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

CBSE Class 12 Pre Board 2019 : Mathematics - Prelim 2 (St Xavier's Sr. Sec. School, Delhi)

3 pages, 37 questions, 0 questions with responses, 0 total responses,

	CBSE 12 Pre Boards	+Fave Message
	Profile Timeline Uploads

Home > cbse12_pre_boards > F Also featured on: School Page cbse12

Formatting page ...

Pre Board Examination 2019 Std. 12 17-01-2019 Set 2 MATHEMATICS Max. Marks : 100 Time : 3 hrs. GENERAL INSTRUCTIONS: i) Attempt all the questions. ii) Section- A consists of 4 questions of 1 mark each. iii) Section-B consists of 8 questions of 2 marks each. iv) Section-C consists of11 questions of 4 marks each. v) Section-D consists of 6 questions of 6 marks each. SECTION A 1. Write the integrating factor of the following differential equation: 2 =1 2. Write the projection of vector 2 +3 - + (OR) Find the angle between vectors - and - . 3. If y= + log then find 4. What is the value of 4 3 , where 3 is matrix of order 3. . SECTION B 5. Find if the vector - + , 3 + + 2 and + - 3 are coplanar. (OR) If vectors = 2 + 2 + 3 , = - + 2 + and = 3 + are such that + is perpendicular to . Find . 6. 5 If A= 4 2 4 3 is symmetric matrix,then find x,yand t. 7 7. Form a differential equation corresponding to 2 = ( )3 by eliminating a. 8. Evaluate: 9. Evaluate: 10. Let be a binary operation on N as a b = HCF (a,b) a,b N, then find 22 4. Also state that a b is commutative or not. 11. A bag contains 2 red and 3 black balls, find the probability distribution of the number of red balls if 2 red balls are drawn without replacement. 12. A die is thrown three times. Events A and B are defined as below: A: 5 on the first and 6 on the second throw. B: 3 or 4 on the third throw. Find the probability of B, given that A has already occurred. 3 7 9 2 16 3 0 dx (OR) 1 1 dx. 3 dx. Std. 12 MATHEMATICS (Set 2) Page 2 SECTION C 13. Let A= R-{3}and B=R-{1}, consider the function : defined by = 1 2 3 . Show that is one-one, onto and hence find . (OR Prove that the relation R in the set A= {1,2,3,.......12} given by R= { , : is divisible by 3} is an equivalence relation. Find all elements related to the element 1. 14. Using properties of determinants prove that: ( + )2 ( + )2 = 2 ( + + )3 . ( + )2 15. Prove that: cos[tan 1 {sin(cot 1 )}] = 16. If 2 + 2 = tan-1 , show that 1+ 2 . 2+ 2 = . + (OR) Differentiate (sinx-cosx)(sinx-cosx)w.r.t x. 17. Find the equation of tangent and normal to the curve = + sin , = 1 + cos at = 2 . 18. If y = 19. Evaluate: 20. Evaluate: 21. Show that the differential equation 2 sin 1 1 2 , prove that: (1 x2 ) d2 y dx 2 3x dy y=0. dx 2 . 2 . + 2 + 2 = 0 is a homogeneous. Also find the particular solution of this differential equation given that y=1, x=0. (OR) Find the particular solution of the differential equation 2 = 1 + , 0. Given that when = 1, = 2 . 22. Find the distance of the point (1,-2,3) from the plane x - y + z=5 measured parallel to the line whose direction cosines are proportional to 2,3,-6. 23. If = 3 + 4 + 5 and = 2 + - 4 , then express in the form of = 1 + 2 . Where 1 is parallel to and 2 is perpendicular to . SECTION D 24. The sum of perimeters of a circle and a square is k, where k is some constant. Prove that the sum of their areas is least when the side of the square is equal to the diameter of the circle. Std. 12 25. MATHEMATICS (Set 2) Page 3 2 3 5 If A = 3 2 4 then find 1 . Using 1 solve the system of linear equations given: 1 1 2 2 + 3 + = 11, 3 + 2 + = 5 and 5 4 2 = 3. (OR) 0 1 2 Using elementary row operations find 1 for A = 1 2 3 . 3 1 0 26. Find the area of the region bounded by { , : 2 4 4 2 + 4 2 9 } using method of integration. (OR) Using method of integration find the area of the region bounded by the lines 2 + = 4, 3 + 2 = 6 and 3 + 5 = 0. 27. Show that the lines +1 1 = 2 2 = 5 5 +3 and 3 = 1 1 = 5 5 are coplanar. Also find the equation of the plane containing the lines. (OR) Find the equation of the plane passing through the point (-1,3,2) and perpendicular to the planes + 2 + 3 = 5and 3 + 3 + = 0. 28. Two groups are competing for the position on the board of directors of a corporation. The probabilities that the first and the second group will win are 0.6 and 0.4 respectively. Further if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3, if the second group wins. Find the probability that the new product was introduced by second group. 29. A dealer wishes to purchase a number of fans and sewing machines. He has only Rs 5760 to invest and has a space for at most 20 items. A fan costs him Rs360 and a sewing machine Rs 240. His expectation is that he can sell a fan at a profit of Rs 22 and a sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit? Formulate this as a linear programming problem and solve it graphically. -x-x-x-x-x-x-x-

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: