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( i ) RECOMMENDED RECOMMENDED RECOMMENDED RECOMMENDED UNIFIED SYLLABUS OFUNIFIED SYLLABUS OFUNIFIED SYLLABUS OFUNIFIED SYLLABUS OF MATHEMATICSMATHEMATICSMATHEMATICSMATHEMA TICS For ClassesFor ClassesFor ClassesFor Classes ((((FFFFrom 2011rom 2011rom 2011rom 2011----12 onward12 onward12 onward12 onwardssss) ) ) ) IIII Paper I : ALGEBRA and TRIGONOMETRYP aper I : ALGEBRA and TRIGONOMETRYP aper I : ALGEBRA and TRIGONOMETRYP aper I : ALGEBRA and TRIGONOMETRY : 33/65 AlgebraAlgebraAlgebraAlgebra Unit 1. Sequence and its convergence (basic idea), Convergence of infinite series, Comparison test, ratio test, root test, Raabe s test, Logarithmic ratio test, Cauchy s condensation test, DeMorgan and Bertrand test and higher logarithmic ratio test. Alternating series, Leibnitz test, Absolute and conditional convergence, Congruence modulo m relation, Equivalence relations and partitions.
( iii ) Unit Unit Unit 2222. .. . Differential equations of the first order but not of the first degree, Clairaut’s equations and singular solutions, Orthogonal trajectories, Simultaneous linear differential
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