A diabetic can eat rice, potato,mango and banana

 A diabetic eats wheat but not rice. The reason is that rice raises the blood sugar by 73%  and roti or chapatti raised the blood sugar by 65%. 

But do you eat dry rice?. 

you mix it with curds, A mixture of rice with curds will bring down rice induced rise in blood sugar.(Curd raises the blood sugar by 41%) 
Similarly, pulses like chole, rajmah, mung dal raise the blood sugar by only 25% and the mixture of rice-chole or rice-dal will bring down blood glucose raised by the rice alone.

Both rice and wheat have same calories and it does not matter whether you eat rice or roti as long as the amount is restricted.
Besides, the quality of the protein in rice is better than that of wheat.

What about potato?

It is true that boiled potato raises the blood sugar by 78%
But you do not eat only potato in your meals. It is a mix of cereals, pulses, vegetables, curds which will bring down the potato induced rise in blood glucose significantly.

Protein content of potato is low(2g/100g) but its biological value is equal to that of egg protein. It is a good source of carbohydrate and it must be a part of our diet. You cannot discard it just because it raised the blood glucose by 78%.
Potato has very low calories (80/100g), high nutritive value and fibre content.

Mango?

 Mango raises the blood glucose by 51% which is much less than rice or potato, which gives us an indication that it is safe to eat a mango. It has low calories (74 / 100G)

Mango has high fibre content and vitamins and 
anti oxidants.

And banana?
It raises the blood sugar only by 51%.Banana has high fibre contents and low calories (115/100g)

Both mango and banana have high fibre content  which helps blood sugar to rise gradually and not quickly. 

Regular consumption of fruit is generally associated with reduced risks of several diseases and functional declines associated with aging. It is true for a normal person as well as a diabetic. So, a diabetic has no reason to avoid fruits.

So eating 1-2 mangoes in summer and one banana daily round the year is healthy. (Don't eat 6 mangoes or bananas)

Eating Marie biscuits every day and avoiding mango or a banana is strange