
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

CBSE Class 12 Sample / Model Paper 2022 : Mathematics - Term I (with Marking Scheme / Solutions)

12 pages, 52 questions, 0 questions with responses, 0 total responses,

	cbse12	+Fave Message
	Profile Timeline Uploads Q & A

Home > cbse12 > SAMPLE / MOCK Question Papers : CBSE Board Class 12 > F Also featured on: cbse12

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

Subject Code - 041 Sample Question Paper CLASS: XII Session: 2021-22 Mathematics (Code-041) Term - 1 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. All questions carry equal marks. 6. There is no negative marking. SECTION A In this section, attempt any 16 questions out of Questions 1 20. Each Question is of 1 mark weightage. 1. 2. a) b) c) -1 d) 1 The value of k (k < 0) for which the function , is continuous at = ={ 3. 1 sin [ sin-1 )] is equal to: a) c) , = is: b) 1 d) If A = [aij] is a square matrix of order 2 such that aij = { A2 is: a) [ 4. c) | ] | Value of , for which A = [ a) 4 c) 4 1 defined as b) | d) [ , , , then = 1 | ] ] is a singular matrix is: b) -4 d) 0 1 5. Find the intervals in which the function f given by f (x) = x 2 4x + 6 is strictly increasing: b) (2, ) d) ( , 2] (2, ) a) ( , 2) (2, ) c) , 6. Given that A is a square matrix of order 3 and | A | = - 4, then | adj A | is equal to: a) -4 c) -16 7. 8. a) 8 c) 4 9. ]=[ ], then value of a + b c + 2d is: 11. b) d) + If ex + ey = ex+y , then a) e y - x c) e y - x 1 1 + Let the relation R in the set A = {x Z : 0 x 12}, given by R = {(a, b) : |a b| is a multiple of 4}. Then [1], the equivalence class containing 1, is: a) {1, 5, 9} c) 12. + , x > 0 is perpendicular to a) (2, 5/2) b) ( 2, 5/2) c) (- 1/2, 5/2) d) (1/2, 5/2) -1 sin (tan x), where |x| < 1, is equal to: c) 1 b) 10 d) 8 The point at which the normal to the curve y = a) 1 b) (1, 2) d) (3, 3) the line 3x 4y 7 = 0 is: 10. 1 b) 4 d) 16 A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A? a) (1, 1) c) (2, 2) + If [ + 1 1 b) {0, 1, 2, 5} d) A 1 is: b) e x + y d) 2 e x - y 13. Given that matrices A and B are of order 3 n and m 5 respectively, then the order of matrix C = 5A +3B is: a) 3 5 c) 3 3 14. b) 5 3 d) 5 5 If y = 5 cos x 3 sin x, then 16. 17. 18. 19. b) y d) 9y For matrix A =[ a) [ c) [ 1 is equal to: a) - y c) 25y 15. 1 ] is equal to: ], b) [ ] The points on the curve axis are: 9 + = d) [ 1 ] ] at which the tangents are parallel to y- b) ( 4,0) a) (0, ) c) ( , ) d) (0, ) Given that A = [ ] is a square matrix of order 3 3 and |A| = 7, then the is: value of = , where denotes the cofactor of element a) 7 c) 0 If y = log(cos 1 b) -7 d) 49 , then 1 is: b) cos a) cos c) sin d) tan Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function Z = 3x + 9y maximum? a) Point B c) Point D 1 b) Point C d) every point on the line segment CD 1 20. = The least value of the function is: in the closed interval [0, ] 1 b) + d) The least value does not exist. a) 2 c) + SECTION B In this section, attempt any 16 questions out of the Questions 21 - 40. Each Question is of 1 mark weightage. 21. = The function : R R defined as a) One-on but not onto c) Neither one-one nor onto 22. If x = a sec , y = b tan , then a) c) b) Not one-one but onto d) One-one and onto 1 is: b) d) 23. 24. at = 1 is: In the given graph, the feasible region for a LPP is shaded. The objective function Z = 2x 3y, will be minimum at: a) (4, 10) c) (0, 8) The derivative of sin-1 ( a) 2 c) 25. If A = [ a) A-1 = B c) B-1 = B ] and B = [ b) (6, 8) d) (6, 5) w.r.t sin-1x, b) d) ], then: b) A-1 = 6B d) B-1 = A < < , is: 1 1 1 26. The real function f(x) = 2x3 3x2 36x + 7 is: a) Strictly increasing in ( , and strictly decreasing in ( , b) Strictly decreasing in ( , c) Strictly decreasing in ( , d) Strictly decreasing in ( , 27. Simplest form of tan-1 a) + + + c) 28. 30. 31. and strictly increasing in (3, , , < b) 1 is: Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is: The value of for which the function decreasing over R is: a) < c) = + + is strictly The point(s), at which the function f given by If A = [ are: R R {0} ] and b) d) A= [ 1 b) No value of b exists d) Let R be the relation in the set N given by R = {(a, b) : a = b 2, b > 6}, then: a) (2,4) R b) (3,8) R c) (6,8) R d) (8,7) R a) c) 1 b) d) is continuous, is/are: 32. < d) a) c) 29. 1 , < ) ={ | | , 1 1 = = and ], then the values of , and respectively 1 33. 34. a) , , b) , , c) , , d) , , A linear programming problem is as follows: = + subject to the constraints, + + , In the feasible region, the minimum value of Z occurs at a) a unique point b) no point c) infinitely many points d) two points only The area of a trapezium is defined by function and given by , then the area when it is maximised is: a) c) 35. 36. a) A c) I A If tan-1 x = y, then: c) <y < a) c) 39. 40. [ [ b) y d) y { , } ] ] 1 b) [ d) 2[ ] ] The point(s) on the curve y = x 3 11x + 5 at which the tangent is y = x 11 is/are: a) (-2,19) c) ( , ) Given that A = [ 1 b) Injective function d) function ], then 14A-1 is given by: 1 1 Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, is best defined as: For A = [ 1 b) I + A d) I a) Surjective function c) Bijective function 38. + If A is square matrix such that A2 = A, then (I + A) 7 A is equal to: a) < y < 37. = b) d) 1 1 b) (2, - 9) d) (-2, ) and (2, -9) ]and A2 = 3I, then: 1 a) c) + + = = b) d) SECTION C + + = = In this section, attempt any 8 questions. Each question is of 1-mark weightage. Questions 46-50 are based on a Case-Study. 41. For an objective function = + , where , > ; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is: a) c) 42. 43. + a) b) c) d) The maximum value of [ c) 45. b) d) = = For which value of m is the line y = mx + 1 a tangent to the curve y 2 = 4x? a) 44. = = + ], 0 is: 1 1 b) d) In a linear programming problem, the constraints on the decision variables x and y are , , . The feasible region a) is not in the first b) is bounded in the first quadrant quadrant c) is unbounded in the d) does not exist first quadrant sin Let A = [ sin , then: sin ], where 0 sin a) |A|=0 c) |A| , 1 1 1 b) |A| , d) |A| [ , ] CASE STUDY 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. Given that the fuel cost per hour is times the square of the speed the train generates in km/h, the value of is: a) c) 3 47. b) d) If the train has travelled a distance of 500km, then the total cost of running the train is given by function: a) c) 1 + + b) d) + + 1 48. The most economical speed to run the train is: 49. a) 18km/h b) 5km/h c) 80km/h d) 40km/h The fuel cost for the train to travel 500km at the most economical speed is: 1 50. a) 3750 b) 750 c) 7500 d) 75000 The total cost of the train to travel 500km at the most economical speed is: 1 a) 3750 c) 7500 b) 75000 d) 15000 --------------------------- 1 Marking Scheme Mathematics (Term-I) Class-XII (Code-041) Q.N. 1 Correct Option d 2 b Hints / Solutions 3 d 4 c 5 b 6 d 7 8 b a 9 a 11 12 d a c )= = = = =1 k = < ] =[ = k= -1 As A is singular matrix | |= = = = + = = = as as | , > , is Strictly increasing in , |=| | , where is order of the square matrix = = + = + + = = = + , > As normal to the curve = ( = = But > , = Therefore point= , 10 ( . = { { , , } + = + + = Differentiating w.r.t. : = = = + = = ( + } = = , > = at some point (x, y) is to given line )} = + = = 13 14 b a 15 c 16 c = 17 b 18 d 19 d 20 c + d a = = = ] + = = = =[ ] , = = ] = 6 = = is at = = = . . is minimum -24 at (0, 8) = ) = = . ., = i.e., every element = Section-B = = is one - one = least value of = c a =[ + = Z is maximum 180 at points C (15,15) and D(0, 20). Z is maximum at every point on the line segment CD = + , [ , ] = + [ , ] Let = = = = + 23 24 = = = 22 As tangent to the curve at the point (x, y) is parallel to y-axis = = and = = , | |= = = + + =| |= = Differentiating w.r.t. : = . . (chain rule) 21 , has a pre in (domain) image is onto is one-one and onto . = = and , < < = (1) Using (1), we get : = = < = , < = Differentiating u with respect to v, we get: 25 26 d b As 27 a = = 28 c = = = + < , is strictly decreasing in , + + ( + = ( + + ) = ) , < = , > > = | |=| | ( + < )= < < tan as | | = | | | |= But A is non-singular matrix | |= = = = > , ={ = , < , = | | = | | either | | = 29 b 30 c 31 a 32 b 33 c 34 c =[ " d c ] = , = = Corner points of feasible region = + (5,0) 150 (9,0) 270 (0,3) 150 (0,6) 300 Minimum value of occurs at infinitely many points 35 36 ]=[ = = = + = " , But = Maximum area of trapezium is < < = + + + > < = when x = 5 = 37 b 38 b 39 b 40 c Since, distinct elements of A have distinct f-images in B. Hence, f is injective and every element of B does not have its pre-image in A, hence f is not surjective. . | |= , ] =[ a 42 b 43 c + b d 46 d 47 b ]=[ + ] Let = =[ + + ] , let = ]=[ ] = = [ , ] = , = and = Maximum value of is 1 Feasible region is bounded in the first quadrant | |= + As , + | | [ , ] Fuel cost per hour = = . = Total cost of running train (let C) = Total cost of running train 500 km= c Section C Distance covered = 500km 48 [ As Z is maximum at (30, 30) and (0, 40) + = = = + .. and = Substituting (1) in (2) : + = + + = .. As line is tangent to the curve line touches the curve at only one point = = 44 45 = = + = Slope of line = = = point is (2, -9) as (-2, 19) does not satisfy the equation of the given line = [ 41 = Let = = = / c Fuel cost for running 500 km 50 d Total cost for running 500 km = + + 49 = = + = . / = + + = . /

Formatting page ...

Tags : cbse, cbse papers, cbse sample papers, cbse books, portal for cbse india, cbse question bank, central board of secondary education, cbse question papers with answers, prelims preliminary exams, pre board exam papers, cbse model test papers, solved board question papers of cbse last year, previous years solved question papers, free online cbse solved question paper, cbse syllabus, india cbse board sample questions papers, last 10 years cbse papers, cbse question papers 2017, cbse guess sample questions papers, cbse important questions, specimen / mock papers 2018.

cbse12 chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: