Page 1 : TERM - Il, , , , , , , , , , , , , , , , , , , , , , , , One Paper, Max Marks: 40, No. Units Marks, ul. Calculus 18, WV. Vectors and Three-Dimensional Geometry 14, Vi. Probability 8, Total 40, Internal Assessment 10, Total 50, , Unit-Ill: Calculus, , 1. Integrals, Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by, Partial fractions and by parts, Evaluation of simple integrals of the following types and problems based, , on them., , , , lS/=+ — \—== Jaren 2+bxte, , px+q px+q a) /, eso +x? di | ae:, mabe co Ferreenix| vi x? dx, x? — a?dx, , Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation, of definite integrals., , 2. Applications of the Integrals, , Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses, (in standard form only) (the region should be clearly identifiable)., , Scanned with CamScanner

Page 2 : 3. Differential Equations, , Definition, order and degree, general and particular solutions of a differential equation. Solution of, differential equations by method of separation of variables, solutions of homogeneous differential, , equations of first order and first degree of the type: = = f(y/x). Solutions of linear differential equation, , of the type:, , dy, = + py = q, where p and q are functions of x or constant., , Unit-IV: Vectors and Three-Dimensional Geometry, 1. Vectors, , Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a, vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point,, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar,, Position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation,, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors., , 2 Three - dimensional Geometry, , Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation, of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation, of a plane. Distance of a point from a plane., , Unit-VI: Probability, 1. Probability, , Conditional probability, multiplication theorem on probability, independent events, total probability,, Bayes’ theorem, Random variable and its probability distribution., , Scanned with CamScanner