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ICSE Class X Prelims 2 2025 : Mathematics (Gopalan National School (GNS), Bangalore) : Preboard 2 January

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Pranshu D
Gopalan National School (GNS), Bangalore
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GOPALAN,~~!l~~~ USCHOOL Class: X SECOND PREBOARD - JANUARY 2025 SUBJECT - MATHE MATICS Date: 17/01/2025 Maximum marks: 80 Time allowed: Three hours Answers to this paper must be written on the answer sheet 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 answers. This question paper has 8 pages. Attempt all questions from Section A and any four questions from Section B The intended marks for questions or parts ofquestions are given in brackets [ J SECTION-A (Attempt all the questions from this section) Question I (15) Choose the correct answer and write the correct option. (i)The remainder when x 4 - x3 + x2 -x + l is divided by (x -1) is: (a) 0 (b) I ( c) - I (d) 2 (ii)GST payable is equal to: (a) ITC - output GST (b) Output GST + ITC (c) Output GST - ITC (d) Output GST (iii)lf the sum of first 'n' terms of an Arithmetic Progression common difference of the A.P. is: (a) 6 (bl 5 (c) 4 (d) -6 Page 1 of 8 i'.-t given by Sn= 3n_l. . . n. then the (iv) In the context of shares: (1) No. of shares = Total Invetment Fate valUe o/ a s1tW'e (2) Rate of return = Ditzideurl * 100 Investment (a) (b) (c) (d) Only 1 Only 2 Both 1 and 2 Neither 1 nor 2 (v) The midpoint of the line AB is (2, 3) where the co-ordinates of points are A (x, 4) and B (4, 6) then the value of xis: (1) 0 (2) -1 (3) 2 Which of the following statements is/are valid? ~ Only 1 (b) Only 2 (c) Only 3 (d) Neither 1 nor 2, 3. (vi) The slope of a line parallel to the line 3x + 2y - 7 = 0 is: (a) -2/3 (b) 2/3 (c) -3/2 (d) 3/2 (vii)The equation of a line with x - intercept= 5 and passing through the point (4, -7) is: (a) y = 3x - 23 (b) y=7x-35 (c) y = 4x + 15 (d) y = Sx - 24 (viii) The modal class of a given distribution always correspond s to the: (a) Interval with the highest frequency (b) Interval with the lowest frequency (c) The first interval (d) The last interval (ix) On solving the quadratic equation ,JZx + 3 - Jx + 1 = 1, x R, the solution is: (a) 3, (b) -2,4 {c) -1, 3 (d) 5, 2/3 Page 2 of 8 J (x) 16 cards are labelled as a, b, c .... , m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is none of the letters of the word MEDIAN? (a) (b) (c) 5/8 (d) none of these (xi) From a solid circular cylinder with height l 0cm and radius of the base 6cm, a right circular cone of the same height and same base is removed, then the volume of remaining solid is: (a) 280n cm3 (b) 330n cm3 (c) 240n cm3 (d) 440n cm3 (xii) ABCD is a cyclic quadrilateral. If <BAD= (2x + 5) 0 and <BCD= (x + I 0) 0 , then x = (a) 65 (b) 45 (c) 55 (d) 5 (xiii) The point. P (-3, -2) on reflection in x- axis is mapped as P'. If P' on reflection in the origin is mapped as P", the co-ordinates of P" are (a) (-3, 2) (b) (3, -2) (c) (3, 2) (d) (-3, -2) (xiv) If A=[~ (a)[! (b) [~ ~ =~] and B = [!1 -3 1 -3 2 (-;_s 6 (d) [~2 1 4 (c) 3 3 -0 6 - 5 ] the value of A+ Bis: -25] -81 -3 ~1 ~1 Page 3 of 8 4 (xv) Assertion(A): 3x2 - 6x + 3 = 0 has repeated roots. Reason(R): The quadratic equation ax 2 +bx+ c = O, have repeated roots if discriminant D>O. (a) A is true, R is false (b) Both A and R are true and R is the correct explanation of A (c) A is false, R is true (d) Both A and R are true and R is not the correct explanation of A. Question-2 (i) Given A= [2 -06], B -- [-43 2] and C = [4 2O] fitnd th e matrix X such that 0 2 0 A+2X=2B+C. [4) (ii) A Guiab jamun, contains sugar syrup approximately 30% of its volume. Find how much syrup would be found in 45 Guiab jamuns, each shaped like a cylinder with two ~ hemispherical ends with length 5 cm and diameter 2.8 cm. Give your answer correct to the nearest cm3. [4) C (iii)Thc sum of first three tenns of a G.P. is 37/12 and their product isl. Find the lirst three tenns. 141 Question-3 (i) Prove that: (a) tan (4] 0 - cot 0 = (2 sm 2 0 - I)/ sin 0 cos 0 cos 0 I-sine (l 1 ) - - +cos - 0l+sin0 2 sec e. Page 4 of 8 (ii) 1n the figure given below, AB and XY are diameters of a circle with centre 0. If <APX =30 , find: (b) <AOX (b) <APy (c) <BPY (d) <OAX. (4) B A (iii) Use graph paper for this question. (5] (a)Plot the points A (4, 6) and B (1, 2) 1 (b)If A is the image of A when reflected in the x-axis, write the co-ordinates of A'. (c)If B' is the image of B when reflected in the line AA', write the co-ordinates of B1. (d) Give the geometrical name for the figure ABA'B' . .,. SECTION-B (Attempt any four questions from this section) Question-4 (i) Richard has a R.D. account in a post office for 3 years at 7.5% p.a. simple interest. Ifhe gets~ 8325 as interest at the time of maturity, find the monthly instalment. (3) (ii) The following are the marks obtained by 70 boys in a class test. Calculate the arithmetic mean of the following using short-cut method: (31 Marks No. of boys - '-- 30-40 10 40-50 12 50-60 14 1 '- - 60-70 12 I 70-80 9 !_ - 90-100 I 80-90 7 6 f Sa-Sb Ba+Sb h ( ... m) l - - = - , prove t at -a = -c 8c-Sd Bc+Sd b i 14 I d Question-5 (i) Flight of planes are controlled by ATC and directions are given accordingly. ATC finds the angle of elevation of aeroplane from a point on ground is 60 . After a flight of 50 seconds, it is observed that angle of elevation changes to 30 . The height of plane remains constant at 5000 _-; m. Find the distance travelled by the plane in 50 seconds and also the speed of the plane in km/hr. I5 I ., - Page 5 of 8 ts (SJ . an examination are given below. (ii) The marks obtained by 200 students in 9040-50 50-60 60-70 70-80 80-90 30-40 100 20-30 Marks 0-10 10-20 - 38 40 29 14 6 27 20 11 IO No. of 5 . to estimate.. on. ogive your distributi Use ve . students abo e for the . Using a graph paper, draw an og1v (a) the median I (b) the lower quartile (c) the number of students who obtained more than SO% marks in the examination (d) the number of students who did not pass, if the pass percentage was 35. Question -6 2 (i) Using quadratic fonnula solve 3x - x - 7 = 0 and give your answer correct to two decimal f3J places. during a (ii) The following table shows the age distribution of cases in certain disease admitted year in particular hospital. I Number of cases Age (in years) 6 5-14 11 15-24 21 25-34 23 35-44 14 45-54 5 55-64 graph. the from Draw a histogram and hence find the mode (3] (iii) 200 logs are stacked in the following manner: . 20 logs in the bottom row , 19 m the next row. 18 m the row next to 1t and so on. In how man rows are th , y e - 00 1ogs placed and how many logs are in the top row. '4' Page 6 of 8 I -------------------Question-7 (i) In fltgure, 0 is the centre of th . I and LN is a diameter. If PQ is a tangent to the circle at Kand <KLN - o e circ e - 30 , find <PKL. (3) (ii) Solve the given inequation and graph the solution on the number line. [3) 2x-5<5x+4< 11,xEI. (iii) Construct a regular hexagon ABCDEF of side 4.3 cm and construct its circumscribed circle. Also, construct tangents to the circumscribed circle at points Band C which meets each other at point P. Measure and record <BPC. [4) Question-8 (i) The polynomials 2x3 - 7x2 +ax - 6 and x3 - 8x2 + (2a + 1) x -16 leaves the same remainder when divided by x - 2. Find the value of 'a'. [3) (ii) Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish? (3) (iii) A mathematics teacher uses certain amount of terracotta clay to form different shaped solids. First, she turned it into a sphere of radius 7cm and then she made a right circular cone with base radius 14 cm. Find the height of the cone so formed. If the same clay is ttuned to make a right circular cylinder of height 7/3 cm, then find the radius of the cylinder so fonned. Also compare the total surface areas of sphere and cylinder so formed. (4] Question-9 (i) Salman invests a sum of money in t 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is t 600, calculate: (a) the number of shares he bought (b) the total investment (c) the rate of return on his in vestment. Page 7 of 8 [3] (ii) Find the value of k' for which the lines k x - Sy+ 4 = O and 4x - 2y + 5 = 0 are perpendicular to each other. 4 (31 (iii) A peacock is sitting on the top of a pillar, whic~ is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake, the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught? [4) Question-I 0 (i) Ananya, a housewife buys the following items from a depart mental store Rate (t) Items Quantity GST rate ~ 40/kg Sugar 5 kg 5% Amul Butter ~ 400/k g kg 12% Shampoo ~ 110 200m l 18% Calculate the total amount of bill paid by her. (31 -. (ii) ABC is a triangle whose vertices are A ( 1, -1 ), B (0, 4) and C (-6, 4 ). D is the midpoint of BC. Find the equation of the median AD. (31 (iii) In a triangle PQR, Land Mare two points on the base QR such that <LPQ = <QRP and <RPM = <RQP. Prove that: (a) ~PQL ~ ~RPM (b)Q LxRM =PLx PM (4) I - - - - - - - - - - - - - -- -- Page 8 of 8 -

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