Let us learn MAKS

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).

1. The number of automorphisms from $\mathbb{C} \rightarrow \mathbb{C}$, that fixes $\mathbb{R}$ is ___ 2. Let K be the splitting field of $x^2+1=0$ over $\mathbb{Q}$. Then [K:$\mathbb{Q}$] is ____. 3. Let f and g be two analytic functions with same real part. Then ●f=g ●f=g^2 ●f-g is constant ●None of these 4. The maximum possible order of any element in $S_7$ is___ 5. The number of primitive 8th roots of unity is___ 6. The ratio between curvature and torsion is constant iff the curve is ____ 7. If the radius of spherical curvature is constant then what can u say about the curve? 8. Let  $A_n$ denotes the area of the polygon in the complex plane with vertices as nth roots of unity. Then $lim\,A_n$ as n tends to $\infty$? 9. Number of generators in group of quaternions is____ 10. The order of 5 Sylow subgroup in a group of order 125 is_____ 11. The number of 5 slow subgroups in a group of order 15 is______ 12. The radius of convergence of $\Sigma \frac{(-1)^n}{n}(z-2)^n$