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ICSE Class X Prelims 2024 : Mathematics (Hiranandani Foundation School (HFS), Powai, Mumbai)

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Std: X HIRANANDANI FOUNDATION SCHOOL, POWAI FIRST PRELIMINARY EXAMINATION 2023 2024 Mathematics Date: 11 - 12 - 2023 Max.Marks: 80 Time: 2 hrs Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. This paper consists of 8 printed pages. SECTION A [40 Marks] (Attempt all questions from this section) Question 1: Choose the correct answers to the questions from the given options. ( Do not copy the question, write the correct answers only.) [15] (i) The marked price of an article is 5000 the shopkeeper give a discount of 10%. If the rate of GST is 12%, then the amount paid by the customer including GST is: (a) 5040 (b) 6100 (c) 6272 (d) 6160 (ii) 25 shares of a company are selling at 20. If the company is paying a dividend of 12%, then the rate of return is: (a) 10% (b) 18% (c) 15% (d) 12% 1 10 5 2 (iii) If X + Y = and X Y = , then matrix X is: 5 7 1 3 6 8 3 4 4 12 2 6 a.) (b) (c) (d) 4 10 2 5 6 4 3 2 Turn Over HFS, Powai .. . .. .2 .. .. Std X / Mathematics (iv)What What must be subtracted from each of 7,9,11 and 15 so that the resulting numbers are in proportion ? (a) 1 (b) 2 (c) 3 (d) 5 (v) If ( x50 + 2x49 +k) is completely divisible by (x+1),then the value of kis : (a) 0 (b) -1 (c) 1 (d) -2 2 (vi) The A.P. 6, 13, 20, ..,216 has 31 terms. The middle term of the A.P. is: (a) 91 (b) 97 (c) 107 (d) 111 (vii)The 6th term from the end of the G.P. : 8,4,2, ., (a) (b) (c) is: (d) (viii)A(1,4), A(1,4), B(4,1), C(x,4) are the vertices of ABC. If the centroid of the triangle is G(4,3), then x is equal to: (a) 2 (b) 1 (c) 7 (d) 4 (ix)The The value of m such that the points A(5, -2 ) B(8,-3) 3) and C(m,-12) C(m, are collinear, is: (a) 29 (b) 33 (c) 35 (d) 41 (x)In In the given figure, AB|| CD and OA = (2x+4) cm, OB = (9x (9x-21)cm, 21)cm, OC = (2x 1)cm 1)cm and OD = 3cm. Then x equals : (a) 2.1 (b) 3 (c) 4 (d) 6 (xi)In In the given figure, O is centre of the circle . If POB POB = 130 , then the value of BAQ ( x ) is : (a) 25 (b) 50 (c) 65 (d) 40 HFS, Powai .. .3 .. Std X / Mathematics (xii)If the volume and the surface area of a sphere are numerically the same, then it s radius: (a) 1 unit (b) 2 units (c) 3 units (d) 4 units (xiii)If tan + cot = 2, then tan2 + cot2 is equal to : (a) 1 (b) 2 (c) 4 (xiv)The median of the following data is : X 10 20 30 40 F 2 3 2 3 (a) 30 (b) 31 (c) 35 (d) 8 50 1 (d) 40 (xv)Assertion (A): The roots of the equation 2x2 6x + 3 = 0 are unequal and irrational. Reason (R): If D < 0 and not a perfect square then roots are unequal and irrational. (a) A is true, R is false. (b) A is false, R is true (c) both A and R are true (d) both A and R are false Question 2: a.) Mohit started paying rupees 800 per month in a 6 year recurring deposit. After 2 years, he started one more R.D. account in which he deposited rupees 1500 per month. If the bank pays 10% per annum simple interest in both the deposits, find at the end of 6 years which R.D. will give more money and by how much? [4] b.) A vessel in the shape of an inverted cone is surmounted by a cylinder has a common radius of 7 cm. It was filled with liquid till it covers one third of the height of the cylinder. If the height of each part (conical and cylindrical) is 9 cm and the vessel is turned upside down, find the volume of the liquid and what height will it reach in the cylindrical part. [4] c.) Prove that: (1 + tan ) + 1 + = [4] HFS, Powai .. .4 .. Std X / Mathematics Question 3: a.) In the adjoining figure, O is the center and AOE is the diameter of the semicircle ABCDE. If AB = BC and AEC = 50 , find : (i) CBE (ii) CDE (iii) AOB. Prove that OB is parallel to EC. [4] b.) A manufacturer buys raw material worth 7500 paying GST at the rate of 5%. He sells the finished product to a dealer at 40% profit. If the purchase and the sale both are intra-state and the rate of GST for the finished product is 12%, find: [4] (i) the input tax (under GST) paid by the manufacturer. (ii) the output tax (under GST) collected by the manufacturer. (iii) the tax (under GST) paid by the manufacturer to the Central and State Governments. (iv) the amount paid by the dealer for the finished product. c)(i) What number should be subtracted from x3 + 3x2 8x + 14 so that on dividing it by x 2, the remainder is 10? [2] (ii) Three numbers whose sum is 21 are in A.P. If 2,2,14 are added to them respectively, the resulting numbers are in G.P. Find the numbers in A.P. [3] SECTION B[40 Marks] (Attempt any four questions) Question 4: a.) If A = 2 , find x and y such that A = I. Where I is unit matrix of order (2 x 2) [3] HFS, Powai .. .5 .. Std X / Mathematics b.) Solve the equation 2 + 5 5 = 0. .Write your answer correct to 3 significant figures. [3] c.) In square ABCD, the bisector of BAC cuts BD at F and BC at G. AB = 10 cm, find area of ACG : Area of ABF. [4] Question 5: a.) Calculate the mean of the distribution given below using step- deviation method: [3] Marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80 No. of 2 6 10 12 9 7 4 students b.) Solve the following linear inequation and represent the solution set on a real number line: 5 3 3 ; . [3] c.) A,B and C are three points on a circle and O is the centre of the circle. The tangent at C meets BA produced at T. Given that ATC = 36 and ACT = 48 , calculate the angle subtended by AB at the centre of the circle. [4] Question 6: a.) The 4th, 6th and the last term of a geometric progression are 10,40 and 640 respectively. If the common ratio is positive, find the first term, common ratio and the number of terms in the series. [3] HFS, Powai b.) If .. .6 .. = Std X / Mathematics , using properties of proportion, find the value of . [3] c.) For the following distribution, draw a histogram and estimate the mode. ( Take 2cm = 4 kg on one axis and 2cm = 5 students on the other axis) [4] Weight(in 44-47 48-51 52-55 56-59 60-63 64-67 kg) No. of 23 25 37 18 7 2 students Question 7: a.) Spherical marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water . Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm . [3] b.) Using ruler and compasses only, construct a ABC such that BC = 5 cm, AB = 6.5 cm and ABC = 120 . (i) Construct a circumcircle of ABC. (ii) Construct a cyclic quadrilateral ABCD such that D is equidistant from B and C. [3] c.) A(2,5), B(4,1), C(2,3) are the vertices of ABC. Calculate: [4] (i)Equation of median AD. (ii)Equation of altitude AM. (iii)Co-ordinate of E, if E is the fourth vertex of parallelogram ABEC. HFS, Powai .. .7 .. Std X / Mathematics Question 8: a.) In a family, there are three children. Assuming that the chances of a child being a boy or a girl are equal. Find the probability that (i) There is one girl in the family. [3] (ii) There is no boy in the family. (iii) There is at least one boy in the family. b.) Construct ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm. (i) Draw the locus of a point which moves so that it is always 2.5 cm from B. (ii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA. [3] (iii) Mark the point of intersection of the loci with the letters P and P. Measure PC and P C. c.) A pole of height 5 m is fixed on top of a tower. The angle of elevation of top of the pole as observed from a point A on the ground is 500 12/ and the angle of depression of the point A from the top of the tower is 350. Find the height of the tower. [4] Question 9: a.) Find the ratio in which the line joining A( -5,2) and B ( 10,6) is divided by X=7 at P. Hence find the co-ordinates of P. [3] b.) Use graph paper for the following questions. Take 1cm = 1 unit on both the axes. [3] plot points A (4,6) and B(1,2) i) Write the co-ordinates of A , the image of A when reflected in x-axis. ii) Write the co-ordinates of B ,the image of B when reflected in the line AA . iii) Give the geometrical name to the figure ABA B . c.) John had 1,000 share of a company with a face value of Rs.40 and paying 8% dividend. He sold some of these shares at a discount of 10% and invested the proceeds in Rs.20 shares at a premium of 50% and paying 12% dividend. If the change in his income is Rs.192. find the number of shares sold by him. [4] HFS, Powai .. .8 .. Std X / Mathematics Question 10: a.) P & Q are centres of circles of radius 9cm and 2cm respectively. PQ = 17cm. R is the centre of a circle of radius x cm, which touches the above circles externally. Given PRQ = 900, write an equation in x and solve it. [4] b.) Following table the marks of students at ICSE examination in Mathematics. Draw an ogive for the table. [6] ( Take 2cm = 10 marks on one axis and 2cm = 20 students on other axis) Marks 30-40 40-50 50-60 60-70 70-80 80-90 90-100 No. of 1 3 11 21 43 32 9 students Use the ogive to estimate: (i)Median (ii)The lowest marks scored by the top 25% students of the class (iii)The highest mark obtained by the lower 20% students of the class. --------------------------------------------------------------------------------------------------

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