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ICSE Class X Prelims 2024 : Mathematics (Seth Juggilal Poddar Academy (SJPA), Malad East, Mumbai)

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A.B.V.M. Agrawal Jatiya Kosh's Seth Juggilal Poddar AcademyucsE) Sub: Mathematics First Prelimirary Examination (2023 -24) STD: X Date: 28/1 1/2023 Marks: 80 Time: 2 hr. 30 mins. Answers to this Paper must be written on the paper provided separately. Youwill not be allowed to write during the first 10 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 Aand any three questions from Section B The intended marks for questionor parts of questions are given in brackets !) SECTIONA (Attempt allquestions from this Section) Question 1) i) The ratio of the radii of the two cylinders is 2:3 and the ratio of their heights is 5:3. The ratio of their volume is: a) 10: 17 bt 20: 27 c) 17:27 d) 27:20 ii) The locus of a point equidistant from two fixed point is a) The perpendicular of the line segment joining two fixed points. b) The circumference of the circle. The perpendicular bisector of the line segment joining the two fixed points. d) Median of a triangle. [15] iii) The solution set which represents the given number line is: -4 -3 -2 -1 0 1 3 2 4 a) {0,1, 2, 3} b) {x:x R, -1<x<4} c) {x:x ER,-1<x<4} dYE-1,0, 1, 2,3} iv) The general term of the Arithmetic Progression 16, 12, 8, 4, 0,......... is : a) 10 - 5n b) 5 - n 20- 4n d) 10 -2n v) Rs.15000 and sel!s it to a A shopkeeper buys an article from awholesaler for liability of the consumer at a profit of 5%. If the rate of GST is 18%, then the tax shopkeeper is a) Rs.150 b) Rs.120 ) Rs.135 d) Rs.145 vi) f(x) What number must be added to the polynomial remainder -1 when divided by x - 1: x + 4x so, that it leaves =3x3 a-7 b) -1 c) 7 d) 1 vii) D pentagon and O is the centre of In the figure ABCDE is a value of circle. The numerical LABC + 2CDE = a) 180 b) 360 c) 90 d) 270 Page 2 of9 the A vii) iX Which of the following s.atement is not true? v ) All the identity matrices are square matrices. b) Allnull matrices are square matrices. c) For the square matrix, the number of rows is egual to the number of d) Asquare matrix, all of whose elements except those in the leading columns. diagonals are zero, is the diagonal matrix. Mx: (a, 2) (5,b) then the values of a and b are a) -5,-2 b) -5,2 c) S, -2 Y5,2 x) re:pectively: Anshika wants to invest Rs.25000in a She buys Rs.100 shares at a Rs.25. Number of shares purchased bycompany. premium of her is: a) 100 b) 2000 c) 250 t 200 xi) If P(2, k) divides the line joining (6,2) and (-2,4) in the ratio 2 : 2, then k = a) 7 c) 2 d) 1 xii) The root of the quadratic equation 4x' = 3x is/are a 4 3 b) 0, c) -3 4 d) 0, 4 3 Page 3 of 9 Qu xiii) Apole 12m high casts ashadow 123 m on the ground. Find the Sun's elevation a) 60 t 30 c) 45 d) 90 Xiv) The sides AB, BC and CA of triangle ABC, touch at P, Q and R respectively. If PA= 4cm, BP = 3cm and AC=11cm, then R BC = a) 10cm b) 11 cm c) 14 cm d 15 cm The following table shows the frequency distribution. Assertion:To find the Upper limit of the continuous and necessary to calculate themedian class, It's not necessaryto make the data cumulative frequency. Statement: Upper limit of the median class is 17.5 Class Frequency 0-5 13 6-11 12-17 10 15 a) Both Assertion and b) Assertion is True Statement are True and Statement is tAssertion is False and Statement is False True d) Both Assertion and Statement are False 18-23 24-29 11 Question 2) Mr. Ram Gopal invested Rs.8000 i.7% Rs.100shares at Rs.80. After a year, i) he sold these shares at Rs.75 each and invested the proceeds (including his [4] dividend) in 18%, Rs.25 shares at Rs.41. Find: a) His dividend for the first year. b) His annual income in the second year. c) The percentage increase in his return on his original investment. ii) [4] In the given figure, Iis the incentre of AABC. B when produced meets the circumcircle of AABC at D. IfeBAC = 55 & LACB = 65 , A Calculate: a) zDCA b)ZDAC c) zDC! d) zAIC ii) x= Given write down [4] i a) The order of the matrix X b) The matrix X Question 3) i) From a solid cylinder whose height is 8cm and radius is 6cm, aconical the cavity of height 8cm and base radius 6cm is hollowed out. Find [4] volume and total surface area of the remaining solid. ii) [4) The mean of the following frequency table is 50. But the frequencies f1 and f2 in the classes 20-40 and 60-80 are missing. Find the values of fi and f Class 0-20 20-40 40-60 60-80 80-100 Total Frequency 17 f1 32 f 19 120 Page 5 of 9 ii) Use a graph paper for this question. (Take 10 small divisions =1 Plot the points P(3,2) and Q(-3,-2). From Pand Qdraw unit on bo perpendicular, PM and QN on the X-axis. a) Name the image of Pon reflection in the origin b)Assign the special name tothe geometrical figure PMQN || and find its area. c) Write anytwo invariant points under reflection in the X-axis. SECTION B [Attempt any four fromthis section) Question 4) i) 800 2 The model of aship is made toa scale 1:300. (3) a) The length of model ship is 2m. Calculate the length of the ship. 18O000 b)The area of the deck ship is 180000 m'. 30ox 30o Calculate the area of the deck of the model. c) The volume of the model is 6.5 m . Calculate the volume of the ship. i) Solve the following inequation and represent the solution set [3 on the number line. -1 2x 5 -3 < 2 3SER i) [4] Using ruler and compass only: a) Construct a triangle ABC with the following data: AB = 3.5cm, BC= 6cm and zABC= 120 diameter. b) In the same diagramdraw a circle with BCas which is Find apoint P on the circumference of the circle equidistant from AB and BC. c) Measure zBCP Page 6 of9 *h xes Question 5) i) Ashima has a cumulative or Recurring deposit account in a bank for 5years at 9%p.a At the time of maturity, she gets Rs.51607.50. Find the monthly instalment. (3] 700 ii) Howmany three-digit natural numbers are divisible by 7? [3] )28 i) (x- 2) is a factor of x + ax' + bx +6. When this expression is divided by (x - 3),it leaves the remainder 3. Find the polynomial. [4) Question 6) i) Mr.Bedivisits the market and the following articles: [3] Medicine costing Rs.950, GST @5% Apair of shoes costing Rs.3000, GST @18% Alaptop bag costing Rs.1000 with a discount of 30%, GST @18%. a) Calculate the total amount of GST paid. b) The total bill amount including GST paid by Mr.Bedi i) The line through P(5,3) intersects y-axis at Q. (3] a) Write the slope of the line. P(5,3) b) Write the equations of the line PQ. o k slope foYm x' c) Find the coordinates of Q. Too eo foY ii) In the adjoining figure, ABC is a right-angled 45 y triangle withzBAC =90 a) Prove that AADB~ ACDA b) If BD=18cm and CD=8cm. find AD. c) Find the ratio of the [4] 8cm area of AADB and area of ACDA 18cm B Page 7 of 9 Question 7) X i) Solve x+ 7x=7 and give your answer to two significant places. i) From the top of a hill, the angle of depression of two consecutive kilometer stones due east are found to be 30 and 45 respectively. Find the distance of the tw stones from the foot of the hill. i) (3) Ifthe image of the point (2,1) with respect tothe line mirror be (5,2), find the equation of the mirror. [4] Question 8) Construct aAABC, given thatAB = 6cm, BC = 7cm and AC = 5cm. Construct inscribed circle of a AABC and measure its radius. ) (3) The three vertices of a p ralelogram are (3,4)(3,8) and (9,8). Find the fourth vertex. (3] ii) If tan + sin = m and tan - sin = n, show that m - n' = 4ymn [4) Question 9) i) i) A person on tour has Rs.360 for his expenses. If he extends his tour for 4 days, he has to cut down his daily original duration of tour as x, form an expenses by Rs.3. Taking the equation in x and solve it. 40students enter for a game of shot-put competition.The distance (4] thrown(in metres) is recorded below: (6] Distance(in m) 12-13 13-14 14-15 Number of students 3 9 12 Page &of 9 15-16 16-17 17-18 18-19 4 2 1 scale of ogive for the above distribution. Use an draw to paper graph a Use theother axis. Hence uSing your on students 2cm=5 and 2cm=lm on one axis graph find: a) The median. b) Upper Quartile. of students c) Number who which is cover a distance above 16.5 m. [3) hemisphere of on a mounted Question 10) cone cm. form of a toy is 15.5 the the in of is height Atoy i) The total 3.5cm. at C. radius area. B meet and surface A Tangentsat total circle. Find the X ii) O is the figure, given In the 30 , find ZACO = If a) ZAOB centre ofthe 30 C b) ZAPB c) ZBAC [4] expression: the solve r) proportion 62 (1+ 1 + x+ x 63(1 -x) propertiesof 1 - rt r 2 Usingthe iii) *****FND*

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