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ICSE Class X Prelims 2023 : Mathematics (Indian Education Society IES Orion, Mumbai)

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INDIAN EDUCATION SOCIETY IES L) ORION (1CSE) SECONDARY (2022-23) Preliminary Examination Subject: Mathematics vaLUE AD0TIO MROUOH ERuCAT STD X Marks: 8OM Date 17/01/2023 Time: 2 hr Answer to this paper must be written on the paper provided separately You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper The given at the head ofthis paper is time allowed for writing the answers. Attempt all questionsform 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 r ofthe answer. Omission of essential working will result in loss of marks. The indented marks for questions or parts question are given in brackets [ ]. Section-A 140 marks] (Attempt all questions from this section) [15x 1 = 15 Marks] QUESTION: 1 Choose the correct answer to the questions from the given options: i) profit. wholesaler for R 20000 and sells it to If the rate of GST is 12%, find the tax paid by him? a) 230 bought aTV from Rahul a d) c)F240 260 b) consumer at 10% 250 Mrs. Asha Mehta deposit Rs 250 per month for one year in a bank's recurring deposit i) account. If the rate of (simple) interest is 8% per annum, then the interest earned by her on this account is a) b) 65 iii)The largest iv) a) 4 if- is a) c) 130 for which 2(x -1) 120 value of x c) b) a root ofthe equation k 1 b) 2 d) 260 s9 and -x d) 3 x 13 x --10 0, = - c) 3 x E W is 0 the value of k is d) v) lfx+ 5 is the mean proportional between x + 2 and x + 9; find the value of x. a) 3 b) 5 c) 7 d) 11 d) -2 vi) If 2x+ 1 is a factor of 2x+ ax-3, find the value of a. b) c) 4 vii) The 0 is image of the point (4, 7) under reflection in the line x (4,-7) d) -4,7) a) (4,7) b) c)(-4, -7) = a) ix) x-V3y + 2V3 =0 The inclination of the line viii) (d) 90 c) 60 b) 30 0 is Ifin two AABC and APQR, p p then. b) A PQR AABC (d) A BCA~APQR a) A PQR ACAB c) ACAB APQR x) In the given figure, tangent PT = 12.5 cm and PA = 10 cm; find AB. 5.25 cm a) b) 5.625 cm c) 6.5cm (d) 7.35cm xi) How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm ? a) 80 b) a)-1 b) 0 c) 1 (d) 2 The probability of getting exactly one head in tossing a pair of coins is xii) a) xv (d) 56 c) 64 (sec 0-1) (1 - cosec 0) is equal to xii) xiv) 20 0 b) 1 c) (d) 2 Which term of the A. P. 1, 4, 7, 10, . is 58? c) 20 a) 18 b ) 19 21 (d) Ifthe order of matrix A is mxn and the order ofmatrix B is n xp then the order of matrix A xB is a) m xn b) nxp c) m xp (d) None of these QUESTION: 2 a) , find the value of X, y and z. [41 b) In the given figure, O is the centre chord BC= chord CD. Find: of the circle, 75 and D BOC ii) ii) 2BAD 20BD LBCD 75 o 4 B c) The shadow of a tower, when the to be 10 m longer than when it angle was metre. of elevation of the sun is 45 , is found 60 . Find the height of the tower in nearest [4] QUESTION: 3 a) In auditorium, seats were arranged in rows and columns. The numbers of rows were equal to the number of seats in each row. When the numbers of an doubled and the numbers of seats in each row the total number of seats increased by300. Find: The number of rows in the i) original arrangement. The number of seats in the ii) auditorium after rows were were reduced by 10, arrangement. b) A hollow sphere of internal and external radii 6cm and 8cm respectively is melted and recast into small cones of base radius 2cm and Find the number of cones formed. c) [41 The following height 8cm. [4 table shows the number of casualties due to accidents at different age group in a city. Age (In years) 5-15 Number of casualties Draw an 6 i) 10 16 ogive for the given distribution taking on y- axis. Use 1cm=10 casualties From the 5-25 |25-3535-45 45-55 55 65 65-75 graph determine: 15 1cm 24 = 10 years graph paper for the same. 8 on x-axis and the lower quartile the upper quartile il) ii) the median. [5 Section- B [40 Marks] from this section) (Attempt any four questions QUESTION: 4 4000 and sells these at a) A shopkeeper buys goods worth { at 5%, find: consumer in the same state. If GST is charged ii) iii) b) CGST paid by the consumer. SGST paid by the consumer. the total amount paid by the a profit of 20% to a 3 consumer. In the given figure, the circle touches the sides AB, BC, CD and DC of a quadrilateral ABCD at the points S P, Q, R and S respectively. If AB = 11cm, BC= x cm, CR= 4cm and AS= 6cm, find the value of x. Q [3] c) In what ratio is the join of A( 3, -1) and B(-7,9) divided by the point P(-1, b)? 4] Hence, find the value of b. QUESTION: 5 a) Find the value of x for which the numbers (5x+2), (4x -1)and (x + 2) are in A.P. [3 b) From the top of a hill the angles of depression of two consecutive kilometre stones, due sast are found to be 30 and 45 respectively. Find the distance of the two stones from the foot of the hill. [3] In the given figure , P is the point on AB such c) that AP: PB = 4 3 and PQ l AC. AR LCP and QS 1 CP. ) Calculate PQ: AC ii) If ZARC = 90 and 2QSP = 90 B and QS = 6cm, calculate the length of AR. 41 QUESTION: 6 a) Meena cumulative time deposit account of 340 per month at 6% per annum. If she gets R7157 at the time of find the total time for maturity, has a which the account was held? b) Solve the equation 2x4 + 5x-5 = 0. Write your answer correct to 2 decimal. (3 13] c) A mathematics aptitude test of 50 students was recorded as follows: 50 6 0 Marks 60-70 70 80D 80-90 14 19 90-100 NO. of students Draw histogram for the a above data using a graph 5 paper and locate [41 the mode QUESTION: 7 a) Solve the inequation 12 +12x < 5+3x,x E R. Represent the solution set 13] on the number line. a = c) Calculate the Height in find matrixXsuch and AX and B b) If A=3 mean 135 140 of the 131 B. = following distribution. 140-145 145-150 150-155155-160 160-165 165170 170-175 cm Number of boys 18 28 24 10 5 2 [4) QUESTION: 8 a) Prove that: b) secA secA-1 + secA = 2 cosec2A secA +1 [3] Using properties of proportion solve for x. Given : Vx +5 + Vx-16 131 V +5 V-16 c) P(3,4), 0(7,-2) and R (-2,-1) are the vertices of a APQR. Find i) the slope of the median of the triangle through LR. ii) the equation of the median of the triangle through ZR.. 4) QUESTION: 9 a) Given that: b) Prove that: a3+3ab2 = b3 +3a2b 63 Using properties of proportion, find a:b. 62 sin8tan6 1-cos6 31 (1+ sece) 131 c) The point P (3,4) is when reflected in the linePP'. i) i) ii) iv axis and 0' is the image of 0 the graph paper, Give : reflected to P' in Using x- (Orlgin) the coordinates of P'and 0 the length of the segment PP and 00'. the geometrical name of the figure POP'O 41 the perimeter of the quadrilateral POP'o'. QUESTION: 10 a) Construct a AABC in which BC = 5cm, AB =6. 5cm and LABC draw it' circumcircle. b) Two coins are tossed simultaneously. Find the at least one head i) ii) at most one head ii) exactly one head = 120 and 13] probability of getting : [3) c) Show that (x + 4) is a factor of 2x3 +9x +x- 12. Hence factorise the given expression completely. [41

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