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CBSE Math Model Question Paper

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Published in: Mathematics
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This is a very useful model question paper in Mathematics for class 12 CBSE.

Shiras M / Thiruvananthapuram

11 years of teaching experience

Qualification: M.Sc maths

Teaches: Mathematics, IIT JEE Mains

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  1. CUT maths to t e max CBSE MODEL-I SHORTCUTS: 9895421213, 9072814774 GENERAL INSTRUCTIONS i. ii. iii. iv. v. All questions are compulsory. The question paper consists of 26 questions divided into 3 sections A, B and C. Section A comprises of 6 questions of 1 mark each, section B comprises of 13 questions of 4 marks each and section C comprises of 7 questions of 6 marks each. All questions in section A are to be answered in one word, one sentence or as per the exact requirement of the question. There is no overall choice. However internal choice has been provided for four questions of 4 marks each and two questions of 6 marks each. You have to attempt only one of the alternatives in all such questions. Use of calculators is not permitted. SECTION A (1 mark.) 1. 2. 3. 4. 5. 6. A = {a, b, c}, B = { How many injective functions can be defined from A to B? Find 'x' if tan-I x + tan-1 4 = [37 . Find x and y if A2 + xl = yA. A is a square matrix of order 3 such that IA I x3 cos(x3) dx. Find: — 7T/3 = -4. Find IA. adj Al. Find a vector of magnitude 3 units in the direction of 2t SECTION B (4 marks) 7. 8. Find the identity element of the binary operation (a, b)*(c, d) = (ca + bd , ac). (a) Solve: 2 tan-I(cos x) = tan-1(2 cosec x) (OR) cosx (b) Write tan-I in the simplest form. I—sin x 1 on N defined by
  2. 9. SHOR CUTS maths to th m Using properties of determinants prove that: 1 1 1 1 1 1 = abc -k ab -k bC -k ca. 10. (a) x = a(cos0 + Osin0), y = b(sin0-0cos0). Find 4 (OR) dy (b) If (x — y)ex-y = a , prove that y— + x = 2y . dx 2 d2y 11. If y = [log(x + show that (1 + x )äF+x x 12. (a) Evaluate: f dx. (OR) (b) Evaluate: f ex [2—2-1 dx. 13. (a) Find the intervals in which the function f(x) decreasing. (OR) x (b) Find the maximum value of f(x) = dx = 8+36x+3x2-2x is increasing or 14. Form the differential equation of the family of circles touching the X-axis at the origin. dy 15. Solve: x— dx = Y — x tan 16. The sum of two unit vectors is a unit vector. Show that the magnitude of their difference 17. Find the equation of the plane, through the line of intersection of the planes x+2y+3z = 4 and 2x+y-z+5 = 0, which is perpendicular to the plane F • (3t —j + 2k) — 3 = 0. 18. Find the probability distribution of the number of kings when two cards are drawn one by one with replacement from a pack of 52 playing cards. x2 -k -k 1) — 2 log x] 19. Find : dx 4 x 2
  3. SHOR CUT maths to the max SECTION C (6 marks) 20. Two schools P and Q want to award their selected students for the values of sincerity, truthfulness and hard work at the rate of æx, æy and æz respectively for each respective value per student. School P awards its 2, 3 and 4 students on the above respective values with a total award amount of æ4600. School Q wants to award its 3,2 and 3 students on the respective values with a total award amount of u 100. If the total amount for one prize on each value is using matrices find the award money for each value. Suggest one other value which the school can consider for awarding the students. 21. Show that the semi-vertical angle of a right circular cone of given slant height and maximum volume is tan-I (N/fi). 2 (x-x2) dx as the limit of a sum 22. (a) Evaluate: 1 (OR IT/ 2 1 logsinx dx = Zlog- . (b) Prove that: 2 2 23. (a) Using integration, find the area of the region bounded by the curves : (OR) (b) Draw a rough sketch of the region enclosed between the circles x2 + y 2 — 4. Using integration, find the area of the enclosed region. z = 4 and 24. Find the perpendicular distance of the point (1,2,-3) to the line — 2 -f -2 25. An aeroplane can carry a maximum of 200 passengers. A profit of Rs.1000 is made on each executive class ticket and Rs.600 on each economy class ticket. The airline reserves at least 20 seats for the executive class. However at least 4 times as many passengers prefer to travel by economy class. Determine the number of tickets of each type to be solved to maximise the profit, by formulating an LPP. 26. In answering a question on a MCQ test with 4 choices per question, a student knows the answer, guesses or copies the answer. Let 1/2 be the probability that he knows the answer, 1/4 be the probability that he guesses and 1/4 that he copies it. Assuming that a student, who copies the answer, will be correct with the probability 3/4, what is the probability that the student knows the answer, given that he answered it correctly? Arjun does not know the answer to one of the questions in the test. The evaluation process has negative marking. Which value would Arjun violate if he resorts to unfair means? How would an act like the above hamper his character development in the coming years? 3

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