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# CBSE Class 12 Pre Board 2019 : Mathematics - Prelim 1 (St Xavier's Sr. Sec. School, Delhi)

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Pre Board Examination 2019 Std. 12 17-01-2019 Set 1 MATHEMATICS Max. Marks : 100 Time : 3 hrs. GENERAL INSTRUCTIONS: i) Attempt all the questions. ii) Section- A consists of 4 questions of 1 mark each. iii) Section-B consists of 8 questions of 2 marks each. iv) Section-C consists of11 questions of 4 marks each. v) Section-D consists of 6 questions of 6 marks each. SECTION A 1. Write the integrating factor of the following differential equation: 1 + 2 + (2 cot ) = 0. 2. Write the vector perpendicular to both vectors = + + = + (OR) Find p for which the vectors 3 + 2 + 9 and - 2p +3 are parallel to each other. 3. If y = sin 1 4. What is the value of 4 3 , where 3 is matrix of order 3? 1 2 1+ 2 + sec 1 1+ 2 1 2 then find . SECTION B 5. Let be a binary operation on Q as a b = 2a + b - ab a,b Q, then find 3 4 and 4 3.Also state that whether a b is commutative. 6. 5 If A= 4 2 4 3 is symmetric matrix,then find x,yand t. 7 7. Evaluate: 8. Evaluate: 9. Form a differential equationcorresponding to = 4 ( ) by eliminating a. 10. Find if the vector - + , 3 + + 2 and + - 3 are coplanar. (OR) If vectors = 2 + 2 + 3 , = - + 2 + and = 3 + are such that + is perpendicular to . Find . 11. Abag contains 2 red and 3 black balls, find the probability distribution of the number of red balls if 2 red balls are drawn without replacement. 12. A die is thrownthree times. Events A and B are defined as below: A: 5 on the first and 6 on the second throw. B: 3 or 4 on the third throw. Find the probability of B, given that A has already occurred. 3 0 3 dx. 3 7 9 2 16 dx (OR) 1 1 dx.

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