1. Find lim \sum_{k=m}^{\infty}a_k as m tends to \infty , if the series \sum_{k=1}^{\infty}a_k is convergent. 2. Every k- cell is _____ 3. Give an example of a non analytic function for which CR equations are satisfied. 4. Prove that if u and v are harmonic functions need not to imply f=u+iv is analytic. 5. Verify the analyticity of the functions |z|^2 and z \overline{z}. 6. The Petersen graph is __________ (Eulerian/ Hamiltonian / Both/ Neither) 7. The radius of curvature at any point on the Helix x=acos \theta, y=asin \theta and z=a \theta tan \alpha is __________ 8. Any countable set in real line has measure _____. 9. The function f(z)=|z|^2, is ____ (Analyic everywhere/Analytic nowhere/ Analytic at z=0 /Noneofthese) 10. Any __________ separable space is separable (Subspace/ Open subspace / Closed subspace).
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