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Ryan International School Bangalore I PREBOARD 2018 2019 Subject : Mathematics Class: XII Date : .0 . 2018 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 [10X2] (i) If f : R (ii) If R defined by ( ) , (iii) For what value of - , then show that , find . , the matrix [ ] is a skew symmetric matrix. (iv) Find the equation of the line passing through ( determinant. (v) Using L Hospitals rule evaluate : is neither one-one nor onto. * ) and ( ) using the + (vi) The radius of a cylinder is increasing at the rate of 2 cm/sec and its height is decreasing at the rate of 8 cm/sec. Find the rate of change of its volume when radius is 3cm and height is 6cm. RIS 12th STD Mathematics I Preboard 2018-2019 [Page 1 of 7]
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