@sonalirangwani , No option is correct according to me.
Graph with 6 vertices and with degree of each vertices as 2 can be disconnected.
Consider a case where 4 vertices are connected in a cycle and reamining two vertices are connected separetely. Also if the graph is disconnected, there is no meaning of talking about Euler circuit. So, both S1 and S2 are false.
In S3, they have not mentioned the no. of vertices, in this case the grapgh can also be disconnected. Consider two component of graph where each component is having 4 vertices of degree 3(Complete graph). So S3 is also incorrect.

option B ?

No. option c is correct

Ya it should be option C

@sonalirangwani , No option is correct according to me.

Graph with 6 vertices and with degree of each vertices as 2 can be disconnected.

Consider a case where 4 vertices are connected in a cycle and reamining two vertices are connected separetely. Also if the graph is disconnected, there is no meaning of talking about Euler circuit. So, both S1 and S2 are false.

In S3, they have not mentioned the no. of vertices, in this case the grapgh can also be disconnected. Consider two component of graph where each component is having 4 vertices of degree 3(Complete graph). So S3 is also incorrect.

S3 is true for 6 vertices!! They didn't mentioned so it should be false! Is it ??

yes @dashish, It will be true for 6 vertices.

S2 they say euler circuit exist so it is possible for atleast 1 graph for all graph its not possible

I think they have taken 6 vertices according to the previous options. If the vertices are 6 then option C may true.