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Ryan International School Bangalore I Pre board Examination 2019 2020 Subject: Mathematics Class: XII Date: .0 . 2019 Maximum Marks : 100 Duration : 3 Hrs ROLL No. : The Question Paper consists of three sections A, B and C. Candidates are required to attempt all questions from Section A and all questions Either from Section B OR Section C. Section A : Internal choice has been provided in the three questions of four marks each and two questions of six marks each. Section B : Internal choice has been provided in two questions of four marks each. Section C :Internal choice has been provided in two questions of four marks each. All working , including rough work, should be done on the same sheet as , and adjacent to the rest of the answer. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables and graph papers are provided. SECTION A ( 80 MARKS ) Question 1 (i) [10X2=20] The binary operation if ( ) is defined on the of all positive integers by find . Also find identity element in (ii) Find the principal value of : (iii) For the matrix * ( + find the numbers where I is the identity matrix of order 2. . ( Relations and Functions ) ) ( Relations and Functions ) and such that ( Algebra ) (iv) Find the value of if the area of the triangle whose vertices are ( ) is 15 sq units. ( Algebra ) and ( (v) Find the value of so that ( ) { Page 1 of 9 is continuous at );( ) (Calculus)
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