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Class 12 ISC Model 2017 : Mathematics

3 pages, 38 questions, 25 questions with responses, 32 total responses,    0    0
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-4Question IX (a) A bag X contains 3 white balls and 2 black balls and another bag Y contains 2 white balls and 4 black balls. A bag and a ball out of it are picked at random. What is the probability that the ball is white? [5] dx (b) Evaluate: 5 4sin x [5] SECTION B [20 Marks] Question X (a) In any triangle ABC, prove by vector method that a b c = = sin A sin B sin C [5] (b) Find the distance between the point ( 1, 5, 10) and the point of intersection of the line x 2 y +1 z 2 = = with the plane 3 4 12 x y+z =5 [5] Question XI (a) The vector equations of two lines are given by [5] (b) Find the cartesian equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes x + 2 y + 3 z 7 = 0 and between these two lines. [5] Question XII (a) If the mean and variance of a binomial distribution are 9 and 6 respectively, find the distribution. [5] (b) There are 4 boys and 2 girls in room A and 5 boys and 3 girls in room B. A girl from one of the two rooms laughed loudly. What is the probability that the girl who laughed was from room B? [5] MARKS:100 TIME:3 Hours Candidates are allowed additional 15 minutes for only reading the question paper. They must not start writing during this time. SECTION A Answer Question I compulsory and any other 5 questions. SECTION B & SECTION C Answer 2 questions either from Section B or from Section C. All work, including rough work, should be done on the same sheet as and adjacent to the rest of the answer. Lack of essential steps will result in loss of marks. SECTION A [30 Marks] Question I Each question carries 3 marks ( ) ( [3X10=30] ) 2 1 2 1 1. Prove that sec tan 2 + cos ec cot 3 =15. [3] e ( tan x + log sec x ) dx [3] 2. Evaluate: r , + (t 2) r = (1 t )i j + (3 2t )k r . Find the shortest distance + (2s 1) r = (s+ 1)i j (2s + 1) k 2x 3 y + 4z = 0 . MATHEMATICS CLASS XII 3. Evaluate: x Lim ( cos x log tan x ) x 2 [3] 4. Two regression lines are represented by 2 x + 3 y = 10 , 4 x + y = 5 . Find the regression line of y on x. [3] 3 5. Evaluate: x 2 dx [3] 3 6. Find the derivative of sin x 2 with respect to x 3 [3] 7. Using determinants, determine whether the system x 3 y + 2 z = 4 , 2 x + y 3 z = 2 and 4 x 5 y + z = 5 is consistent or not. [3] 8. A fair die is thrown once. What is the probability that an even number or a number greater than three will turn up? [3] -2-

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