NTRCA college written syllabus

E:\NTRCA\Exam\17th Exam'20\Written\Syllabus\Written_College level_17th Exam-2020 (1-52 code) (Main).doc    33 
•convert a transformation into a matrix  
eigenvalue problem 
 
transformations, Kernel and image of a 
linear transformation and their 
properties, matrix representation of 
linear transformati ons, change of bases.  
 Eigenvalues and Eigenvectors: 
Eigenvalues and Eigenvectors.  
4a 
•identify the condition of general form of a pair  
of straight lines 
•measure angle between pair of straight lines 
• construct equations of bisectors of angles 
between the lines 
4b 
 
• find out the conditions in which general  
equation of second degree represents  
various types of conics  
 
4c 
•solve problems using properties of Parabola,  
Ellipse and Hyperbola 
Unit 4 
 Two-dimensional Geometry:  Pair of 
straight lines (ho mogeneous second 
degree equations, general second 
degree equations representing pair of 
straight lines, angle between pair of 
straight lines, bisectors of angle 
between pair of straight lines), General 
equations of second degree (reduction 
to standard form s). 
 
 Conics: Properties of Parabola, Ellipse 
and Hyperbola.   
10 
5a 
•recognize plane and straight line by their 
equation 
5b 
•solve problems related to planes and straight  
lines in three dimensions 
 
5c 
•solve geometric problems using vectors 
Unit 5 
 Three-dimensional Geometry: 
Coordinates, Distance, Direction cosines 
and direction ratios, Planes (equation of 
plane, angle between two planes, 
distance of a point from a plane), 
Straight lines (equations of lines, 
relationship between planes and lines, 
shortest distance). 
 Vector Geometry: Vectors in three 
dimensional space with applications to 
geometry.  
10 
6a 
• Define limit continuity and differentiability 
6b 
•analyze a function about its limit, continuity or 
differentiability at a certain point or interval 
 
6c 
•solve real life problems 
Unit 6 
 Limit and continuity: Definitions and 
basic theorems on limit and continuity, 
Limit at infinity & infinite limits, 
Computation of limits, Indeterminate 
form (L’Hospital’s rule).  
 Differentiation: Tangent lines and rates 
of change, Definition of derivative, One -
sided derivatives, Rules of 
differentiation (proofs and applications), 
Successive differentiation, Leibnitz's 
theorem (proof and application).  
 Applications of Differentiation: Mean 
value theorem, Maximum and minimum 
values of functions, Concavity and points 
of inflection, Optimization problems.  
10 
7a 
•formulate using integral calculus to determine 
the area, volume and surface 
7b 
• determine the  area, volume and surface using  
Unit 7 
 
 Integral calculus: Indefinite integrals, 
Definite integrals, Determination of area, 
volume and surface. 
10