civil services exam ( IAS) 2007

Questions of linear algebra based on direct sum , linear dependence and independence , solutions of linear system, rank and nullitiy .question are conecpt based and practice is must for the solution of the question in the examination hall.these all topics are inter related .to clear understanding geometrical understanding is must.linear algebra is first step to learn analysis.it is new approach in mathematics to teach linear algebra to give an idea of analysis.abstract algebra is new addition in civil services.question related to abstract agebra are based on the topic order of the element in the group, generator of cyclic group,isomorphism and homomorphism of group, find the identity element and inverse of a element in the group structure.the number of question in this section are less than linear algebra.but topics in this section are not well defined. Many times question arise from field, integral domain and Gaussian integer ring also.visulisation is the key to understand the abstract algebra.it start from set concept.with the advancement new-new structure imposed on this.this is the key to understand any algebraic formation.you can not learn this from middle.calculas is tool ,which can utilize to understand many geometrical properties.geometry is the also tool to study geometrical properties of the curves.but it is cumbersome.so calculas is easy approach to solve these curve properties.calculas is the most marks feachting topic in the civil (pre.) examination.