e aoe ues Series #-Sueceed 1-25)/15 rattno. (_[_ le] Sample Question Paper 01 Mathematics 12" (code-041) "ener Isructons | (@ This question paper contains 38 questions. All questions are compulsory (i Question paper is divided into FIVE sections - Section A, B, C, D and E. (Gi) In Section A, Question number 1 to 18 are Multiple Choice Questions (MCQ) and Question ‘number 19 and 20 are Assertion-Reason based questions carrying 1 mark each. | {iv) In Section B, Question number 21 to 25 are Very Short Answer (VSA) type questions carrying 2 marks each, |.» inseation ©, Question number 261031 are Short Answer (SA) type questions carvings... ume: 3 HS. ‘marks each. Max. Marks : 80 (0) InSeeson D, Question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each. | (sil In Section E, Question number 36 to 38 are Case Study Based questions carrying 4 marks each, | (vil There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 3 questions in Section C, 2 questions in Section D and 2 questions in Section E. (&) Use of calculator is NOT allowed. Section A Multiple Choice Questions (Fach Que. caries) 1. a =37-+2) +5 and b =61 -j-5k, then find ( decreasing in (5.2) (@+b)@-B) (© decreasing inf - 2 4 @B (a) 10 (26 , ” 2 (©) : (€) decreasing info] Qt ae } then which of the following is. 4 -6 4, From the set {1,2,3, 4, 5) two numbers a and Src? Wa b)are chosen at random, The probability (a) Aladja) #111 that “is an integer, is (b) A(adj A)#(adj A) A ocd i 1 1 3 ©. ads A)n(ad) aA =1All-[9 a sy OF 5 rs (8) None ofthe above 5, Evaluate the determinant]! ! 4. The function f(x) = 4sin? x-6sin? x 2 ea ‘+ 12sinx + 100is strictly (3 wo (@ increasing inf 0.2 or wa ming)iy +b, z= ey + deand | y+0i,2= cy +a" are perpendicular to each other, if | @S+S=1 (©) aa’ o=1 -Ity= tans— Hoge oe (©)secx ~ 3x42 (d) None of these 8 wexe[ : -[3 3} then matrix Xis eae 1-12 Foe oy | at 70 or 8. The direction ratios of the line passing through two points (2,~4, 5) and (0,1,—1)is. (2,-6.5) 0)(-2,5,-6) (6,-2.-6 (€)(-6,-2,5) etl _ge-t 10.f For IS equal to 1a) 45" OS log2 les (& Hog(2-*)~210g 45") + C © Boge) + Blog {5*)+C tf | (d) None of the above MEET (257 4)-[7 152] noes @ty)is @1 2 | @4 (5 || 12. The integrating factor ofthe differential equation x77 +2y =x? is @* bx? | @ae @ay | | 13. Ify = cos™ x, then (1-x? yp is equal to @)ay Om Ox, (d)x?y fae 44. The value ottan [asic #h an oy (b) re n F # 45. If y= Ae™ + Be, then od is equal to oF (@) 25y ()5y (0 -25y (d) 15y 16. The number of points of discontinuity off defined by f(x)=|z|-[r+1]is @i 2 (oo 17. "tan? @x) dis equal to (a5 wt | 18.16 7: [@\(B!, then the angle betweené | and Bis | @o 30" er ast Assertion-Reason Based Questions In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct answer out f the following choices, (@) Both Aand Rare true and Ris the cor explanation of A. (©) Both A and R are true but R is not the correct explanation of A. (©) Ais true but Ris false. (4) Ais false but Ris true, 19. Assertion (A) A 2x2 matric A=) : 12 elements are given by ay = ix, is [ 4] Reason (R) If Ais a4x2 matrix, then the elements in Ais 5, 20, Assertion (A) We can write sin“ y= (gina)! Reason (R) Any value in the range! Principal value branch is called prin, value of that inverse trigonometric fu Ls)Sample Question Paper 01 [ Section B Very Short Answer Type Questions (Each Que. carries2™) 21. Find Ialand (8) if {@l=21Bland (@+B)-(a-B)=12. Or Find the unit vector perpendicular to each of the vectors @ = 47 +3] + and Ba2i-j+2k. 22. Check, if the relation Ron the set A={1,2,3,4,5,6], then defined as R= ((x,y):yis divisible by x} is (@ symmetric i) transitive. Or Find the value of tan“!(1) + cos] (4) 28 sove r+ h=2e¥ +1;y=0, when x=0. ix in( 2 )4Y y at , 42ND yy sin 4) =0;y= or savesse( 2) x-yee(2) 0-3 when x=1. 27. Find the value of fx (1-x)" dx. Or Evaluate [5a git cos*x a 28. tty = (ay +(sina)" then find 29. 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 ‘92. Find the area of the smaller part of the circle v2 33. Prove that the relation R on Z, defined by R {(a,b):(a— b)is divisible by 5} is an equivalence relation. x74y? =a” cut-off by the line x= 23. Show that the function SDE + cos x, x 2, f@)= continuous at x = 0. 24. Show that the function f defined by fx) =(x— Det +1is an increasing function forall x>0. 25. If a line has direction ratios 2, -1, 2, then determine its direction cosines. Section C Short Answer Type Questions (Each Que. carries 3M) replacement, then find the mean of the number of rotten apples. Or Ina Shop X, 30 tins of ghee of Type Aand 40 tins of ghee of Type Bwhich look alike, are kept for sale. While in Shop Y, similar 50 tins of ghee of type Aand 60 tins of ghee of Type Bare 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. 30. If Z=2.x +3y, subject to constraints x+2y$10,2x+y<14, x, y20, then find the corner points of feasible region. 31. Evaluate fx(tan" x) de | Section D Long Answer Type Questions (Each Que. caries 5M) Or Show that the relation Rin the set Aof points in a plane, given by R= ((P, Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related toa point P #(0,0)is the circle passing through P with origin as centre,40 Ta Find the vector and cartesian equations of | the line which is perpendicular to the lines | i j with equations “#2 el 2 a 2 and passes through the point (1, 1, 1). Also, find the angle between the given lines. Or Find the shortest distance between the lines © given by j P=Q+AN GHA + (SHANE | | iSucceed Mathemati, — and P= (2u-1)i H4H-1) j +6 ~3ye 2-3 5 a5.1fA=|3 2-4} then find A~ i 2 Using A™, solve the following system o equations 2x-3y +5z=11 Bx 42y—42=-5 xty-22=-3 Section E Case-Study/Passage-based (4 Mark Questions) 35. P(x)=~6x? + 120x + 25000 (in &) is the total | profit function of a company, where x | denotes the production of the company. Based on the above information, answer the following questions. (i) Find the profit of the company, when the production is 3 units. (ii) Find P(6), (iii) Find the interval in which the profit is strictly increasing. Or Find the production, when the profit is maximum, auditorium for its cultural activities purpose. The shape of the floor of the auditorium is rectangular and it has a fixed perimeter, say P. | | | 87. Ina college, an architecture design a | Based on the above information, answet!# following questions. ‘ (i) IfJand brepresents the length and breadth of the rectangular region t® find the relationship between |, b="! q (Gi) Find the area (A) of the floor a5@ function of J (iii) College manager is interested in maximising the area of the floot 4 For this purpose, find the value! or E Find the maximum area of the foe!» 38. In an office three employees Vinay * and Iqbal process incoming copies of? Hi certain form, Vinay process 50% of, forms, Sonia processes 20% and Iqb™!"™ so remaining 30% of the forms. wt HeSample Question Paper 01 error rate of 0.04 and Iqbal has an error rate of 0.03. Based on the above information answer the following questions. (i) The total probability of committing an error in processing the form. (ii) The manager of the company wants to do a quality check. During inspection he selects a form at random from the days output of processed forms. If the | form selected at random has an error, the probability that the form is not | processed by Vinay. |