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SCHOOL II EXAMINATION PREBOARD MATHEMATICS TIONAL B.D.M.JNTERNATI CLASS -X (Session - 2023-2024) SET- Que MAXIMUM MARKS: 80 B TIME:3 hours General Instructions: 1. Paper has This Question 5 Sections A, B, C, 20 MCQs carrying D andE. mark each A 3. Section B has 5 questions carrying 02 marks each. 4. Section C 6 questions carrying 03 marks each 5. Section 6. Section has has carrying 05 marks each. (04 integrated units of assessment D has 4 questions E has 3 I 2. Section case based marks each) with 2 respectively. 2 Qs of5 marks, choice in has internal However, choice 7. All Questions are compulsory. An internal provided. marks has been Qs of3 marks and 2 Questions of 2 questions of Section E been provided in the marks sub- parts the values of of1, 1 and2 marks each an 2 8. Draw neat figures wherever required. if not stated. Take n =22/7 wherever required SECTION A each. 1 mark of20 questions of A consists Section pfq', where p and a =p'g and b= integers such that 1. 2. and b be two positive p" numbers. IfHCF(a,b) 30 (b) (a) 15 Let a = Which one is uot the q and LCM(a,b) (c) 35 graph ofquadratic q are prime = g,then (m+n).(r+s) = p (d) 72 polynomial? (b) (a) (c) 3 pair of linear equations The given is non-intersecting. Which true? (a)a2 C1 b2 C2 a1 bi c1 a2 b2 C2 bi C (c) a2 b2 C2 al a2 b1 c1 (b) ta' a' b1 H ot h (d)b2 of the following statements =0 a,x+b,y+c a,x+b,y+G=0 c2 Page 1 of 6 is 4 (a)S0 S. her (a) 6 (c) (b) 7. of one of these -9 is-1 and that , (d)9 is4c O 8 (a) 9. of (b) is a chord intersect (a) I0. sin If a series 6 PQ (a) = o the othe at of the its mean exceeds by 12, then (d) (c) 4 10 8 cm ofa length point its circle of diameter AC and BD intersect each tebo other 9cm (d) (c) 8cm 7cm (b) Mode If 6.8 diagonals 4cm. If the AD BCand ADBC= with suchthat AO/0C = DO/OB =/2, then (a)6cm 1 (c) ABCDis a trapezium at of (b)7 1 I he Tirst term diference. terms is : their 104 is c (-2 ,-3)and (3,7) divided by The ratio in which the linc segmentioiningthe points the y-axis is 3:2 (a) 2:3 (d) 1:2 1:3 (R) d (d)80 (b)70 Two APs have the same commOn is -8. Then the difference betwee l zR is (c)600 509,then AQPR, ZA-70,zB 1fAABC- mode exceeds the medianby 8 10 cm. Thetangents at P and ) The length of TP = T. 8/3 cm (b) 10/3 (c) 17/3 cm cm (d)20/3 cm +cos 9 =V2. then tan 0+cot 6= 1 (b) 2 (c) (d) 3 4 11. R Given thatsin 0= find cos 0. b Vb2-az (a) (c) Vb2-a2 s 12. If8 tanx =15. then 15 cos x -8 sin x (d) Vb2-a2 = (a)8/15 (b) 15/8 (c) (a) 0 Apole 6 m high casts a shadow 2V3 m long on the ground,then the (a) 60 (b) 45 (c) 30 (d) 90 1 13. 14. The number (a) 15. 28 (b) 42 made by a circular wheel (c) 75 of radius 0.7 (d) ofgetting probability (a)7 (b) 14 (c) a bad egg in a lot of400 is is m in rolling a distance of 176 m is 40 Ifthe radii oftwo circles are 8 cm and 6 cm respectively, then the equal to the sum of the arcas ofthe two circles will be: (a) 10 cm (b) 64 cm (c)20 cm (d) 14 cm 16. The 17. revolutions of Sun'selevation radius 0.035.The number of the circle having area of bad eggs in the lot is: 21 (d) 28 A card is selected at random from a wellshuffled deck of 52 cards, from which 2 red removed and kept aside. The probability of getting a red face card is: queens are (a)2/25 (b)3/26 (c) 4/25 (d) 3/13 18. Consider the following frequency distribution: Class Frequency The median (a)6-12 0-6 6-12 12-18 12 10 15 class 18-24 24-30 11 is: (b) 12-18 (c) 18-24 (d) 24-30 DIRECTION: In the question number 19 and 20, a statement of Reason (R). Choose the correct option: statement ofAssertion a (A)isfollowed by (Assertion): Relation between Surface area(S)and Volume(V) ofa: spbereis S The volume and surface area of a sphere are related to each other by -36mV2 radius, (A)and reason (R)are true and reason (R)is the correct 0 StatementA R(Reason) Statement (a)Both assertion explanation (R) is (A) 1s true but reason (c)Assertion (A) is false but reason (c) Assertion Statement A and reason (R)is not the (A) and reason (R)are true assertion (Assertion):If S, is of assertion first terms n of an A.P., then its nth term given by Sn-Sn-l an 10th Statement R (Reason) :The (a) Both (b)Both assertion assertion (A)and term of an Arithmetic 8, 11, Progression:5, reason (R) are true and reason (R)is the (A)and reason(R)are true (c)Assertion (A) is true but reason (R) is and reason (R) is not is 14,.. explanation Solve for x and In given figure y when: 0.2x + 0.3y of5 questions of 2 marks each. 0.5y= 2.3 0.4x + =1.3; 4=/2and ANSQ AMTR,then M prove that APTS~ APRQ. R OR which inscribed in a quadrilateral ABCD in In the givenfig. a circle ZB -90. AD=23 cm AB =29 cm and DS=5 cm, find the radius of is R If the circle. D P, two tangents, PA and PBaredrawn to a 0. At a point E on the circle, atangent is drawn intersect PA and PB at Cand D, respectively. If PA= 10cm, 23. From an external point circle with centre to find the perimeter 24. Ifcos 0 =sec If6x of APCD. +sin 0 =V2 cos 0, then OR and 6/x show that cos - sin 9 =V2 sin 9. =tan 0, then find the value of 9(x- 1 /x ) (A). of assertion true. B consists of assertion the correct SECTION B Section 35. correct explanation false. (d)Assertion (A) is false but reason (R) is e2, (A) true. 20. e1. of assertion (A) explanation of false. (R) is sum the correct is (b)Both : B (A) 25. Inthegiven been drawn of figure, ares have with vertices A, B, C and D of fquadrilateral Find the area of the shaded region. radius 7cm ABCD as centres. cach SECTION C 26.Given that v3 27.Ifthe zeroes ofthe polynomial then find the values 28.Yash scored answer. Had answer, then prove that 6 - 7V3 is js irrational. ofp and x + of3 marks each. C consists of 6 questions Section tq are px irrational. double in tothe value zeroes of the polynomial 2x'-5x-3. q answer and losing 1 mark for each wrong and 2 marks been deducted for each 4 marks been awarded for each correct answer incorrect Yash would have scored 50 marks. How many questions were there in the test? 40 marks in a test, getting 3 marks for each right OR The area of a rectangle reduces decreased However, iflength in Find the dimensions ofthe 29. PA and PB 5 by 160m , if its length is increased by m and breadth is reduced by 4 m. by 10 m and breadth increased by 2 m, then its area is decreased by i00 m rectangle. drawn to a circle of centre O froman Chord AB makes an angle of 30 withthe radius are tangents external point P. ofcontact. ofthe chord is 6 cm, find the and the length ofthe radius OA. at the point If length length ofthe tangent PA OR Sides AB and AC andmedian AD of a triangle ABC median PM ofAPQR. Show that AABC~ APQR. 30, Prove 31. Two that: sin A(1 +tan A) +cos different dice are () has a (11) has a product (iii) is sum less +cot A) =sec A +cosec throwntogether. Find numbers. a root ofthequadratic roots, find the value of k. 32.(a)If-5 is quadratic formula: if DE | D D consists of 4 questions 2x'+px-15 of5 markseach. =0 and the quadratic equation p(x+tx) +k=0has equal (3) V3x? +10x +7V3 =0 33. (a) State and prove Basic Proportionality theorem. (b)In the figure, number obtained less than 16 Section Solve by A. the probability that the SECTION (b) sidesPQand PR and than 7 of odd a doublet A(1 are respectively proportional to (2) | OB and EF|| BC, then prove that DF OC. (3) (2) OR (3) (a) Prove that the lengths of tangents drawn from an external point to a circle are equal. a circle is a rhombus. the parallelooram circumscribing theorem, prove that (b)Using the above Paaa A of6 (2) tre The radius of the hemisphere form of a right circular cone mounted on a hemisphel height ofthe cone is 4 cm. vlindrical tub full of water in such the The solid is placed in a and whole solid is cvlinder is 5cm and its height is submerged in water. If theradius of the the that the yolume of the water left in the find tub is a nean the following frequency of distribution rthe 0-30 Classes 12 Frequency| the missing frequencies 91, find is 30-60 60-90 90-120 21 X 52 120-150 and x y. fcm, 150-180 Total 150 OR Calculate the Marks mean, median and less than Frequency mode from the following data: less than less than less 10 20 30 40 50 5 20 45 80 100 than less than less than less than less than 60 70 80 115 125 SECTION E SectionEconsists 36. India cost is of 3 case studybased questions competitive of manpower manufacturing location due tothe low and strong technical and engineering capabilities contributing to higher quality production runs. of TV setsin numberevery year.It and 22600 sets in 9th year. The production a fixed (i) In which year, the production (ii) Find the production Rs 29,200? is 6th year in (1) during 8th year. t ed at Find the production tr burst h 16000sets OR con cow factory increases uniformly by a produced me during (ii)Find the difference and 4th year. 3 years. (2) first during 7th year of the production (1) ation seco e tab es an figu = 1.7 =45 's ini 37. In order to conduct Sports Day activities have been drawn with chalk powder at each, a rectangular in in your School, have been placed at a AD, as shown in given figure below. Niharika distance AD on the 2nd line and posts a green l l Preet runs 1/5 th the distance a red (1) (ii) lines a distance of m shaped ground ABCD, 100 flower pots along distance of m from each other AD runs 4 th the flag. on the eighth line and posts flag. the position ofgreen and What is the distance between Find red flag? (1) both the flags? OR has to post a flag at one-fourth segmentjoining the in the line green flag, distance from he post his flag? (2) green and red flags, then where should If another boy Joy halfway (iii) IfRashmi has to post a blue flag exactly flags, where the two segment joining between the line should she post her flag? (1) Page 5 of 6 of 4 marks each. 130 R0-100 There are two bank of a river, just opposite to cach other. Onetemple is 50 m man, vho is temples, one on cach bigh. A standing on the top of 50 m high temple, observed from the top that the angles of depression the top and of the foot ofthe and 60 respectively. (TakeN3-1.73) 30 are other temple Use the above information ()Draw a neat labelled (i)Find the width to answer the questions that follow figure to ofthe river. show the above situation diagrammatically. (1) (iii)Find the height ofthe other temple. OR (2) Find the difference of the height of these two temples. (1)
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