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PUC II YEAR MATHEMATICS, , POCKET MARKS PACKAGE, , TOP SCORER POCKET MARKS PACKAGE, , PUC II YEAR MATHEMATICS (DECEMBER 2021), MID TERM – MODEL QUESTION PAPER - 01, Time : 3 Hrs 15 Min, , Subject : Mathematics, , Max Marks : 100, , Instructions : (1) The question paper has five parts namely A, B, C, D and E. Answer all the part, (2) Use the graph sheet for the question on linear programming in PART-E, , PART-A, One Marks Questions (Answer All the Question), , 𝟏𝟎 × 𝟏 = 𝟏𝟎, , 1. A relation R on set A={1,2} defined by R={(1,1),(1,2),(2,1)} is not transitive. Why?, 2. Write the domain of the function 𝑦 = 𝑐𝑜𝑠 −1 𝑥., 𝑖, 3. Construct a 2 × 2 matrix 𝐴 = [𝑎𝑖𝑗 ] whose elements are given by 𝑎𝑖𝑗 = 𝑗, 1 2, 4. If 𝐴 = [, ], find |2𝐴|, 4 2, 3 −4, 5. If 𝐴 = [, ] and 𝐵 is a square matrix of order 2 and 𝐴𝐵 = 𝐼 then find the matrix 𝐵, −1 2, 6. Differentiate log⁡(𝑐𝑜𝑠𝑒 𝑥 ) with respect to x., 𝑑𝑦, 7. If 𝑦 = 𝑐𝑜𝑠 −1 (𝑠𝑖𝑛𝑥), then find 𝑑𝑥, 𝑥 3 +5𝑥 2 −4, , 8. Evaluate ∫, 𝑑𝑥, 𝑥2, 9. Define linear objective function in the linear programming problem., 10. Define the term constraints in the linear programming problem., , PART-B, Two Marks Questions (Answer Any Ten Questions), 𝟏𝟎 × 𝟐 = 𝟐𝟎, 11.Show that the relation R in the set of all integers Z defined by 𝑅 = {(𝑎, 𝑏): 2⁡𝑑𝑖𝑣𝑖𝑑𝑒𝑠⁡𝑎 − 𝑏} is an, equivalence relation., 12. Determine whether the relation R in the set 𝐴 = {1,2,3, … … .13,14} defined by, 𝑅 = {(𝑥, 𝑦): 3𝑥 − 𝑦 = 0} is reflexive, symmetric and transitive?, 𝜋, 1, 13. Evaluate 𝑠𝑖𝑛 [ 3 − 𝑠𝑖𝑛−1 (− 2)], 1 0, 3 2, 14. Find X, if 𝑌 = [, ] and 2𝑋 + 𝑌 = [, ], −3 2, 1 4, 2 3, 1 −2 3, 15. If 𝐴 = [, ] and 𝐵 = [4 5] then find 𝐴𝐵 and 𝐵𝐴, show that 𝐴𝐵 ≠ 𝐵𝐴, −4 2 5, 2 1, 16. Find the area of Triangle whose vertices are (3,8), (−4,2)⁡𝑎𝑛𝑑⁡(5,1) using determinants, 17. If the area of triangle with vertices (−2,0), (0,4)⁡𝑎𝑛𝑑⁡(0, 𝑘) is 4 sq units. Find the value of k using, determinants., 𝑑𝑦, 18. Find 𝑑𝑥 if⁡𝑥 2 + 𝑥𝑦 + 𝑦 2 = 100, 2𝑥, , 𝑑𝑦, , 19. If 𝑦 = 𝑠𝑖𝑛−1 (1+𝑥 2), |𝑥| ≤ 1 Find 𝑑𝑥, 20. Find the intervals in which the function f given by 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 6 is, (a) strictly decreasing (b) strictly increasing, 𝑥−1, 21. Find the slope of tangent to the curve 𝑦 = 𝑥−2 ,⁡⁡⁡𝑥 ≠ 2⁡at⁡𝑥 = 10, 𝑠𝑖𝑛−1 𝑥, , 22. Evaluate ∫ √1−𝑥 2 𝑑𝑥, ANAND KABBUR 9738237960, , Page 1

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PUC II YEAR MATHEMATICS, 1, 1, 48. Find the integral 𝑎2 −𝑥 2 w.r.t x and hence evaluate ∫ 2𝑥−𝑥 2 𝑑𝑥,, , POCKET MARKS PACKAGE, , PART-E, 𝟏 × 𝟏𝟎 = 𝟏𝟎, , Ten Marks Questions (Answer Any One Questions), , 49. a) A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on, machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B, to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per, package on bolts. How many packages of each should be produced each day so as to maximise his, profit, if he operates his machines for at the most 12 hours a day, 𝑘𝑥 + 1⁡⁡⁡𝑖𝑓⁡𝑥 ≤ 5, b) Find the value of k if 𝑓(𝑥) = {, is continuous at 𝑥 = 5, 3𝑥 − 5⁡⁡⁡⁡⁡𝑖𝑓⁡𝑥 > 5, 50. a) Solve the following linear programming problem graphically :, Minimise and Maximise 𝑍 = 600𝑥 + 400𝑦, subject to 𝑥 + 2𝑦 ≤ 12, 2𝑥 + 𝑦 ≤ 12, 4𝑥 + 5𝑦 ≤ 20, 𝑥, 𝑦 ≥ 0, 3 2, b) If 𝐴 = [, ], then find the numbers a and b such that 𝐴2 + 𝑎𝐴 + 𝑏𝐼 = 𝑂, then find the inverse, 1 1, of 𝐴 using this equation, where 𝐼 is the identity matrix of order 2, , MID TERM MODEL BLUE PRINT - 02, PUC II YEAR MATHEMATICS (DECEMBER 2021), Time: 3hrs 15 min, Chapter, , Contents, , 1, 2, , Relations and Functions, Inverse trigonometric, functions, Matrices, Determinants, Continuity and, Differentiability, Applications of, Derivatives, Integrals, Linear programming, Total, , 3, 4, 5, 6, 7, 12, , Max Marks: 100, Part-A, (1), 2, 1, , Part-B, (2), 2, 1, , Part-C, (3), 2, 1, , Part-D, (5), 2, -, , Part-E, (6) (4), -, , Total, Marks, 22, 06, , 2, 1, 1, , 2, 3, , 2, 4, , 2, 2, 2, , -, , 1, 1, , 18, 19, 33, , -, , 2, , 2, , -, , -, , -, , 10, , 1, 2, 10, , 4, 14, , 3, 14, , 2, 10, , 2, 2, , 2, , 28, 14, 150, , Note:, This Blueprint has been prepared by experts, based on weightage of topics, (This is not the official blueprint published by P.U.E board) so 1 or 2 marks, may vary in question papers pattern., ANAND KABBUR 9738237960, , Page 6

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PUC II YEAR MATHEMATICS, , POCKET MARKS PACKAGE, , PART-E, Ten Marks Questions (Answer Any One Questions), 1, , 49. a) Find the integral √𝑥 2, , +𝑎2, , 𝟏 × 𝟏𝟎 = 𝟏𝟎, 1, , w.r.t x and hence evaluate ∫ √𝑥 2, , +7, , 𝑑𝑥, , 𝑘𝑐𝑜𝑠𝑥, , ⁡⁡⁡𝑖𝑓⁡𝑥 ≠ 𝜋/2, b) Find the value of k if 𝑓(𝑥) = { 𝜋−2𝑥, is continuous at 𝑥 = 𝜋/2, 3⁡⁡⁡⁡⁡𝑖𝑓⁡𝑥 = 𝜋/2, 50. a) A factory manufactures two types of screws, A and B. Each type of screw requires the use of, two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6, minutes on hand operated machines to manufacture a package of screws A, while it takes 6, minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of, screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell, a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can, sell all the screws he manufactures, how many packages of each type should the factory owner, produce in a day in order to maximise his profit? Determine the maximum profit. (J19), 3 1, b) If 𝐴 = [, ], satisfies the equation 𝐴2 − 5𝐴 + 7𝐼 = 𝑂, then find the inverse of 𝐴 using this, −1 2, equation, where 𝐼 is the identity matrix of order 2., , MID TERM MODEL BLUE PRINT - 03, PUC II YEAR MATHEMATICS (DECEMBER 2021), Time: 3hrs 15 min, Chapter, , Contents, , 1, 2, , Relations and Functions, Inverse trigonometric, functions, Matrices, Determinants, Continuity and, Differentiability, Applications of, Derivatives, Integrals, Linear programming, Total, , 3, 4, 5, 6, 7, 12, , Max Marks: 100, Part-A, (1), 1, 1, , Part-B, (2), 2, 1, , Part-C, (3), 3, 1, , Part-D, (5), 2, -, , Part-E, (6) (4), -, , Total, Marks, 24, 06, , 1, 1, 2, , 1, 2, 3, , 3, 1, 2, , 2, 2, 2, , -, , 1, 1, , 22, 22, 28, , -, , 2, , 1, , -, , -, , -, , 07, , 2, 2, 10, , 3, 14, , 3, 14, , 1, 1, 10, , 1, 1, 2, , 2, , 28, 13, 150, , Note:, This Blueprint has been prepared by experts, based on weightage of topics, (This is not the official blueprint published by P.U.E board) so 1 or 2 marks, may vary in question papers pattern., , ANAND KABBUR 9738237960, , Page 9