Page 1 : Time: 90 Minutes Max. Marks: 40, , , , General Instructions:, (i) All questions are compulsory., (ii) There are 40 questions in all., (iii) This question paper contains Multiple Choice Questions (MCQs), Case-based MCQs and, Assertion-Reason MCQs., (iv) Only one of the options in every question is correct., , (v) An OMR sheet of every practice paper is given. The candidate has to give his/her answer by, darkening the circle against that question., , , , Question numbers 1 to 30 are multiple choice questions. Choose the correct option., 1. Let f: N——~Z such that, , , , n= when mis odd, f=) %, is, -> when # is even, (a) onto but not one-one (b) one-one and onto both, (c) neither one-one nor onto (d) one-one but not onto, 2. The function f(x) = log [x* + yx" +1] is a/an, (a) even function (b) odd function, (c) even increasing function (d) decreasing function, 3. Iff:R—R be defined by fat yre R. Then fis, (a) One - One (b) Onto (c) Bijective (d) fis not defined, 4. If A={a, b, c, d, ec} and B = (1, 2, 3, 4), then the number of relations that can be defined from, Ato Bis, (a) 20 (b) 2” (2? (4) 9, 5. Arelation R = {(v, y): |x-y| is divisible by 3; x, y € R; set of real numbers}, then R is, (a) Symmetric (b) Reflexive (c) Transitive (d) All of these, , 6. The value of sin (sin) is, , @ = w = oF a =, 7. What is the value of tan|}-cos-t(=1)]>, (a) 1 (v) ¥3 () 0 (d) None of these, , Scanned by TapScanner

Page 2 : 10,, , 11., , 12., , 13., , 4., , 15., , 16., , 17., , , , 005, The matrix A =/0 5 0] isa, 500, (a) Scalar matrix (b) Diagonal matrix (c) Unit matrix (d) Square matrix, -14 4 oe, If a-( 3] ana B -|t 3] ten fina 7a + 58, 72 7 -7 33 22 21, (a) 5 = (b) ie 31 | ©) ES al @ |, =, , If a-[} 9] emen ais, , 0 0 00 00 40 0, (a) [ >| (b) [3 al (ce) [‘o 40 (a) [o 40, If A+B+C=7, then, tan(A+B+Q tanC cosC, , , , , , , , , , , , , , , , , , tan (A + B) 0 sin B] equal to, cos(A+B) -sinB 0, (a) -1 (b) 0, () 1 (d) None of these, -a 1 1, al dA, If A= » 2 = 1] tren “4 equals, (a) 1+3B (& 3B, (c) -3B (@) 1-38, b+e b ¢, If} a c+a_ c |=k(abe), then the value of k equals, a b atb, (a) 0 (b) 2, () 4 (a) -4, > 7 wo, For any 2 «2 matin if A (adj a= |) vol:then [A] is equal to, (a) 20 (b) 100 (c) 10 (d) 0, The inverse of the matsx | > lis, pee 10 pad i 3, @) 5 3 ( H 2) ; ‘| @ f a, Use matrix method to solve the following system of equations: 5x - 7y = 2, 7x- 5y = 3., 1 1 11 oe _10 1, @) x=spy=sp (xa apyRgp © xFLy=l (4) X=sp Y= ay, Find the values of a so that the function fly) defined by, sintax, x#0, f=) may be continuous at x = 0., 2 » 378, (a) +1 (b) 1 (ce) =1 (d) None of these, , Scanned by TapScanner

Page 3 : 18., , 1 » ifxs3, If fo) =jaxtb, if 3<x <5. Determine the values of a and b so that f(x) is continuous., , , , , , , , , , , , , , , , , , iT . Ss, (a) a=3,b=3 (bl) a=3,b=4 (c) a=3,b=-8 (d) None of these, If x° + y* = 3avy, find 2., ay-x* ay-x° ay-x", (a) frm (b) ya () 0 (d) Pe, 3 dy x, If x =a sec’) and y =a tan’, find 7— at 0 =, (a) +5 (») a () v3 (d) 8, Find arrnienseacottanyoasi, (a) - (b) tan ? (c) sec*t (d) atant, Differentiate sin'(=5) wart. tan x, - le x< 1., (a) -2 (b) 2 () 0 (d) 1, Differentiate x‘ with respect to x log v., (a) (b) x” Oy (a) -x*, Find the value of log,2 with respect to x., -1 1 1 1, ) (logsp Flog? (b) 0 () loge (a) log?, If flv) = x7 + 2x +7 find £"(3)., (a) 18 (b) 8 {c) 10 (d) 3, If xyl +y +yvl +x =0 and x = y, then find the value of 2,, =I l 1 -l, “ 1+" Ort ® 1-x* a I=-x*, The maximum value of (—) is, Ie, (a) we ( ( (3), nn y= 2x +3sin vat x=0is, , (a) 3 ) + (03 @ -+, , The coordinates of the polst on the carve (x? « 1) (y= lincliansicapniidimmntiindiin, greatest slope are given by, w (va3+3) «) (-v3,3-42), , el ', , fe) (0,3) (d) none of these, , In an LPP, if the objective function Z = ax + by has the same maximum value on two corner, points of the feasible region, then the number of points of which Z,,,, occurs is, ICBSE 2020 (65/4/1)|, , {a) 0 (b) 2 (c) finite (d) infinite, , Scanned by TapScanner

Page 4 : Case Based Questions-I, Read the following and choose the correct option in the questions that follow., , P(x) = -5x* + 125x + 37500 is the total profit, , function of a company, where x is the, production of the company., , , , 31. What will be the production when the profit is maximum?, , (a) 37500 (b) 12.5 (ce) -12.5 (d) -37500, 32. What will be the maximum profit?, , (a) %38,28,125 (b)%38281.25 (ec) 739,000 (d) None, 33. Check in which interval the profit is strictly increasing, , (a) (12.5, «) (b) for all real numbers, , (c) for all positive real numbers (d) (0, 12.5), 34. When the production is 2 units what will be the profit of the company?, , (a) 37500 (b) 37,730 (c) 37,770 (@) None, , Case Based Questions-II, , Read the following and choose the correct option in the questions that follow., Owner of a whole sale computers shop plans to sell two type of computers - a desktop and, portable model that will cost 225000 and %40000 respectively., , , , 35. If the number of desktop model and portable model in the stock are x and y, to get, maximum profit after selling and store of shop have capacity to keep computer not, exceed 250 units, then which of the following is correct?, , (a) x+y=250 (b) x+y>250, {e) x+y2250 (d) x+y<250, , 36. If owner of shop does not want to invest more than %70 lakhs on both type of computer, then which of the following is correct?, , (a) x+y<1000 (b) 5x + 8y > 1400, , Scanned by TapScanner

Page 5 : (c) 5x+8y<1400 (d) 5x + 8y= 1400, 37. If the profit on the desktop model is 24,500 and on portable model is 75000, the profit Z is, , expressed as, (a) Z=45x + 50y (b) Z = 4500x + 5000y, (c) Z=5000x + 4500y (d) Z=x+y, 38. The number of units of each type of computers which the owner of shop have in stock to, get maximum profit is, (a) x= 250, y= 100 (b) x = 100, y= 250, (c) x= 200, y= 100 (ad) x = 200, y=50, , For question numbers 39 to 40, two statements are given-one labelled Assertion (A) and the other, labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as, given below., , (a) Both A and R are true and R is the correct explanation for A., , (b) Both A and R are true and R is not the correct explanation for A., , (c) Ais true but R is false., , (d) Ais false but R is true., , 39. Assertion (A) : Let: R— R such that f(x) = x”, The function fis an onto function., , Reason (R) =: A function g : A > B is said to be onto function if g(A) = B ie., range of g = B., , , , cos§ sin® >_[ cos26 sin20, 40. Assertion (A): If A= cain nl than A = <sin20 cos20)", cos® sin® » [| cosn8 sinn®, , 1 FAM! ins | thon A"=|-sinn® cosnd, , , , , , , , Scanned by TapScanner