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1 SAMPLE PAPER 2 CLASS XII MADRAS REGION Mathematics NCERT 12 th CBSE pattern paper CODE: MA-SP2 General Instructions 1. The question paper consists of 26 questions which is divided in three sections. 2. Section A consists of 6 questions of 1 mark each. 3. Section B consists of 13 questions of 4 marks each. 4. Section C consists of 7 questions of 6 marks each. Time 3 hrs Max Marks : 100 Section A 1. Write a 3x3 skew-symmetric matrix. 2. Find the product of the order and degree of the following differential equation : 3. Write a differential equation for, where and are arbitrary constants. 4. Write the projection of vector along the vector. 5. Write the value of 6. Write the direction cosines of the normal to the plane Section B 7. There are 3 families A, B and C. The number of men, women and children in these families are as under : MEN WOMEN CHILDREN FAMILY A FAMILY B FAMILIY C Our website: Page 1 of 5

2 Daily expenses of men, women and children are Rs 200, Rs 150 and Rs 200 respectively. Only men and women earn and children do not. Using matrix multiplication, calculate the daily expenses of each family. What impact does children in the family create on the society? 8. If, then find the value of 9. If then using properties of determinants, prove that. 10. If, then find the matrix Find the inverse of matrix and hence show that. 11. If the function, then show that is not differentiable at. 12. If, then show that. If. 13. If prove that 14. Evaluate : 15. Evaluate : Our website: Page 2 of 5

3 16. Find as limit of sum. Evaluate : 17. Show that the lines and intersect each other. Also find their point of intersection. 18. Find the vector and cartesian equations of the plane which bisects the line joining the points at right angles. Let be a point in the space and Q be a point on the line, then find the value of for which the vector is parallel to the plane 19. From a set of 100 cards numbered 1 to 100, one card is drawn at random. Find the probability that the number on the card is divisible by 6 or 8, but not by 24. Section C 20. Show that the relation in the set given by is an equivalence relation. Show that all the elements of are related to each other and all the elements of are related to each other, but no element of is related to any element of 21. Using integration, find the area bounded by the curves and. 22. Find the point on the curve, where the tangent to the curve has the greatest slope. Our website: Page 3 of 5

4 23. Find the general solution of the differential equation : Solve the following differential equation, given that 24. Find the Vector and Cartesian equations of the plane passing through the intersection of the planes and and the point 25. Assuming that the chances of a patient having a heart attack is. It is also assumed that a medication and yoga course reduces the risk of heart attack by 30% and the prescription of a certain drug reduces its chance by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga. 26. A dealer deals in two items only - item A and item B. He has Rs 50,000 to invest and a space to store at most 60 items. An item A costs Rs 2,500 and an item B costs Rs 500. A net profit to him on item A is Rs 500 and on item B Rs 150. If he can sell all the items that he purchases, how should he invest his amount to have maximum profit? Formulate an LPP and solve it graphically. A dietician wants to develop a special diet using two foods X and Y. Each packet (contains 30 g )of food X contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Our website: Page 4 of 5

5 Each packet (contains 30 g )of food Y contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires at least 240 units of calcium, at least 460 units of iron and at most 300 units of cholesterol. Make an LPP to find how many packets of each food should be used to minimize the amount of vitamin A in the diet, and solve it graphically. Our website: Page 5 of 5

Rao IIT Academy/ 2015/ XII - CBSE - Board Mathematics Code(65 /2 /MT) Set-2 / Solutions XII - CBSE BOARD CODE (65/2/MT) SET - 2

Rao IIT Academy/ 2015/ XII - CBSE - Board Mathematics Code(65 /2 /MT) Set-2 / Solutions XII - CBSE BOARD CODE (65/2/MT) SET - 2 Rao IIT Academ/ 5/ XII - CBSE - Board Mathematics Code(65 / /MT) Set- / Solutions XII - CBSE BOARD CODE (65//MT) SET - Date: 8.3.5 MATHEMATICS - SOLUTIONS. Let a iˆ 3iˆ kˆ b iˆ ˆj and a b 3 5, b a b Projection