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ISC Class XII Prelims 2025 : Mathematics (St. Xavier's Collegiate School (SXCS), Kolkata)

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Ari Roy
Jalpaiguri Government Engineering College (JGEC), Jalpaiguri

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ST. XAVIER'SCOLLEGIATE SCHOOL, 30MOTHER TERESASARANI, KOLKATA-16 Date: 16.12.2024 REHEARSAL EXAMINATION, ISC 2025 Class: 12 Full Marks: 80 MATHEMATICS Duration : Three hours start writing during th s time.] rStudents are allowed additional 15 minutes for ONLY reading the paper. They must NOT Section BOR Section C. EITHER from questions Sudents are required to attempt all questions from Section A and all same shect as, and adjacent to, the rest of the answer. All working, including rough work, should be done on the of questions are given in brackets 1. parts The intended marks for questions or Mathematical tsbles and graph papers are provided. SECTION A (65 Marks) |15 x1=1S] Question 1. correct options and in sub-parts In sub-parts (i) to (xi) choose the questions as instructed. () AB" both Iif Ais a2 x 3 matrix such that AB and (b) 2 x 1 (a) 2 x 2 (ii) The value of f cos x dx equals (a) 180 (b) - sin x tc (ii) If x<0,cot-()= tan (a) 180 (xii) to (xv),answer the are defined, then order of the matrix B is (d) 3x3 (c) 3 x 2 sin x +c (b) - tan x (c) sinxtc (d)-sinx +c (c) tanx (d) + tanx ,2/3 differential cquation 1 +(T =is (iv) The sum of order and degree of the (d) 2 (c) 3 (a) 4 (v) (b)5 B in 90% cases. Aspeaks truth in 80% cases and The probability that they contradict each other is stating the sarme fact is (a) 17 (6) (c) A(adjA)| is 3x3 such that |A|=3, then the value of (d) 81 (vi) IfA is a square matrix of order (c) 27 (b) 3 (a) 9 differentiable (vii) The function f(r) = x<x, x R is (a) only at x =0 (b) only at x =1 (c) on R- {0} (d) on R (viii) The derivative of sin x* with respect to x is logx (c) x* cos r* (1 + logx) (d) x cos x* set X={x, y, z, t}. (,y),(z, z),(t, t)} is the identity relation on the (ix) Assertion (A): The relation I = ((,x), identity relation ifevery element of X is related to itself. the (a) x* cos x* (x) (b) x*+1 cos x* Reason (R): A relation I on a set X is (b)A is true but R is false explanation of A (a) Both A and R are true and R is the corect (d) A is false and R is true correct explanation of A (c) Both A and R are true and R is not the = A + yl, then the value of x+y is Iffor square matrix A, A -3A+I=0and A-1 (d) 3 (c) -3 (b) 2 (a) -2 2x (xi) IfA and Bare two events such that P(A|B) = (a) P(B|A), and P(A) + P(B) = then P(B) = (b); order 2 is 5. If C is the matrix of (xii) The value of the determinant of a matrix A of then what is the value of deteminant of C, cofactors of the matrix A, ball second (21 21 (21 (21 (21 14| 14] heads, of 75%shows heads it If up tossed. comes student is 6] threeand group group intostudents satistying second group, divided first and the abiding the the cach ladder solution meeting along were of and classify students in first law incrcasing. the and pulled students particular class and white. betweon that and of Then f(r).without ondest. dx awards strength random any of toin is honest also A. t ladder 2x-1 numbcrof strictly during sct find one is least giving number the at biased wall. 0. *)+(2-a)= angle at has comlbined Find 2t on then by drawn chosen (i) Evaluate: the the at the is cos test miss relation one for group the dy. a 0 of the coin? is 2xe)dy. from function, ball > unannounced values Double foot another is is aro x,x will y secondthefind (E+:sx<1 coins fast two-headed abe t, The away while ballsfirst student of dx OR sln students.method, How OR OR the coin, invertible that prove + three wall. basis the f(x) m Two 3) 13, m/sec,12 (y thnt (1, workers, an the x two-hcaded vertical is of the the obedient givesmatrix = curve OR balls.probability 3), give that function One ladder + yedx on was (2, real 1.5 (1 a group will probabilityschool Using the coin. hard 2), isa white of it that against xmsinthe and to that teacher ratcthe a unbiased dx 0. equation: ((1, 7)1/%6 the =. second is tangent of prove a compriscs x) probab lity vigilantgroup. which and One the from w foot 1,x leans (tan find R cos 2x and the the tan(logy),at the coins. thethird sec x+cOsec x And (x- greenthen y= the selectedcontains in differential log find wall, is that *+ long singroup in interval third Evaluate: Jsec x+c when 3) (4- 4 white, of the that number threc the probability twice, yecos contains equationEvaluate:2, 13mthe of cos sin-x+ were first condition is (1, fromchanging are and what group that the the ladder absent is time the 1ff() (xiv) Evaluate: The Evaluate: students Find bagdrawn () Ifx = There then A away the third to times Solve The Let Solve: the 3.QuestionQuestion groups. 10. Question Questlon 2. If 11. Question A is 4. Find 5.Question 6. added 12. A Question 7. 8.Question Question is 9. Questionthe (ii) (i) (i) Question (ii) the four (xii) (i) (i) (i) 10 (XV) relation. the If replucement. ground ground is;.Ifa Question17. (i) Find find the the foot equation of the perpendicular of Also (i) +4k plane Find Question15. Question16. (i) () Ifvectors Find d () (iv) (iii) () 7The Find For units(a)Perpendicular () (a) toThe instructed. questions () as In (a) Assertion Both(d) (c) (b)Reason sub-parts -. to Assertion BothAssertion Question13. Question14. (u) Find thrown. the game, a A Square is. that corner a o + xthe the and the cxpected The the what distanceparallel straight a(3 equation -2y a and thhate b 5tarea equation value man man volume picece (R): (A): Assertion Assertion + are Also () - + folding of to 7k is is( tparallelogram wo line decided wins 2j 4z of value and heightof of false true of of find and the the y-axis If - = of 3 uni t t i n + of t h e 5). and and b).(aup A, point (iii) and of the 2i 10. the and and z-axis line a the box the of plane vectors the tofor S + reason reason the choose Also side b reason cylinder the throw maximum reason (2, 2)+ projection OR flaps are amount getting through perpendicular is unit(b) I 3, 24 maximum? through show z= are are non-collinear b) and 3k a 4) to cm is is = the di e ABCD whose side a drawn true false 1 true but respectively. fom true l + he from (2,-1,0) that isvolume. is thrice SECTION maximum voume of correct is of wins number the to and the the a be from vector planeY(3Also drawn points box. |61 . Reason Reason or but plane angle OR made OR (d) (b) vectors options the and loss greater + to find What parslled parallel ( 2 , from point quit thus B into between paraild fon is is this than 1, units(c) 2 (15 not should a of and t h AB e he as the P2, 1 ) and Marks) obtained 6+ to to same i-jis vector v2? box 4 and maximum the correct and pointP. 4, them, to and thatcanbe zNiS be in corect without 2) magnitude, when the aris (-I,3,4) -) contains loscs the sub-parts expanatioa ine =-11 then diagonal to voune. side be eplnation the top gets I prove of by inscnbed ina then otherwise tine the nd is the a DB (iv) cuting penenulr numbergt that for line a+b square ()units are to for Assertion sin; giea (\NTY when a sphre of Assertoo =+ is o squre perpeTr be by a x151 5 cut to tar t h e troa 3}+ the i an4 rahs te e S oKh ( ) Evaluate : logr d. OR Question22. Question21. Question20. Question19, Solve 2x + 3y the 26, LP.P (ii) (a) From Hence, (ii) isThe Theincreasing.AC (i) zero. willbeThe average demand (G) mean mark the of cstimate cquations Mathematics Marks in obtained x *-yz0, graphically and y, the probable of () (iv) (iii) the A If If company total demand o,=5,r revenue cost English Marksin sells function received. its function (ii) instructed. questions () as In (a) sub-parts IfCx) (d) (Reason(R): c) (b) Assertion(A): (a) Both BothAssertion Asscrtion Assertion function Assertion = - then is is 0 false true < 4500, given +8=0, of corelation. find: values 19 17 English 24. in is 21 below: 14 the output 22 19 which 19 15 for which 14) of the quantity (4] x then cost are find estimated at the cost to maximum? be function. the MR [21 for will Assertion. for Assertion. be (i) and bounded (ii) + choose 600x, (b) thcn x by the curve the SECTION = 12the correct y = point 2xx wherc options (15 (c) AC Marks) and -MxC = in 10 C and the straight sub-parts is line y= kx+4 =9 (d) x and x= 25% 4y of the region If -24x total explanation explanation revenue region.Sketch theof x = 11 = k lo, e by r s1 lines and product is and and , regression and 10 p of and Minimize 2x =rcasonreason byx candidates of AC monopoly a reasonreason regression V6-x, If at + score =-,then the (b) = y the are are lines 2xfixed is 8,Z=regression for rate true true true. is faBse for 17 20 in is Mathcmatics 4x y 11 x>0, 2x costs of? English given but and what on + +Find 13 12 find + x Reason coefficients, 3y OR OR for 10 Reason and 3y level by +7 23 and per t h e 21 18 y0.subject the x x= = if Mathematics on is is of product unit. value 25 t h e 0 the not the output 100 y and to range The are marks of the correct 11 14 constraints: -4p. respectively Oy x,correct are 3x variable (c) of the +4y obtaincd 8 12 are Find the Coefficient Question18. +5, (iii) =-. to (v), Also answer the [Sx[=5] y find the area 14|

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