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CBSE XII Pre Boards 2015 : MATHEMATICS with Answers (KV Chennai)

8 pages, 31 questions, 10 questions with responses, 26 total responses,

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KENDRIYA VIDYALAYA SANGATHAN, CHENNAI REGION PRE BOARD EXAMINATION (2014-15) Class: XII Max.Marks: 100 Subject: Mathematics Time: 3Hours General Instructions: (i) Total number of questions in the paper is 26. (ii) The question paper consists of 6 questions (Q.No.1 to 6) of 1 mark each, 13 questions (Q.No.7 to 19) of 4 marks each and 7 questions (Q.No.20 to 26) of 6 marks each. (iii) There is no overall choice. However internal choice has been provided in 4 questions four marks each and two questions of six marks each. You have to attempt only one of the alternatives in all such questions. . (iv) If you wish to answer any question, already answered for any reason, cancel the previous answer. (v) Use of calculator is not permitted. 1. What is the range of cos 1 x ? d2y dy 2. Find the order and degree of the differential equation 1 . dx 2 dx 3 3. If e 4. If p e 4 x 3x 2 , find the values of a and b. 4 2 is a unit vector and x p . x p 80 , then find x ax bx dx . 5. Write a unit vector of magnitude 9 units in the direction of vector 2i j 2k . 6. Write the direction ratios and direction cosines of the vector 2i j 3k SECTION- B 7. Let A=NXN and * be a binary operation on A defined by (a , b) * (c , d ) = ( a + c , b + d ). Show that *is commutative and associative. Also, find the identity element for * on A, if any. a a 2b 1 1 cos 1 tan cos 1 b b a 4 2 4 2 8. Prove that tan (OR) 12 1 3 1 56 sin sin 13 5 65 1 Prove the following cos 1

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