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STD :- XII SUB :- MATHS DATE :- 08 - 01- 2020 ST.GREGORIOS HIGH SCHOOL PRELIMINARY EXAMINATION (2019 20) TIME :- 3HRS MAX.MARKS:- 100 (Candidates are allowed additional 15 minutes for only reading the paper. They must not start writing during this time.) Section A Internal choice has been provided in 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 the working including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer. The intended marks for the questions are given in brackets[ ]. Mathematical tables and graph paper are provided. Slide rule may be used. SECTION A [10 2] Question 1. (i) (ii) (iii) (iv) (v) For the operation * defined below, determine whether * is commutative or + ab associative. On Z , define a * b = 2 . 3 2 k For what value of k, the matrix is not invertible? 5 1 Using determinants, find the equation of the line joining the points (1, 2) and (3, 6). x2 y2 1 c , then prove that dy y . If tan x2 y2 dx x Evaluate e x (1 tan x tan 2 x)dx . 3 d4y 1 dy . (vi) Find order and degree of the differential equation: 1 dx 4 dx x cos x sin x lim (vii) By applying L Hospital s Rule, find the limits of . 2 x 0 x sin x (viii) A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?. (ix) A speaks truth in 75% cases and B speaks truth in 80% cases. Find the probability that they contradict each other while narrating a certain fact. (x) Solve : sin 1 cos(sin 1 x) . 3
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