed.
else if the ball is blue then do following
1. Label this box as blue.
2. Change the label of other box from blue to red
3. Change the label of last box from red to mixed.

1. Pick a ball from the box labeled 'mixture' (easier, because it definitely contains a single colored balls)
2. There are 2 possibilities , 1. the ball is red or 2. the ball is blue
3. If the ball is red, then we know that the box named 'blue' has a mixture colored balls because the second possibility for this box which is 'red' is not true, as we have identified the box with red balls
4. The box named ' red' has blue balls
5. If the ball taken out is blue, then the box with 'red' name has mixture colored balls and the box with 'blue' name has red colored balls

pick the box labeled with "mixed" one, here is the explanation:
label "mixed", since it's wrong, which means it has either red or blue in it only.
if the ball comes out in red, changed the wrong label to "red"
Now, since we changed the "mixed" label to "red", we need to change "red" label to "blue", because it's definitely wrong, then change "blue" to "mixed".
Similar deduction can be done when blue ball comes out from the "mixed" label box.

pick one ball from the box labelled mixture..whichever colour is that ball that box contains only that same color balls..( because if the label says mixture, you are sure that it doesn't have red and blue balls ,it could be anything)..remaining two boxes very easy to find out...