#1
| |||
| |||
Mathematics Question Paper for 2nd PUC
I need Karnataka Second PUC Mathematics Question Paper, can you please provide here? Here are some questions for Karnataka Second PUC Mathematics: Give an example of a relation which is symmetric and transitive but not reflexive. Define optimal solution in linear programming problem. An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represents the number of black balls, what are the possible values of X? If the radius of a sphere is measured as with an error, , then find the approximate error in calculating its volume. A die is thrown. If E is the event ‘the number appearing is a multiple of 3’ and F is the event ‘ the number appearing is even’, then find whether E and F are independent? For detailed paper here is attachment: Karnataka Second PUC Mathematics question paper has question from following topics: UNIT I: RELATIONS AND FUNCTIONS 1. Rela tions and Functions Types of relations : Reflexive, symmetric, transitive , empty, universal and equivalence relations. Examples and problems. Types of functions : One to one and onto functions, inverse of a function composite functions, mentioning their properties only , examples and problems . Binary operations : associative, commutative, identity, inverse with examples 2. Inverse Trig onometric Functions Definition, range, domain, principal value branches. Mentioning domain and range of trigonometric and inverse trigonometric functions. Graphs of inverse trigonometric functions. P roperties and proof s of inverse trigonometric functions given in NCERT prescribed text book, mentioning formulae for sin - 1 x sin - 1 y, cos - 1 x cos - 1 y, 2 tan - 1 x = tan - 1 ( ) = sin - 1 ( ) = cos - 1 ( ) without proof. Conversion of one inverse trigonometric function to another w.r.t to right angled triangle. Problems. UNIT II: ALGEBRA 1. Matrices Concept, notation, order, Types of matrices : column matrix, row matrix, rectangular matrix, square matrix, zero matrix, diagonal matrix, scalar matrix and unit matrix. Algebra of matrices : E quality of matrices, Addition, multiplication, sc alar multiplication of matrices , T ranspose of a matrix . Mentioning properties with respect to a ddition, multiplication , scalar multiplica tion and transpose of matrices . S ymmet ric and skew symmetric matrices : Definition s , properties of symmetric and skew symmetric matrices : proof s of i) If A is any square matrix A+A′ is symmetric and A - A′ is skew symmetric ii) Any square matrix can be expressed as the sum of a symmetric and a skew symmetric matrix . Concept of elementary row and column operations and finding inv erse of a matrix restricted to 2x2 matrices only . Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries) You need Karnataka Second PUC Mathematics Question Paper, here I am giving: more paper detail to atteched a pdf file...................... Last edited by Udai Kant; December 9th, 2019 at 10:53 AM. |