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CBSE Class 12 Exam 2021 : Mathematics : Pre board vkv jaipur

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DOE PRACTICE PAPER 1 (TERM 1) (SESSION 2021 22) CLASS XII MATHEMATICS (CODE: 041) Time Allowed: 90 Minutes Maximum Marks: 40 General Instructions: 1. This question paper contains three sections A, B and C. Each part is compulsory. 2. Section - A has 20 MCQs, attempt any 16 out of 20. 3. Section - B has 20 MCQs, attempt any 16 out of 20. 4. Section - C has 10 MCQs, attempt any 8 out of 10. 5. There is no negative marking. 6. All questions carry equal marks. SECTION A In this section, attempt any 16 questions out of Questions 1 20. Each question is of 1 mark weightage. Each MCQ has four options with only one correct option, choose the correct option. 1 1 1. The range of the function f(x) = tan x cot x is 1 (a) [ - , ] (b) [ 0, ] (c) [0, ] (d) { } 2 2. 4. 5. 2 2 1 2 1 1 1 The value of the expression sec (2) + sin ( ) + tan ( 3) is (a) 3. 2 5 6 (b) 3 (c) 3 (d) 1 6 The relation R in the set {a, b, c} given by R = {(a, a), (b, b), (a, b), (b, a)} is (a) symmetric and transitive, but not reflexive (b) reflexive and symmetric, but not transitive (c) symmetric, but neither reflexive nor transitive (d) an equivalence relation A = {1, 2, 3, 4}, A relation R in the set A is given by R = { (1, 1), (2, 3), (3, 2), (4, 3), (3, 4) }, then relation R is (a) Reflexive (b) symmetric (c) Transitive (d) Equivalence If A is any square matrix of order 3 3 such that |adj A| = 256, then the sum of all possible values of |A| is (a) 256 (b) 16 (c) 16 (d) 0 1 1 1 6. 7. 8. 9. 10. 11. If x 2 0 5 y 1 1 1 3 4 a b If X 5 6 , w here X c d ,Then a c b d 2 3 (a) 13 (b) 5 (c) 8 (d) 3 If A is a symmetric matrix then which of the following is not Symmetric matrix, (a) A + AT (b) A.AT (c) A - AT (d) AT If A is a non-singular square matrix of order 3 such that |A| = 3, then value of |2AT| is (a) 3 (b) 6 (c) 12 (d) 24 If y = 1 1 x b a x c a 1 1 x c b x a b 1 1 x abc (b) x a c (c) x b c , then dy = dx (b) 30 1 1 1 1 1 (d) 0 x xb x c (c) 34 The function given below at x = 4 is 2 x 3, x 4 f ( x) 2 x 5, x 4 1 a Suppose P, Q and R are different matrices of order 3 5, a b and c x d respectively, then value of ac + bd is, if matrix 2P + 3Q 4R is defined (a) 9 13. 1 (a) 0 (b) 2 (c) 1 (d) 3 2 If A is a diagonal matrix of order 3 x 3 such that A = A, then number of possible matrices A are (a) 4 (b) 8 (c) 16 (d) 32 a b c (a) x 12. 1 O ,Then x + y = 0 1 (d) 15 1 (a) Continuous but not differentiable (b) Differentiable but not continuous (c) Continuous as well as differentiable (d) Neither continuous nor differentiable 14. 3 2 3 If x 3 x y y 2021 xy then 3x 2 6 xy y 3x 2 3 y 2 x 3x 2 6 xy y (b) 2 3 y 3x2 x 6 xy y 3x 2 (c) 2 3 y 3x 2 x 3x 2 6 xy y (d) 2 3x 3 y 2 x (a) dy dx 1 15. 16. 17. 18. 19. The slope of the tangent to the curve y = x3, at the point (2, 8) is (a) 2 (b) 6 (c) 11 (d) 12 Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px+qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is (a) p = 2q (b) q = 2p (c) p = 3q (d) p = q 2 2 The points on the curve 4x + 9y = 36 at which tangent to the curve is parallel to x-axis, is (a) ( 2, 0) (b) (0, 2) (c) (0, 3) (d) ( 3, 0) 3 2 The interval in which y = - x + 3x + 2021 is increasing is (a) (- , ) (b) (0, 2) (c) (2, ) (d) ( - 2, 0) 1 1 1 2 If x = loge y, then (a) y 20. 1 d y dy 2 2 dx dx (b) 2y 1 (c) 2y (d) y dy If x = sin3 t, y = cos3 t then dx (a) tan t (b) cot t (c) - tant (d) cot t SECTION B In this section, attempt any 16 questions out of Questions 21 40. Each question is of 1 mark weightage. 1 Each MCQ has four options with only one correct option, choose the correct option. 2 21. 1 1 If sin x sin y , cos 1 x cos 1 y 1 3 (a) (b) (c) (d) 3 3 2 22. Let f : R R be defined as f(x) = 7x 5, then (a) f is one-one onto (b) f is many-one onto (c) f is one-one but not onto (d) f is neither one-one nor onto 23. A relation R in the set of real numbers R is given by R = {(a, b) : a >b, a , b R}, The relation R is (a) Reflexive 24. (b) symmetric (c) Transitive 1 1 (d) Equivalence If a 2 s in x c os x b, then 1 (a) a 0, b 1 (b) a , b 2 (c) a , b (d) a 0, b 2 2 2 1 25. 3 1 2 If A 0 1 2 , then | adjA | 0 2 1 1 1 (a) 26. 27. 1 9 (b) 29. 30. 32. (b) 5y x x2 y2 ) a , then 2 If log( 2 x y y x (b) If tan y x, , then (a) 2 34. 35. (c) - 5x y dy dx y x 1 1 1 1 x y (c) (b) 1 when x 1, value of 4 (b) 2 1 (d) - 5y x (d) x y The area of a triangle with vertices ( 3, 0), (3, 0) & (0, k) is 9 sq. units. The value of k is (k > 0) (a) 3 (b) 6 (c) 9 (d) 12 1 1 1 x 6 If 0 1 1 y 3 , then 2 x y z 0 0 1 z 2 (a) 2 33. (d) - 81 The interval on which the function f (x) = 2x3 3x2 36x + 10 is decreasing is (a) (- , - 2) (b) (- 2, 3) (c) (2, 3) (d) (3, ) 2 3 If the curve ay + x = 7 and x = y, cut orthogonally at (1, 1), then the value of a is: (a) 1 (b) 3 (c) 6 (d) 6 (a) 31. (c) 9 If A and B are two square matrices of same order such that, AB = A and BA = B, then (A + B)(A B) = (a) A2 B2 (b) 2A 2B (c) 2A + 2B (d) O dy If 5x + 5y = 5x+y, then dx (a) 5x y 28. 1 81 (c) 3 1 1 (d) 5 2 d y is dx 2 (c) 1 1 (d) 1 If a non-singular Matrix A satisfy 2A2 + A I = O, then A 1 = (a) 2A I (b) 2A + I (c) 4A + 2I (d) 2A 4I The maximum value of the function f(x) = 4.sin x. cos x is (a) 2 (b) 4 (c) 1 (d) 8 1 1 36. 37. If the objective function z = ax + y is minimum at (1, 4) and its minimum value is 13, then value of a is (a) 1 (b) 4 (c) 9 (d) 13 Let L be the set of all lines in a plane. A relation R in L is given by R = {(L1,L2):L1 and L2 intersect at exactly one point, L1,L2 L}, then the relation R is 38. (a) Reflexive (b) Symmetric If f : X Y is defined, then f is 39. (a) Bijective function (b) Many-one one and onto (c) Many-one one and Into function (d) One-one one but not onto The feasible region for an LPP is always a _____________ polygon 40. (a) Convex (b) Concave (c) either (a) or (b) (d) neither (a) nor (b) The tangent to the curve y = ex at the point (0, 1) meets x-axis axis at (a) (1, 0) (c) Transitive (b)) ( - 1, 0) (c) (0, 0) SECTION C 1 1 (d) Equivalence 1 1 1 (d) (2, 0) In this section, attempt any 8 questions out of Questions 41 50. Each question is of 1 mark weightage. Each MCQ has four options with only one correct option, choose the correct option. Questions 46-50 46 are based on a Case-Study 41. 42. 43. 44. 45. The feasible region, for the inequalities + 2 6, 0, 0 lies in (a) First Quadrant (b) Second Quadrant (c) Third Quadrant (d) Fourth Quadrant Which of the following function is decreasing on (0, 2 ) (a) sin x (b) cos x (c) tan x (d) sin 2x If the function f(x) = sin x ax + b, is decreasing on x R, then a belongs to (a) (1, ) (b) [0, ) (c) (0, ) (d) [1, ) In a linear programming problem, If the feasible region is bounded then objective function Z = px + qy has (a) Maximum value only (b) Minimum value only (c) Maximum and minimum value both (d) Neither maximum nor minimum value 6 x 8 A If 3 2 is singular matrix, then the value of x is (a) 3 (b) 2 (c) 0 CASE STUDY 1 1 1 1 1 (d) 2 The fuel cost per hour for running a train is proportional to the square of the speed it generates in km per hour. If the fuel costs 48 per hour at speed 16 km per hour and the fixed charges to run the train amount to 1200 per hour. Assume the speed of the train as km/h. Based on the given information, answer the following questions. 46. 47. 48. 49. 50. Given that the fuel cost per hour is times the square of the speed the train generates in km/h, the value of 16 is: (a) 1 (b) 2 (c) 3 (d) 4 If the train has travelled a distance of 1000 km, then the total cost of running the train is given by function: 375 60000 (a) v 4 v 375 60000 (b) v 8 v 375 60000 (c ) v 2 v 375 1200000 (d ) v 2 v The most economical speed to run the train (in Km/hr) is: (a) 50 (b) 80 (c) 400 (d) 800 The fuel cost (In Rs.)for the train to travel 1000km at the most economical speed is: (a) 15000 (b) 75000 (c) 100000 (d) 150000 The total cost of the train to travel 1000km at the most economical speed is: (a) 15000 (b) 30000 (c) 100000 (d) 150000 1 1 1 1 1

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