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PUC II YEAR MATHEMATICS, , POCKET MARKS PACKAGE, , TOP SCORER POCKET MARKS PACKAGE, , PUC II YEAR MATHEMATICS (DECEMBER 2021), MID TERM β 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), , ππ Γ π = ππ, , 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 π¦ = πππ β1 π₯., π, 3. Construct a 2 Γ 2 matrix π΄ = [πππ ] whose elements are given by πππ = π, 1 2, 4. If π΄ = [, ], find |2π΄|, 4 2, 3 β4, 5. If π΄ = [, ] and π΅ is a square matrix of order 2 and π΄π΅ = πΌ then find the matrix π΅, β1 2, 6. Differentiate logβ‘(πππ π π₯ ) with respect to x., ππ¦, 7. If π¦ = πππ β1 (π πππ₯), then find ππ₯, π₯ 3 +5π₯ 2 β4, , 8. Evaluate β«, ππ₯, π₯2, 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), ππ Γ π = ππ, 11.Show that the relation R in the set of all integers Z defined by π
= {(π, π): 2β‘πππ£ππππ β‘π β π} is an, equivalence relation., 12. Determine whether the relation R in the set π΄ = {1,2,3, β¦ β¦ .13,14} defined by, π
= {(π₯, π¦): 3π₯ β π¦ = 0} is reflexive, symmetric and transitive?, π, 1, 13. Evaluate π ππ [ 3 β π ππβ1 (β 2)], 1 0, 3 2, 14. Find X, if π = [, ] and 2π + π = [, ], β3 2, 1 4, 2 3, 1 β2 3, 15. If π΄ = [, ] and π΅ = [4 5] then find π΄π΅ and π΅π΄, show that π΄π΅ β π΅π΄, β4 2 5, 2 1, 16. Find the area of Triangle whose vertices are (3,8), (β4,2)β‘πππβ‘(5,1) using determinants, 17. If the area of triangle with vertices (β2,0), (0,4)β‘πππβ‘(0, π) is 4 sq units. Find the value of k using, determinants., ππ¦, 18. Find ππ₯ ifβ‘π₯ 2 + π₯π¦ + π¦ 2 = 100, 2π₯, , ππ¦, , 19. If π¦ = π ππβ1 (1+π₯ 2), |π₯| β€ 1 Find ππ₯, 20. Find the intervals in which the function f given by π(π₯) = π₯ 2 β 4π₯ + 6 is, (a) strictly decreasing (b) strictly increasing, π₯β1, 21. Find the slope of tangent to the curve π¦ = π₯β2 ,β‘β‘β‘π₯ β 2β‘atβ‘π₯ = 10, π ππβ1 π₯, , 22. Evaluate β« β1βπ₯ 2 ππ₯, ANAND KABBUR 9738237960, , Page 1
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PUC II YEAR MATHEMATICS, 1, 1, 48. Find the integral π2 βπ₯ 2 w.r.t x and hence evaluate β« 2π₯βπ₯ 2 ππ₯,, , POCKET MARKS PACKAGE, , PART-E, π Γ ππ = ππ, , 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, ππ₯ + 1β‘β‘β‘ππβ‘π₯ β€ 5, b) Find the value of k if π(π₯) = {, is continuous at π₯ = 5, 3π₯ β 5β‘β‘β‘β‘β‘ππβ‘π₯ > 5, 50. a) Solve the following linear programming problem graphically :, Minimise and Maximise π = 600π₯ + 400π¦, subject to π₯ + 2π¦ β€ 12, 2π₯ + π¦ β€ 12, 4π₯ + 5π¦ β€ 20, π₯, π¦ β₯ 0, 3 2, b) If π΄ = [, ], then find the numbers a and b such that π΄2 + ππ΄ + ππΌ = π, then find the inverse, 1 1, of π΄ using this equation, where πΌ 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 βπ₯ 2, , +π2, , π Γ ππ = ππ, 1, , w.r.t x and hence evaluate β« βπ₯ 2, , +7, , ππ₯, , ππππ π₯, , β‘β‘β‘ππβ‘π₯ β π/2, b) Find the value of k if π(π₯) = { πβ2π₯, is continuous at π₯ = π/2, 3β‘β‘β‘β‘β‘ππβ‘π₯ = 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 π΄ = [, ], satisfies the equation π΄2 β 5π΄ + 7πΌ = π, then find the inverse of π΄ using this, β1 2, equation, where πΌ 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