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

CBSE Class 12 Pre Board 2021 : Mathematics - Set 1 (CBSE Gulf Sahodaya Qatar Chapter, Doha)

6 pages, 77 questions, 4 questions with responses, 5 total responses,

	CBSE 12 Pre Boards	+Fave Message
	Profile Timeline Uploads

Home > cbse12_pre_boards > F Also featured on: School Page cbse12 and 3 more

Formatting page ...

CBSE Pre Board Examination 2020-21 Mathematics Class XII Max. Marks: 80 Time Allowed: 3 hrs General Instructions: 1. This question paper contains two parts A and B. Each part is compulsory. Part A carries 24 marks and Part B carries 56 marks. 2. Part-A has Objective Type Questions and Part -B has Descriptive Type Questions. 3. Both Part A and Part B have choices. Part A: 1. It consists of two sections- I and II. 2. Section I comprises of 16 very short answer type questions. 3. Section II contains 2 case studies. Each case study comprises of 5 case-based MCQs. An examinee is to attempt any 4 out of 5 MCQs. Part B: 1. It consists of three sections- III, IV and V. 2. Section III comprises of 10 questions of 2 marks each. 3. Section IV comprises of 7 questions of 3 marks each. 4. Section V comprises of 3 questions of 5 marks each. 5. Internal choice is provided in 3 questions of Section III, 2 questions of Section-IV and 3 questions of Section-V. You have to attempt only one of the alternatives in all such questions. 1. PART A Section - I Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. Consider the set A has 5 elements, then the total number of injective functions from Set A onto [1] itself is ________. OR Let : is defined by ( ) = | |. Is function onto ? Give reason. 2. If R is a relation defined on set = {1, 2, 3} as = { (1, 1), (1, 2), (2,3)}. Is Relation R is [1] transitive, if not which ordered pairs should be added to make it transitive ? 3. The relation = {( , ): | | 3 } in set = {1, 2, 3, .10} is an equivalence [1] relation. Write the equivalence class related to 2. OR Let = {1, 2, 3, 4} and = {5, 6, 7}. Let : is defined as = { (1, 6), (2, 5), (3, 6), (4, 7)}. Is function bijective. Give reason. 4. If AB = 16I, then write 1 in terms of B. [1] 5. If for matrix A, |A| = 5, find |4A|, where matrix A is of order 2 2. [1] OR Find the invers of matrix [7 1 ] 4 3 6. Given square matrix A of order 3, such that | | = 15, find | . |. [1] 7. If 2 log = ( ) + , then find ( ). [1] OR 1 Evaluate: 1|(1 )| . 1 , x axis and between = 1, = 4. 8. Find the area of the region bounded by the curve = 9. Write the order and degree of the differential equation cos ( ) = 0 [1] [1] OR Show that the differential equation 2 / + ( 2 ) = 0 is homogeneous. 10. Find a unit vector in the direction of + where = 2 + 5 = 4 + [1] 11. If is a unit vector and ( ). ( + ) = 80, then find | |. [1] 12. Find the projection of on ( + ) where = + 2 4 = 2 + 3 + [1] 13. Write the direction cosines of a line equally inclined to the three coordinated axes. [1] 14. Write the vector equation of the line 15. A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, 5 3 = +4 7 = 6 [1] 2 [1] given that the red die resulted in a number less than 4. 16. Find the value of , for which the following distribution is a probability distribution. X 30 10 50 P(X) 1 2 1 5 Section-II Case study based questions are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark. 17. Case Study based-1 A square sheet of cardboard with each side cm is to be used to make an open top box by cutting a small square of cardboard from each of the corners and bending up the sides. Page 2 of 6 [1] (a) The volume V cm3 of the box is given by ______________ [1] (i) ( ) = 4 3 4 2 + 2 (ii) ( ) = 4 3 4 2 + 2 (iii) ( ) = 4 3 4 2 + 2 (iv) ( ) = 4 3 + 4 2 + 2 (b) Perimeter of the given net of the box is _________________ [1] (i) ( ) = 8 2 (ii) ( ) = 4 (iii) ( ) = 8 2 (iv) ( ) = 2 (c) (d) The rate of change of Volume with respect to x is ____________ (i) 12 2 8 + 2 (ii) 12 2 8 + 2 (iii) 8 (iv) 12 2 + 8 + 2 The local maximum volume of the box at = ________ (i) (e) 3 (ii) (iii) 6 [1] 3 (iv) 6 The maximum volume of the box at = 3 is _______________ (i) 4 18. [1] (ii) 6 (iii) 27 [1] (iv) 2 Case Study based-2 A car dealer offers purchasers a three-year warranty on a new car. He sells two models, the Zippy and the Nifty. For the first 50 cars sold of each model the number of claims under the warranty is shown in the table below. One of the purchasers is chosen at random. Let A be the event that no claim is made by the purchaser under the warranty and B the event that the car purchased is a Nifty. (a) (i) 0.1 (b) [1] P (A B) is _______ (ii) 0.2 (iii) 0.01 (iv) 0.02 P (A ) is ________ (i) Page 3 of 6 1 4 [1] 1 (ii) 2 3 (iii) 4 2 (iv) 5 (c) Given that the purchaser chosen does not make a claim under the warranty, find the probability that [1] the car purchased is a Zippy. (i) 0.2 (d) (ii) 0.4 (iv) 0.8 Given that the purchaser chosen does not make a claim under the warranty, find the probability that the car purchased is a Nifty. (i) 0.8 (e) (iii) 0.6 (ii) 0.6 (iii) 0.4 [1] (iv) 0.2 Write the correct statement. [1] (i) The given information in a table is a probability distribution. (ii) Making a claim is independent of the make of the car purchased. (iii) Making a claim is not independent of the make of the car purchased. (iv) All the above are wrong statements. Part B Section III All questions are compulsory. In case of internal choices attempt any one. 19. Write tan 1 [ 20. If A =[2 1+ 2 1 [2] ] , 0 in the simplest form. 3 ] be such that 1 = , then find the value of . 5 2 [2] OR Given a square matrix A of order 3 3, such that |A|= 12, find the value of |A. adj A|. 21. Find the value of so that the function defined by ( ) = [2] + 1, cos , > is continuous at = . 22. Find the equation of the tangent to the curve = 3 2 which is parallel to the line [2] 4 2 + 5 = 0. 23. 1 2 +3 Evaluate 0 5 2 +1 [2] OR 2 Evaluate 0 cos (1+sin ) (2+sin ) 24. Using integration, find the area of the region bounded by the parabola = 2 and the line = | |. [2] 25. Find the particular solution of the differential equation (1 + 2 ) + (1 + 2 ) = 0 given that [2] when = 0, = 1. 26. and ( ) Find a vector of magnitude 6, perpendicular to each of the vectors ( + ) where = + + = + 2 + 3 Page 4 of 6 [2] 27. Find the equation of the plane passing through the line of intersection of the planes [2] . ( + + ) = 1 and . (2 + 3 ) + 4 = 0 and parallel to the x axis. 28. Two dice are thrown. Find the probability that the numbers appeared have a sum 8 if it is known [2] that the second die always exhibits 4. OR Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females. Section IV All questions are compulsory. In case of internal choices attempt any one. 29. Consider the binary operations defined as = | | and # = , , . Show that * is commutative but not associative, # is associative but not commutative. 30. If = + (cos ) find 2 [3] [3] . OR If = ( ) , then show that = ( 1) ( +1) . 31. Show that the function ( ) = | 3|, is continuous but not differentiable at = 3. [3] 32. Find the intervals in which the function is given by ( ) = ( 1)( 2)2is strictly increasing [3] or strictly decreasing. [3] 33. Find 34. Using integration find the area of the region in the first quadrant enclosed by the , the line = and the circle 2 + 2 = 32. (2+ )(4+ 2 ) [3] OR Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3). 35. Find the particular solution of the differential equation = cos ( 2 ) , given that = 2 when = 2 . [3] Section V All questions are compulsory. In case of internal choices attempt any one. 36. 1 1 0 2 2 4 Given = |2 3 4| and = | 4 2 4| verify that = 6 , use the result to solve the 0 1 2 2 1 5 system of linear equations =3 , 2 + 3 + 4 = 17, + 2 = 7 OR Page 5 of 6 [5] 1 2 If = [2 1 2 2 37. 2 2] find 1 and hence prove that 2 4 5 = 0. 1 Find the equation of the perpendicular drawn from the point (1, 2, 3) to the plane 2 3 + 4 + 9 = 0. Also find the coordinates of the foot of the perpendicular. [5] OR Find the equation of the line passing through the point (4, 6, 2) and the point of intersection of the line 38. 1 3 = 2 = +1 7 and the plane + = 8. Solve the following LPP graphically Minimise = 5 + 10 subject to the constraints + 2 120 + 60 2 0 , 0 OR The corner points of the feasible region determined by the following system of linear inequalities: 2 + 10 + 3 15 , 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let = + , where , 0, what is the condition on , that maximum Z occurs at both (3, 4) and (0, 5). Show this information by plotting the graph and identify the feasible region. -o0o0o0o- Page 6 of 6 [5]

Formatting page ...

Top Contributors
to this ResPaper
(answers/comments)

Rishabh Raj
(3)

Priya Kharwar
(2)

Formatting page ...

Tags : cbse pre boards, prelims 2015 - 2016, preliminary examinations, central board of secondary education, india schools, free question paper with answers, twelfth standard, xiith std, board exams, mock, model, sample, specimen, past, free guess papers.india, delhi, outside delhi, foreign, cbse class xii, cbse 12, 12th standard, cbse papers, cbse sample papers, cbse books, portal for cbse india, cbse question bank, cbse question papers with answers, 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 questions papers, cbse important questions, specimen / mock papers.

cbse12_pre_boards chat

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