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

CBSE Class 12 Board Exam 2020 : Mathematics (Series 5)

16 pages, 68 questions, 0 questions with responses, 0 total responses,

	cbse12	+Fave Message
	Profile Timeline Uploads Q & A

Home > cbse12 >

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

Formatting page ...

SET 1 Series : HMJ/5 . Code No. . 65/5/1 - - Roll No. Candidates must write the Code on the title page of the answer-book. - (I) 15 (II) - (II) - - NOTE Please check that this question paper contains 15 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (III) Please check that this question paper contains 36 questions. (IV) Please write down the Serial Number of the question in the answer-book before attempting it. (V) 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. (I) - 36 (IV) , (III) (V) - 15 - 10.15 10.15 10.30 - - MATHEMATICS {ZYm [aV g : 3 K Q>o A{YH$V A H$ Time allowed : 3 hours . 65/5/1. 334A : 80 Maximum Marks : 80 1 P.T.O. : (i) - , , 36 (ii) - 1 20 20 (iii) - 21 26 6 (iv) - 27 32 6 (v) - 33 36 4 : (vi) - - , - , - - (vii) , , (viii) 1 10 : 1. A 3 A (adj A) = 10 I , |adj A| (a) 1 2. (b) 10 (c) 100 (d) 101 A 3 3 |A| = 8 , |3A| (a) 8 .65/5/1. (b) 24 (c) 72 2 (d) 216 General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper comprises four sections A, B, C and D. This question paper carries 36 questions. All questions are compulsory. (ii) Section A Question no. 1 to 20 comprises of 20 questions of one mark each. (iii) Section B Question no. 21 to 26 comprises of 6 questions of two marks each. (iv) Section C Question no. 27 to 32 comprises of 6 questions of four marks each. (v) Section D Question no. 33 to 36 comprises of 4 questions of six marks each. (vi) There is no overall choice in the question paper. However, an internal choice has been provided in 3 questions of one mark, 2 questions of two marks, 2 questions of four marks and 2 questions of six marks. Only one of the choices in such questions have to be attempted. (vii) In addition to this, separate instructions are given with each section and question, wherever necessary. (viii) Use of calculators is not permitted. Section A Question numbers 1 to 10 are multiple choice questions. Select the correct option : 1. If A is a square matrix of order 3, such that A (adj A) = 10 I, then |adj A| is equal to (a) 1 2. (b) 10 (c) 100 (d) 101 If A is a 3 3 matrix such that |A| = 8, then |3A| equals. (a) 8 .65/5/1. (b) 24 (c) 72 3 (d) 216 P.T.O. 3. d2y y = Ae5x + Be 5x , dx2 (a) 25 y 4. 5. (b) 5 y . x2 ex3 dx . 1 x3 (a) e +C 3 1 x4 e +C 3 (c) 1 x3 e +C 2 (d) 15 y (d) 1 x2 e +C 2 ^i, ^j, k^ , (a) ^i ^j = 1 6. (b) (c) 25 y (b) ^i ^j = 1 (c) ^i k^ = 0 (d) ^i k^ = 0 ABCD E EA + EB + EC + ED (a) 0 7. x 2 1 (a) (b) AD 2 3 = y 3 4 z = 1 k (b) (c) 2BC x 1 k = (d) 2AD y 4 z 5 = , k 2 2 2 3 (c) 2 (d) 2 8. 2x + 3y > 6 : (a) (b) , 2x + 3y = 6 (c) XOY- , 2x + 3y = 6 (d) XOY- 9. 52 , , (a) .65/5/1. 1 3 (b) 4 13 (c) 4 1 4 (d) 1 2 3. If y = Ae5x + Be 5x, then (a) 25 y 4. . x2 ex3 dx equals . 1 x3 (a) e +C 3 d2y is equal to dx2 (b) 5 y (b) (c) 25 y 1 x4 e +C 3 (c) 1 x3 e +C 2 (d) 15 y (d) 1 x2 e +C 2 5. If ^i, ^j, k^ are unit vectors along three mutually perpendicular directions, then (a) ^i ^j = 1 (b) ^i ^j = 1 (c) ^i k^ = 0 (d) ^i k^ = 0 6. ABCD is a rhombus whose diagonals intersect at E. Then EA + EB + EC + ED equals (a) 0 7. (b) AD (c) 2BC (d) 2AD x 2 y 3 4 z x 1 y 4 z 5 = = and = = are mutually 1 1 k k 2 2 perpendicular if the value of k is 2 2 (a) (b) (c) 2 (d) 2 3 3 The lines 8. The graph of the inequality 2x + 3y > 6 is (a) half plane that contains the origin. (b) half plane that neither contains the origin nor the points of the line 2x + 3y = 6. (c) whole XOY plane excluding the points on the line 2x + 3y = 6. (d) entire XOY plane. 9. A card is picked at random from a pack of 52 playing cards. Given that the picked card is a queen, the probability of this card to be a card of spade is 1 4 1 1 (a) (b) (c) (d) 3 13 4 2 .65/5/1. 5 P.T.O. 10. 3 , A 5 , B P(A B) (a) 2 5 (b) 3 5 (c) 0 (d) 1 11 15 , 11. A _______ , A 12. 1 0 1 1 A + B = 1 1 A 2B = 0 1 , A = _________ 13. f(x) = ax + x (a > 0, b > 0, x > 0) _____. 14. x dx + 2y = x2 _____. b dy 15. 2 dy 1 + = x ______ dx (3, 4, 7) (1, 1, 6) _______. _______ 16 20 16. 17 sin 1 sin 8 . .65/5/1. 6 10. A die is thrown once. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A B) is (a) 2 5 (b) 3 5 (c) 0 (d) 1 Fill in the blanks in Questions from 11 to 15. 11. A relation in a set A is called _______ relation, if each element of A is related to itself. 1 0 1 1 and A 2B = , then A = _________. 12. If A + B = 1 1 0 1 13. The least value of the function f(x) = ax + b (a > 0, b > 0, x > 0) is _____. x 14. The integrating factor of the differential equation x dy + 2y = x2 is _____. dx OR 2 dy The degree of the differential equation 1 + = x is ______ . dx 15. The vector equation of a line which passes through the points (3, 4, 7) and (1, 1, 6) is _______. OR The line of shortest distance between two skew lines is _______ to both the lines. Q. Nos. 16 to 20 are of very short answer type questions. 17 . 16. Find the value of sin 1 sin 8 .65/5/1. 7 P.T.O. 3 4 A 1 1 17. A = 1 18. f, , x = 3 , k 2 xx 39 , x 3 f(x) = k ,x=3 19. f(x) = x4 10 , f(2.1) y = 2 sin2 (3x) x = 6 4 . 20. . |x 5|dx 1 21 26 2 4x + 3 2 2 21. f(x) = 6x 4 , x 3 , x 3 (fof) (x) = x, f R = {(a, b) : a < b} (i) , (ii) 22. dx . x2 + 3x + 2 23. x = a cos ; y = b sin , dx2 . x d2y ecosx sin2 x .65/5/1. 8 3 17. For A = 1 4 write A 1. 1 18. If the function f defined as 2 xx 39 , x 3 f(x) = k ,x=3 is continuous at x = 3, find the value of k. 19. If f(x) = x4 10, then find the approximate value of f(2.1). OR Find the slope of the tangent to the curve y = 2 sin2 (3x) at x = . 6 4 . 20. Find the value of . |x 5|dx. 1 Section B Q. Nos. 21 to 26 carry 2 marks each. 4x + 3 2 2 21. If f(x) = , x , then show that (fof) (x) = x, for all x . Also, write 3 3 6x 4 inverse of f. OR Check if the relation R in the set of real numbers defined as R = {(a, b) : a < b} is (i) symmetric, (ii) transitive . x 22. Find . 2 dx. x + 3x + 2 23. If x = a cos ; y = b sin , then find d2y . dx2 OR Find the differential of sin2 x w.r.t. ecosx. .65/5/1. 9 P.T.O. 2 24. 1 1 25. . 1 1 2x e dx 2x2 . x . x(1 x)n dx . 0 26. A B , P(A) = 0.3 P(B) = 0.6, P(A B ) 27 32 4 27. x : sin 1 (1 x) 2 sin 1(x) = 2 dy 28. y = (log x)x + xlogx , dx 29. y dy y x sin + x y sin = 0 x dx x x = 1 y = 2 30. a = ^i + 2^j + 3^k b = 2^i + 4^j 5^k , , ABC A (1, 2, 3), B(2, 1, 4) C (4, 5, 1), .65/5/1. 10 2 . 1 1 24. Evaluate . 2 e2x dx. x 2x 1 1 . 25. Find the value of . x(1 x)n dx. 0 26. Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6, find P(A B ) Section C Q. Nos. 27 to 32 carry 4 marks each. 27. Solve for x : sin 1 (1 x) 2 sin 1(x) = . 2 28. If y = (log x)x + xlogx, then find dy . dx 29. Solve the differential equation : y dy y x sin + x y sin = 0 x dx x Given that x = 1 when y = . 2 30. If a = ^i + 2^j + 3^ k and b = 2^i + 4^j 5^ k represent two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram. OR Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B(2, 1, 4) and C (4, 5, 1). .65/5/1. 11 P.T.O. 31. A 5 10 B 8 8 3 20 4 A ` 100 B ` 120 - 32. X 30 A 40 B Y , 50 A 60 B B Y 33 36 6 33. (1, 1, 1) x+2 y 3 z+1 x 1 y 2 z 3 = = ; = = 1 2 4 2 3 4 .65/5/1. 12 31. A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A requires 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. Given that total time for cutting is 3 hours 20 minutes and for assembling 4 hours. The profit for type A souvenir is ` 100 each and for type B souvenir, profit is ` 120 each. How many souvenirs of each type should the company manufacture in order to maximize the profit ? Formulate the problem as an LPP and solve it graphically. 32. Three rotten apples are mixed with seven fresh apples. Find the probability distribution of the number of rotten apples, if three apples are drawn one by one with replacement. Find the mean of the number of rotten apples. OR In a shop X, 30 tins of ghee of type A and 40 tins of ghee of type B which look alike, are kept for sale. While in shop Y, similar 50 tins of ghee of type A and 60 tins of ghee of type B are there. One tin of ghee is purchased from one of the randomly selected shop and is found to be of type B. Find the probability that it is purchased from shop Y. Section D Q. 33 to 36, carry 6 marks each. 33. Find the vector and cartesian equations of the line which is perpendicular to the lines with equations x+2 y 3 z+1 x 1 y 2 z 3 = = and = = 1 2 4 2 3 4 and passes through the point (1, 1, 1). Also find the angle between the given lines. .65/5/1. 13 P.T.O. 34. x2 + y2 = 9 (x 3)2 + y2 = 9 : 4 . 2 .(x x) dx 1 35. (ax + by) , x y = c2 36. a, b, c p, q, r , log a p 1 log b q 1 =0 log c r 1 2 3 5 A = 3 2 4 , A 1 1 1 2 A 1 , 2x 3y + 5z = 11 3x + 2y 4z = 5 x + y 2z = 3 ____________ .65/5/1. 14 34. Using integration find the area of the region bounded between the two circles x2 + y2 = 9 and (x 3)2 + y2 = 9. OR 4 . Evaluate the following integral as the limit of sums .(x2 x) dx. 1 35. Find the minimum value of (ax + by), where xy = c2. 36. If a, b, c are pth, qth and rth terms respectively of a G.P, then prove that log a p 1 log b q 1 =0 log c r 1 OR 2 3 5 If A = 3 2 4 , then find A 1. 1 1 2 Using A 1, solve the following system of equations : 2x 3y + 5z = 11 3x + 2y 4z = 5 x + y 2z = 3 ____________ .65/5/1. 15 P.T.O. .65/5/1. 16

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: