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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. SECTION A (1 Mark) CUT maths to the max CBSE MODEL 2 SHORTCUTS: 9895421213, 9072814774 GENERAL INSTRUCTIONS 3x-2 . 2x—3 = 1 — 2xyz. 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 mark 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. 1. 2. 3. 4. 5. 6. Show that the function f(x) = IS the inverse of itself. Find the principal value of cos-l (cos Differentiate cos- cos2x Evaluate: f sin 2x e dx. 1 Evaluate: x(l — dx. Form the differential equation corresponding to the curve y — ae SECTION B (4 Marks) 7. 8. f is a function from R + to [4m): f(x) = x2 + 4, show that f is invertible and find f I cos x (a) Write tan-I in the simplest form. I—sin x (OR) (b) If cos-l x + cos-l y + cos-l z = , Prove that x2 + Y2 + z 2 1
  2. a—x 9. Solve: a—x a—x -2 a—x a—x 10. If y = sm 1 with respect to x. (OR) dy _ (1+10gy)2 = eY-x Prove that — dx logy 11. Verify Mean value theorem for the function f(x) 12. Evaluate: f x tan-I x dx. (OR) e2X+l Evaluate: f dx e2X—1 CBSE MODEL 2 = in [1,4]. 13. A rectangular sheet of tin 45cm by 24 cm is to be made into a box without top by cutting of squares from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum? (OR) Find the intervals in which the function f(x) = sin x - cos x is increasing or decreasing in (0,27T). 14. Solve: (1 + eY) dx + ey (1 — i)dy 15. Show that the family of curves for which the slope of tangent at any point (x, y) on it is is given by x2 — y 2 = cx. 2xy 16. A die is thrown thrice. Find the mean number of doublets. 2y-3 2—z x+2 Y z—2 17. Find the shortest distance between the lines 3 and 2 2 2 18. The dot product of a vector with the vectors t — 3k, t — 2k and t + j + 4k are 0, 5 and 8 respectively. Find the vector. dx 19. Find sin x(2cos2 x — 1) SECTION C (6 Marks) 20. The management committee of a residential colony decided to award some of its members(say x) for honesty, some(say y) for helping others and some others(say z) for supervising the workers to kept the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times 2
  3. S OR CUT maths to the max CBSE MODEL 2 the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others, using matrix method find the number of awardees of each category. Apart from these values, suggest one more value which should be included for award. 21. Find the equation of normal to the curve 4y = x2, which passes through the point (1,2). 22. Evaluate: —dx I + tan x (OR) Evaluate (x2 — x)dx as the limit of a sum. 23. Find the equation of the plane passing through the point P(l,l,l) and containing the line ( 3i + j +5k) + A(3i j 5k) .Also, show that the plane contains the line (OR) A variable plane which is at a constant distance p form the origin meets the coordinate axes in points A, B and C respectively. Through these points, planes are drawn parallel to the coordinates planes, show that locus of the point of intersection is 1 1 1 2 2 2 x y Z 1 2 P 24. Find the area of the region {(x, y): y 2 2 6x, x2 + y 2 16}. 25. Suppose the reliability of HIV test is specified as follows. Of people having HIV, 90% of the test detects the disease but 10% go undetected. Of people not having HIV, 99% of the test is judged HIV ve but 1% are diagnosed as showing HIV + ve. From a large population of which only 0.1% has HIV, one person is selected at random, given the HIV test, and the pathologist reports as HIV +ve. What is the probability that the person actually has HIV? What is your opinion about the discrimination of the society towards the HIV patients? 26. A merchant plans to sell two types of computers- a desktop model and a portable model which will cost ? 25000 and ?40000 respectively. He estimates that the total monthly demands of computers will not exceed 250 units. Determine the number of units of each type of computers the merchant should stock to get maximum profit if he does not want to invest more than ? 70 lakhs and if his profit on the desktop model is ?4500 and on portable model is ? 5000. How has the transition from desktops to laptops and from laptops to tablets helped the educational sector? 3

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