Formatting page ...
Children's Academy Group of Schools o Bachani Nagar o Ashok Nagor Malad () Kandivli (E) o Ghodbundor Road o Thakur Complox Thano (w) Kandivli (E) PRELIMINARY EXAMINATION 2024-25 pIsCIPU ARE OUR TRACADITION Subjeet : Grade: MATHEMATICS Time 02/12/2024 Date 80 Marks : 3 hours first 15 minutes }ou will not be allowed to write during the This time is to be spent in reading the question paper for writing the answers The time given at the head of this paper is the time alloed This paper consists of 8 prited pages from Section B. Atempt all questions from Section A and any four questions shown and must be done on the same sheet as 4ll working. including rough work, must be clearly the rest of the answer " marks. Omission of essential working will resull in loss of sheet. All figures in geometry have to be copied in the answer in brackets || The intended marks for questions or parts of questions are given SECTION A (Attempt all questions from this Section) Question S Choose the correct alternative from the options given along with the |15] questions: (1) If nth term of G.P. is 2" then sum of its first 6 terms is 126 )(a) 154 (d) (c) 64 (i ) (iii) 163 The locus of the door knob, as the door opens is a) a line (b an arc (c) an oval (d parallel lines Iftwo equal circles of radius 2.5 cm touch each other externally then the number of direct common tangents are one (C) three (b) Iwo (d) four Mathematics/Grade NPreliminary Exanination/Page Iof 8 CABN/UA/2024-25 of a Assertion: The points A(-1,0), B(3,1), C(2.2) and D(-2,1 ) are vertices (iv) parallelogram. and BD are (,1). Reason: The co-ordinates of midpoint of both the diagonals AC (a Both Assertion and Reason are false. (b) Assertion is true but Reason is false. (c) the correct Both ASsertion and Reason are true but Reason is not explanation of Assertion. correct explanation Both Assertion and Reason are true and Reason is the of assertion. (v) (-5,-5), the value of mn is The reflection of point (3,-5) in the line x = m is point 3 (a) (vi) (b) -5 (d) 4 + cosec If tan + cot 8 =5 then the value of sec' (b) ) 23 (c) -2 is 25 (d)27 21 semicircle is drawn (vii) In the adjoining figure ,O is the centre of the circle,and a P with OA as diameter. If LAPO=200 then measure of ZOAR is (a) 250 (b) 40 509 (d) 70 (viii) A dress is marked at 1,800. Ashop offers 10% discount. and the GST rate is 5%. What is the final price after discount and GST? 1,701 1,881 (b) (d) R1,539 (ix)The scale factor ofapicture and the actual height of Sonia is 1:8. If her height in the picture is 18 cm, then her actual height is (c (x) 1710 (a) 14.4 m (c) 1.78 m The common difference of the AP: (b) 2.25 m c 1.44 m 1 1-p 1-2p 1-3p (b) (a) 1 (d) 1 is (xi) Ifx= 2 is a solution of the quadratic equation kx+ 2x -3 =0 then the value ofk is (a) -1 (b) -4 1 (c): (xii) Which of the following is the slope of a line perpendicular to AB ifA(-3, 2) 4 4 and B(6, 8) (a) -C 3 (b) 2 3 2 2 2 (c) - 3 (xii) If a regular hexagon is inscribed in acircle of radius r, then its perimeter is (a) 37 (b) 6r 9r (d) 12r (xiv) Rakesh invests 12,000on 100 shares at 75 each. Ifthe company (c) declares a 16% dividend, what is his total dividend? (a) 1,600 (c) 2,400 Z1,920 (d25S60 (b) (xv) The inclination of line with equation v2xV6y-3 =0 is (b) 45o (c) 600 (d) 900 Question 2 ) Tania runs a bakery shop. The amount of mixture required to make [4] one biscuit is 22 cu cm, Before it is cooked, the mixture is rolled into a sphere. After the biscuit is cooked, the biscuit becomes a cylinder of radius 2 cm and height-2.1 cm, The increase in volume is due to air being trapped in the biscuit. (a)What is the volume of abiscuit after it is cooked ? 6.4 (b) What is the volume of air trapped, while cooking the biscuit? (c) Calculate the maximum number of biscuits that can be packed in a box of dimension 16cm x 12 cm x10.5 cm. 6 AP and BPare tangents to the circle with centre O. If ZCBP = 25 and 14) 2CAP= 40 . Find the measures of (a) LADB GS (b) LAOB I30 (c) LACB (d) LAPB 0 S Mathematics/Grade X/Preliminary Examination/Page 3of 8 CABN/UA/2024-25 (iii) Prove that 1+tanA -tandy? - tan'A 1+cot A (4| 1-cotA Question Y1 (i) Three numbers are in A.P. and their sumn is 15. If 1,4 and 19 are added |4) to these numbers respectively, the resulting numbers are in G.P. Find the original number ) Solve the following quadratic equation for x and give your answer correct 14| to 2significant figures: (x -1)2 +9(x - 1) + 1= 6 ) (ii) Use graph paper for this question. Take 2em = unit along both the axes. Plot points A(0,4), B(1,) and C(4,0) (5| (a) Reflect point B through origin and name it as point F. (b) Reflect points A and B under the x -axis and name them as points E andD respectively. (c) Reflect points Band C under the y -axis and name them as points HandG respectively. (d) Join points A, B, C, D, E, F, G, Hand Ain order and name the geometrical figure formed. (e) Name an invariant point under line y=1 SECTIONB39 (Atempt anyfour questions from this Seetion) Question 4 o A-l6 -a B-3and C-then find A +AC -SB 31 Mrs. Roy went to a departmental store and bought the following items: Sr. No, Item 3 Calculate Price Quantity Rate of G.S.I. Walnut 750 per packet 2 packets 5% Atta 40 per kg 0% Butter 20 kg ? 200 per packet 5 packets 12% C (a) the total C.G.S.T paid (h) the amount she gets back if she pays 1fathemutics/Grade NPreliminary Examination/Page 4 of 8 CABNUA2024-2 [3| (iii) |4| In the given figure (not drawn to scale), BC is parallel to EF, CD is parallel to FG, AE: EB = 1:2, LBAD= 80 , B LACB = |15 , ZADC = 25 and AC is bisector of LBAD. Prove AAEF~ AAGF (a) (b) Find: AG: AD i. area of AACB:area quadrilateral BEFC Question 5 O Agirl spots a balloon moving with the wind in a horizontal line 4) at a height of $1 m from the ground. The angle of elevation of the balloon from the the girl is 60. After some time, the angle of elevation reduces to 30 . Find distance travelled by the balloon during the interval. ii) (Take v3 =1.7) Daily wages of 160 workers in a building project are given below: Wages (R) Number 100 200 300 300 400 12 20 30 38 0 100 200 (6] 600- 700 400 500 500 600 700 800 24 16 12 8 of workers Draw an ogive for the above data and estimate the following: (a) Median. (b) Inter quartile range. percentage of workers who earn more than? 450 a day. (c) Question 64 The 4" term of G.P. is -24 and the seventh term of G.P. is 192. I3) Find (a (b) the first term and the common ratio of the G.P. -1023 sum of first 10 erms Use factor theorem to prove 2x+1 is factor of the polynomial ( |3| 2x'+ 5x' - 4x -3. Hence factorise the polynomial completely. Matihematics Grade NPreliminary Examination/Page 5of 8 CABN/UA2024-25 checkpoints: A, (i) A circular track has three on the circumference B, and C, located such that The shortest distance between A and B is 5 km. between B and C is 6 km. The shortest distance and Cis 7 km. shortest distance between A The from B track such that it is equidistant circular the on positioned Adrone is to be drone and locate the possible positions of the compass, and ruler Using and C. I km = Icm) determine its distance from B. (Take scale Question7 o 1+3+5tto n terms |3 =9,then find the value of n. If 2+5+8+*to 8 terms |3| 6041 at the time of maturity. Find the interest is 9% per annum and she receives ? amount Rekha deposited each month. 280 14] random in a particular ii) An insurance company selected 1000 drivers at accidents. The data obtained city to determine a relationship between age and for l year are listed in the following table. (i) 20 months. The rate of Rekha opened a recurring deposit account for Numberof accidents Age |2 3 Over 3 Under 20 50 62 53 35 20 20-29 64 93 67 40 36 30-39 82 68 32 4 40-49 38 32 20 7 3 Over 49 43 50 35 28 24 4 Compute the probabilities of the following events for a driver chosen at random in the city: (a) E, : being under 20 years old and having exactly three accidents in I year. (b) E; : being 30-39 years old and having one or more accidents in l year. (c) E:: having no accidents in I year. (d) E: being under 20 years old 6rhaving exactly three accidents in I year. Question 8 Solve the following inequation, write the solution set and represent it on the real number Iine. 4r- 19 <-2s+x. xeZ Mathemutics/Grade N/Preliminary Examination/Page 6 of 8 CABNUA/2024-25 3| (ii) A man invests 22.500 in 50 shares available at 10% discount. 13 If the dividend paid by the company is 12%, calculate (a) The nunber of shares purchased (b) The annual dividend received. The rate of return he gets on his (c) (it) investment. The equations of twO straight lines, Li and L; are xyI and x +y= 5 respectively. Find: |4| (a) the equation of line Li which is parallel to L and has y-intercept 3 (b) the value of k. itf the line Limeets the ine L; at a point Pk. 4). (c) the ratio in which the y-axis divides linc joining P and Q (.2) Question 9 (i) The daily expenditure on food of 25 households in a locality was |3| recorded as follows: Class interval (in ) 400 - 450 450 - 500 500- 550 550 - 600, 600 - 650 Number 12 of households Estimate the mode by drawing a histogram. (ii) In the given figure , chord ED is parallel to diameter AC. If LCBE-59", AC=8, BT= 3, AT=2. then calculate (a) (b) LDEC length of TE > (ii) The Government is planing to procure tents for the pilyrims during Kumbh Mela, such that the diameter of the circular base is 42 m,height of the cvlindrical part is 5m whereas the total height of the tent is 25 m. Lower cy lindrical purt is made up of white colored thick fabric which costs 2 60 per squte meter. Top conical part is nade up of PVC coated bluc tabrie which costs 270 per square meter. (a) Calculate the total cost of the fabie requircd lor Itent (h) Ii the ground space requirement of one pilgrim is 6 sq. meter, how manv p1lerms can be tccouodated in a tent" 1ansir (Grnte NTreiminry Examintionlae f8 CBVUA 2024-25 Question 10(\0 Given x= ti) Va'+b24a2-b2 showthat h' Val+b2-Va'-b? 2a'x (3 x2+1 3| A person on tour has 4200 for his expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by 70. Find the original duration of the tour. ( Mii) Calculate the mean of the following frequency table by step deviation method Class interval Frequency 5-10 10-15 15-20 20-25 |25-30 30-35 35-40 40-45 45-50 10 6 4 12 8 4 ****The End******* *: 3
|
