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Class X Prelims 2024 : Mathematics (B D M International (BDMI), Kolkata)

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B.D.M.INTERNA ATIONAL (2023-2024) PRE-B0ARD-II EXAMINATION TIME: MATHCMATICS CLASS-X 3Hrs. Maximnum Marks:80 SET-A General Instructions: This E. Question has 5 Sections A,B,C,Dand Section A has Paper 3. 20 MCQs each. carrying 1 mark Section B each. has 5 questions 4. marks carrying 2 Section C has each. 6 5. questions carrying: marks Section D has 4 (4 marks each) marks eacn. 6. with Section E has 3 questions carrying 5 assessment units of case based Integrated respectively. sub-parts of the values of each 1,1 andl2 marks choice in 2Qs of 5marks, 2 Os 7. All an internal Questions are However, compulsory. An internal choice has been of 3 marks and 2 Os of 2 marks has been provided. E. provided in the 2 marks questions of fSSection 8. =22/7 wherever required if not Draw neat figures wherever required. Take stated. 1, 2.. 33 SECTION 1 The perimeter sector both (-ve) 3 of of (20 questions a circle 22cm b. The zeroes ofquadratic a. polynomial b. both (tve) l mark each) 1 cm and 14 of radius C. 28 cm sector d, x+99x+127 are and one c. one(tve) angle 45 is 39 cm (-ve) d. both equal HCF of two consecutive even numbers is d. 4 0 C. 2 b. 1s equal to InAABC, DE ||BC, AD=2 cm. DB= 3cm. then D : BC a. 4 1 2:3 a. 5 IfA a. 6 the 1l cm a. 2 of A is C. 3:2 b. 2:5 an acute angle and 2 b. 1 tan Ifthe sum of two numbers of such numbers is is A+ cotA =2,then C. 0 1215 and their the value of d. 3:5 sinA+ cosA is d. HCF is 2 81, then the possible number of pairs 2 a. 7 b. 3 Ifthe differenceof mode and median of a data and mean a. 12 4 C. is d. 5 36,then the difference of its median is b. 18 C. Page 1 of 7 24 d. 8 then by 12 mean C. exceeds mode ofa series If & #a 4 a. PB from apoint is cqualto POA and then Iftangents PA of80, 60 angle other at an b. A-cosec a. 50 A)(1+cot (1+tan A +sec 1 b. a. 0 9 O with center circle Pto b. d. 70 C. to touches X-axis, polynomial ax* + bxtc c. real representing If the parabola are zeroes its andcqual b. real real a. not signs and. D(6,2) form and square a d. distinct ABCDthen C(2,1) 12 A(5,p), If points B(1,5), C. selected 13 The probability 14 b. 7 IfV2sin(60 a. 1, then HCF, then perimeter of 18 cm is contain 53 Sundays C. C. DE d. 5 d. c. 300 is of twonumbers that 1 d. 0 revolutionswill cm. HoW many 1260 and their it make to 10 cover 792 C. 198400 LCM is 900 more than d. 205400 =3cm,EF =2 cm, DF=2.5 cm, BC =4 cm, then AABC is b. 20 cm volume and surface diameter of the hemisphere is b. 7 units C. 12 cmn area d. 15 cm of a solid hemisphere are numerically c.9 units d. Page 2 of 7 4 units m? 350 is 194400 b. 203400 If the 4.5 units will A =? 4 the product If AABC~ADEF such 17. random 2 7 two numbers The sum of LCM and HCF of a. a. at 30 b. 15 their 18. = is 16 a. 3A) The diameterof a wheel b. 250 a. 200 15 p= ? year, that aleap 1 a. ofopposite 8 d. 6 then 3 b. 7 a. 80 d. -1 thequadratic 11 to cach are inclined A)isscqual C. 2 10 by median d. 10 6 its 8 mode exceedsthe its equal then the of, Assertion(A) : Inthe question number 19 and 20, a statement ofReason (R). DIRECTION the Choose correct a. Both assertion (A)and : thefollowing choicesreason(R)isthe correct explanation and reason (R)are true of (R)is (A)and reason (R) are of assertion (A) Assertion (A)is true but reason (R)is false. Assertion(A) is false but reason (R)is true. d. Statement are D A (Assertion): and (3,5) nt the correct and reason true assertion Both C. AABC out (A) assertion b. 19. answer E If the coordinates joining half of to AC of mid-points units BC=20 oftwo sides and equal of explanation AB and of the sides ofthe (-3,-3)rrespectively,then Statement R (Reason): Theline segment parallel to the third side isfollowed by a statement of a triangle is the mid-points it. Progression. 20. Statement (Assertion): A -5, -5/2, Statement R (Reason): The terms negative rational numbers. an of Arithmetic SECTION 21. If 49x +5ly 22. D is point a 499, 51x = onthe side 49y BC of + ... isin 0, 5/2, Arithmetic cannot (5 QQuestions B have both positive and Progression of = 501,then find the value a triangle ABC such that 2 marks each) ofx andy. ADC = ZBAC. Show that CA?=CB.CD. OR Prove that the line passes through Segmentjoining the points of contact of two center. its 23. A circle touches 9 cm and all the four sides of quadrilateral a CD = 8cm. Find the length of the minute hand 24.The length from 7:05p.m. to 7:40p.m. 25. Iftan (2A+5B) of of side AD. is 6 cm. Find is of a circle, ABCD whose sides are AB =6cm. BC= a clock =/3 and cot (2A -B) parallel tangents the area swept by it when not defined, then find the valuesof it moves A and B.[0 < A, B< 90). OR If Cos (A + B)=Cos A Cos B -Sin A 2 SECTION 26.Given that 27. zeroesof the polynomial If the Sin B, then C(6 is irrational, prove that find the value of Cos 75 , Questions of 3 marks each) +3v2 5 is irational. xt px +q are double in value to the zeroes of the polynomial 2x - 5x-3, then find the values ofp and q. Page 3 of 7 28. A train covered certain distance at a train would 6km/hr.,it would journey. unitorm speed. 1E the a hours 6 have taken more than the scheduled time. OR An aeroplaneleft 1500km its 30 had to increase time, usual 29.If specd. cos A +sin A = V2cos 30. it incircle of respectivcly. Two different a triangle E 250 ABC, -sin A) AB =AC, with median AD of another a of ABC triangle Determine the sides AB, BC, CA at I) are respectively APQR. Prove that destinatioe specd. A. touches BC. bisects 2sin the order to km/hr.from reach its its OR cven number on both I1. iii. by of AABC ~APQR. proportional to sides PO dice are rolled together. Find the probability of getting dice to be 5, of numbers on two thesum i. A., Provethat AC spced show that (cos A an isosceles SidesAB and and and PR and median PM 31. its been 6kr Find the length usual The E, F later minutes away in timeandin thanits scheduled have dice, doublet. SrcTION D (4 32. The a following table showsthe particular MARKS academicsession. Less than 10 NUMBER Class Find the mean, median Less Less Less than than than 20 30 34 40 46 7 OF marks Questions of 5 marks each) obtained by 100 students of 21 X in a school and mode of this distribution. Less Less Less Less than than than than 50 60 70 80 66 77 92 100 during STUDENTS OR The mean of the following frequencydistribution 50.Find f; and CLASS f Hence. find a.) If3is equation x* a root of +k (2x + b.) Solve Mode 60-80 f1 12 f2 the equation x 20-40 k+2) +p=0 are by quadraticformula: is 51.6 and the total number of observation is also. 40-60 0-20 FREQUENCY |7 33. the 80-100 100-120 5 - X+k=0,find the value ofp so that the roots of the equal. 2 x +7x +5/2=0 34. State and prove Basic Proportionality Theorem. (3) Using theabove theorem prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (2) OR Prove that the lengths of tangents drawn from an externalpoint to a circle are equal. (3) Using the above theorem prove that zPTO LOPO, if TP and TQ are two tangentsto a with center from an external point T. (2) =2 O Page 4 of 7 circle n.DA dome. The 35. A building isinthe form diameter building of the dome is if it contains a of cylinder equal to 2/3 67m 21 of Surmounted of the total by a hemispherical Find height of the building. the height base of the air. SECTION E (CASESTUDY BASED QUESTIONS) (1+1+2) Case Study -1 :Q 36. using one or more geometic of a plane were used in the covering tessellations Historically, on floors, walls, paintings shapes, called tiles, with no overlaps and no gaps. patterns tessellation ofS Seville, made using ancient Rome and in Islamic art. You may find Museum tiled floorinthe archaeological etc. Shown below is A tiling or tessellation of a flatsurface a squares, triangles and hexagons. is after being inspired by the above design. To floorpattern the Cartesian plane. He used regular of makinga thepattern craftsman thought he made work, his tessellation pattern in ensure accuracy hisfloor A for triangles octagons, squares and 8i 9 -8 follow: questions that Use the above figure to answer the joining points What is the length of the line segment (i) (ii) The be the point ofintersection centre 'Z'of the figure will WXOP. Then what are the coordinates of What are the coordinates of the point on the diagonals of y axis equidistant from A OR What of Z? quadrilateral (iii) B and F? is the area ofTrapezium AFGH? and G? 9 12 base ieof1, e compuls Q 37: Deat LR-2217 Helght Tower 80 80,m m 459 30 A. After a i.) ii.) iii.) is shown 2 secondsthe Of elevation Answer tower from bird observation the questions Ground levar of 80m. height flies away point A bird is sitting horizontally but onthe remain at top of tower as shown constant height. at point Now,the angle C. chan ges from 45 to 30 as shown. based on above BC Find CE Find Find the speed of the bird, when from point it flies A to D OR, Ifthe bird covers distance Case Study-3 AD in 5 seconds then visitors to the that find the speed of thebird in m/s. Q 38: In November 2020, sorme new animals were added zoo increased daily by 10. A total month. (1+1+2) to zoo. a As a result, the number of of 6150 people visited the zoo during Based on the above information, answer the following: i.) How many visitors visited the zoo on 1" November? ii) iii) On which day ofthe month did 250 visitors How many people visited the zoo in the last if the zoo? 5days of the month ofNovember? OR, How much collection November visit (in rupees) from sale each entry ticket cost Rs 50? Page 7of 7 of tickets wherev figures whereve (1+1+2) QBird figure, mare nthe Case Study- 2 In 2 was done in thezoo on 1

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