Cmi.sample Qp

MSc/ Ph.D: Mathematics Sample Objective Type Questions State whether the following are true or false. (2 marks each) F or each incorrect answer you loose 1 mark 1. There exists a field of order 60. 2. The number of abelian groups of order n is an increasing function of n. 3. Any Lebesgue integrable function on [0,1] is Riemann integrable. "

4. The matrix A =

1 2 0 1

#

is diagonalisable over C.

5. The function f : C −→ C, f (z) = |z|3 , is complex analytic at 0. 6. The function f : R −→ R, f (x) = |x|3 , is differentiable at 0. 7. Let p : R2 −→ R be the map p(x, y) = x. Then p maps closed sets to closed sets. 8. R2 can be expressed as a countable union of straight lines. 9. x4 + 1 is irreducible over Q. 10. Let f : C −→ C be once differentiable everywhere. Then f has a power series expansion around 0.