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15 votes

Here the trick is :

To identify that connected component which is maximum sized i.e. maximum no of edges with given no of vertices..Having done that we can accomodate for remaining vertices..

So we know in K4 , no of edges  =  6

And in the question also no of edges  = 6

Hence using 4 vertices we are able to cover 6 edges and hence it accounts for 1 connected component..

Now we are left with 6 vertices ..So maximum of 6 connected components are possible with these 6 vertices..

Hence total no of connected components = 1 + 6

                                                             = 7

Hence 7 is the correct answer..

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With this data for numerical type question :

we know the maximum number of edges in k components with n vertices

 E≤ $\frac{(n-k+1)(n-k)}{2}$

6 ≤ $\frac{(10-k+1)(10-k)}{2}$

12 ≤ $(11-k)(10-k)$

Now maximum value of K that satisfy is 7 , you can try with 8,9,10 also.
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