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ICSE Class X Prelims 2025 : Mathematics (Anand Niketan, Shilaj, Ahmedabad)

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ANAND NiKETAN SHILAJ CAMPUS Pre-Board II(2024-25) Subject: Mathematics Maximum Marks: 80 Duration: 3 Hrs Std: X Date: 02/01/2025 Answer allquestions in Section A, Section B. Allworking inchuding rough work, must be clearly shown, and must he done on the sane sheet as the rest of the answer. Omission of essential working will result in loss of narks. The intended marks for questions or parts of questions are given in brackeis / SECTION A- (40 Marks) (Atempt all questions from this section.) Question-1.Choose the correct answer from the following questions. [] i) GST payable is cqual to: (a) Input -Output (b) Input +Qutput (c) Output - Input (d)Output + Input ii) A man depositcd I000per month in a R.D account for 3ycars at 8% p.a. the maturity valuc is. (b) 40,440 (d) 44,444 (a) 44,400 (c) 40,000 ii) On adate 24-07-2023 JP Power company shows its share value price 2 and if face value of the company is 5 than share is said to be, (a) Under Par (b) Above Par (c) At Par (d) Bclow Par iv) If 2+ 4x < 2x-5 < 3x, x E Z, then the solution sct is: (a) {5,4} (b) (-5,-4) (c) {-5, -4,-3} (d) {-4,-3, -2, -1 v) The nmean proportion between ab and is: b (a) a (b) a? (c) ab (d) Vab Page 1 of 7 vi) If polynomial p(r) is divided by (x + a) then the reminder is: (a) p( ) (b) ap(r) (d) p(x) + a (c) p(-a) vii) Which of the following is a row matrix? (a) Matrix P order 2 x 2 (b) Matrix Q order lx 2 (c) Matrix R order 2 x 1 (d) Matrix R order 3 X 2 vii) Assertion (A ): Points (1,7),(4,2),(-1,-1) and (-4,0)are the vertices of asquare. Reason(R): If allthe sides of a quadrilateral are equal and the diagonals are also equal, then the quadrilateral is a square. (a) Both A and R are true and R is the correct explanation of A (b) A is True and R is False (c) Both A and R are true andR is not the (d) A is False but R is True corrcct explanation of A ix) The slope of the line parallel to y-axis? (a) 0 (b) | (c) -1 (d) Not defined x) In the given figure DE || BC and AD : BD =5 : 4 then ar (ADEF) : ar (ACFB) is: (a) 25 : 81 (b)16 : 9 (c) 9:16 (d) 64 : 25 xi) In the figure if angle ABC =69 , angle ACB=31 then find angle BDC. B69" 31 (a) 60 (b) 70 (c) 80 (d) 100 Page 2 of 7 xi)) The total surface area ofa cone whose radius is - and slant height 2lis: (a) 2rr(l+r) (b) r (l +) (d)2arl (c) mr(l t r) xiii) 2cos + 2 1+ cot2 (a) | (b)2 (c) 0 (d) 0.5 xiv)The class mark for the class interval 70 80 is: (b) 65 (d) 70 (a) 75 (c) 85 xv) Two dicc arc are thrown togcther. Thc probability of getting the samc number on both the dicc is: (a) (b) (c); (d) Question 2 (a) When divide by (x-3), the polynomials x3- px' +x +6 and 2x3- x'-(p + 3)x 6 [4] (b) leave the same remainder. Find the value of p. Also find the remainder in each case. The line segment joining P(-4,5) and Q(3,2) intersects the y-axis at R. PM and QN are perpendiculars from P andQ on the x-axis. Find: (i) the ratio PR : RQ (ii) the area of trapezium [4] PMNQ. P( 5) Ci3. 2) M- (c) 0) o N3 0} A model of aship is made to a scale 1:300. , (4] (i) The length of the model of the ship is 2 m. Calculate the length of the ship. (ii) The area of the deck of the ship is 180000 m . Calculate the area of the deck of the model. (ii)The volume of the model is 6.5 m'. Calculate the volume of the ship. Question 3 (a) The sum of the 5th and 9th terms of an A.P is 26 and the sum of the 7 th and I lth terms of an (4] A.P is 42. Find the first three terms of an A.P. Page 3 of 7 (b) The outer and inner diameter of a hemispherical bowl is 17 cm and 15 cm respectively. Find the cost of polishing it all over at 50 paise per Cm' (c) Use graph paper. (take 1 cm = 1unit on both axes) (5) ()Plot the points A(-2,0), B(4,0), C(1,4), and D(-2,4) (i ) Draw the line of symimetry of AABC. Name it L . (iii) Point D is reflected about the line L, to get the image E. Write the coordinates of E. (iv) Name the figure ABED. (v) Draw all the lines of synmmetry of the figure ABED. SECTION B- (40 Marks) (Attempl any four guestions from this Section. ) Question 4 (a) Ashok investcd ? 26400 on 12%, 25 sharcs of a company. If hc rcccivcs a dividcnd of number of sharcs hc bought (ii) Market valuc of cach sharc. ? 2475, Calculatc: (i) The (b) Solve the following incquation and represcnt it on number linc. 13x - 5 < 15x + 4 < 7x+ 12, (c)) Prove that : [3] [3] xER sin tan 1 - cos [4] = (1+ sec0) Question5 (a) In the figure, chords AC and BD of a circle with centre O, intersect at right angles at E. If angle OAB= 25 , calculate angle EBC. (3] 25 B (b) Mohan has a cumulative account in abank for 2 years at 6% per annum simple interest. If he gets * 1200 as interest at the time of maturity, then find the monthly installment and the amount (3] of maturity. Page 4 of 7 Findthley. c) Calculate the mean by short cut method. Class Frequency 45-50 S0-55 [4] S5-60 (60-65 65-70 70-75 30 25 14 12 75-80 Question 6 (a) The line through a point P(5,3) intersects y-axis at Q, making an angle of 45 with the x-axis. (i) Write the slope of the line PQ. (ii) Write the equation of line PQ. (iii) Find the co-ordinates of [3] Q. XP(5.3) (b) In thc givcn figurc, AB is adiamctcr of a circlc with ccntrc O. A circlc is described on AO as [3] diamctcr. A chord AD of the biggcr circle intcrsccts the smaller circle at C. Provc that, BD = 2 (0C) |A (c) B In a GST chain, a dealcr X purchases an article for 8000 and supplics it to anothcr dcaler Y (in (4] the same state) at a profit of I000. The dealer Ysells it to consumer Z at a profit of? 2000. If the rateof GST is l12% and if all transactions were intrastate calculate, () Input Tax for dealer X(ii) Input tax payable by dealer Y (iii) Total cost price of the article for consumer Z (iv) Output GST for consumer Z. Question 7 (a) A person standing on the bank of the river observes that the angle of elevation of the top of a (S] tree standing on the opposite bank is 60 . When he moves 50 maway from the bank, he finds the angle of elevation to be 30 . (Refer figure given below.) Calculate: (i) the width of the river (ii) the height of the tree. Page S of 7 Tree D' (b) 30 60 CRiver B The marks obtained by 120 students are given below. Draw an ogive of using a graph sheet. Take 1 cm the given axis. Use graph to estimate the = 10 marks on one axis and 1 cm = 10 students distribution along the other who did not pass thc test if the following. (i) The median marks. (ii) The pass pcrccntagc was 50. (iii) of students Thc uppcr quartilcnumber marks. Marks 0-10 10-20 20-30 30-40 40-50 50-60 Numbers 60-70 70-80 80-90 90-100 of workers 16 22 26 18 6 4 [5] 3 Question 8 (a) Two dicc arc thrown simultancously. (i) 10as the sum of Find the probability of two geting: (ii) A doublet of even numbers that turn up number (iii) A total of at least 10. (b) (c) (3] Using properties find the value of x when, V3x + 4 + V3x5 V3x +4 - V3x 5 A hemisphcrical bowl of diamctcr 7.2 cm is fillcd is pourcd into an with invertcd conc of radius 4.8 cm. Findcomplctcly saucc. This sauce thc hcight of thechocolate conc. (3] [4] Question 9 (a) From the histogram shown in figure represents the marks of maths test. By using the data () Frame a frequency distribution table with class size of 10 marks. (ii) Determine the mode. (3] Page 6 of 7 18 16 + 14 12 10 studar od NUmber X 0 5 (b) How many terms of the G.P 3, 9, 27, 81,..... must be taken to make the sum 3279? (c) The speed of an express train is x km and the speed of an ordinary train is 12 hr km hr (3] less than that [4] of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train. Question 10 (a) Find the positive value of kfor which the equations x + kx + 64 =0and x - 8x + k = 0 (3] willhavc rcal roots. (b) (c) [3] Given A= , and Iis identity imatrix of ordcr two. Find A - 5A +71. 2 Construct a AABC with AB =7cm, BC = 8cm and angle ABC is equals to 60 . Locate by construction, the point P such that P is equidistant from B and C, and P is equidistant from AB [4] and BC. Page 7 of 7

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