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0. XAWICR'O SCHDOL, RAISAAI 25 Pre-1C8E Examination 2024 - TIME: SUB: MATHEMATICS; CLASS 10, M.M: 80; 3 HOURS provided separately Hitime is to be spent in Answers to this paper must b e t n Ves l nt be allowrd to write durig s rtading the question paper. The time given at dof this pAper is the time =llowrd for writing the answers four questions ro Attempt all questions from section A and any shown, and must be cleariy All working. inchuded rough work. must tt resta te is wo essential of Omission same sheet as the rest of the answet. of questions are given in ioss of rnarks The intended marks for questions or parts brackets || Section A(40 Marks) questions from the given Question 1. Choose the correct aDswers to the (15] options. (Do not copy the question. Write the correct answer only.) o The maximum probability of sure event is (A) O (8) 1 4el Which of the following equations has 2 as a root? IA) x- 4x 5 0 (C) 2.5 (D) 2.0. (B)x3x - 120 0 (D) 3x- 6x-2 0. (C) 2x-7%6 uij Values of k or which the quadratic equation x- 6x + k 0 has real and (D) <9, (C) <6 (AI >-9. distinct roots is: w The three vertices ofa scalene triangle are always equidistant from a fixed pont The point is: (A) Orthocentre (B) Incentre (CCentroid (D)Creumcentre. ifx. 5.4,5,9 are in proportion then x is: A} 25 i (B) 9.72 4C] 3 (D) 28.33. Zero of the polynomial p() = 3x +4 is: (A); (vi) 31 term of the A.P: 10, 7, 4, (A) 74 (Br-80 (C)94 , is (D) None of these. (vi The points A(9, o), B(9, 6), C-9,9) and D(-9,0) are the vertices of (A) rectangle (B) Square (C) rhombus (DY trapezium. jix The inclination of the line, x - V3y + 2V3 = 0 is (C)609 (D) 90 ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribingit i and cADC - 1409, then zBAC is equal to: (C) 40 (D) 50 (A) 800 be: the volurne will then doubled heieht is radius is balved and if cylinder, n a) In (D) four timecs. halved radius (C) doubled (B) a sphcre of (A) same fron nade be rodius 1 cm that cun D 100000. (C) 10000 number of balls of he 10 cm is (A) 100 (B) T000 (D) 2. to (ii) (scc8-1)(1- cosec?0) is cqual (A)1 (B) 1 (C) 0 frequency cuve is also called (iv) Cumulative (B) median represcnt solution set (xv 5x < 23 when x N, (A) histogram ( (D)ogive. (C) bar graph (D) All of these. (CH1.2,3,) (B) (1,2,3,4,5) (A) (1,2,3,4} He deposits Rs. deposit account in a bank. recurring a has find: {aJAhmed maturity, Question 2. gets Rs., 66250 at the time of he If years. 2 for month 2500 per ( ) the rate of interest. (i) the interest paid by the bank, is the third between two numbers x andy and 48 proportion mean the is (b}6 the numbers. proportional of x and y. Find ? 1000) to a dealer in JeA dealer in Shimla (H P) supplies goods/ services (worth Solan (H P). The dealer in Solan supplies the same goods/services to a dealer in Kolkata at a profit of 600. Assuming that the dealer in Kolkata is the end-user of the product and the rate of GST is 12 %, find Ynput-tax for the dealer in Solan. (jiCP for the dealer in Solan. (Output tax for the dealer in Solan. (MCP for the dealer in Kolkata. (4+4+4] Question 3.or A -19i,B-1 i.M-( and BA - M , ind the values of 'a' and b' ,(bP is a point on the line joiningA(4, 3) and B(-2, 6) such that 5AP = 2BP. Find the co-ordinate of P. lc Draw a Histogram for the given data, using a graph paper: Estimate the mode from the graph. Weekly wages (in rupees) No. of pcople 400 - 500 8 500 - 600 600-700 20 700-800 15 800-900 10 900-1000 14+4+5| 2 (6D 123 Seotion B(40 Marka) 84. The square of two natural numbers is numbers. Question 4. (a) The difference of the the Find number. times the smaller re of the larger number is 25 square 3 : 1. If its the base of a cylinder are in the ratio (b) The height and the radius of surface area. volume is 1029n cm; find its total findn (c) f = , use properties of proportion to (3+3+4] 6y+3 =0re parallel. Find the Questlon 5. (a) a The lines 4x + 3y =9 and px value ofp'. a right circular conical vessel are 9856 cm brThe capacity and the base area ofcurved surface area of the vessel. nd 616 cm respectively. Find the cm. AB-6 cm, Be AC 54cm, dorConstruct an isosceles triangle ABC such thatbisector Find CP= 5 su point P on this (3+3+4| Bisect Cinternally and mark 5a cm AB. line from P and also 5 cn from the the points Q and R which are and B (x: 18x-9 2 15 + 12x, XER}. Question 6.(aA - (x: 11x-5 > 7x + 3, xcR} on a number line. 4 Find the range of sct A nBand represcnt it of AB. (ii) In what ratio is the 6IfA -4, 3) and B (8, -6) () Find the length line joining A and B, divided by the X-axis? 2 minutes to from a light house 100 m high totakes (cYA man in a boat rowing away Find the 450, 60 house from change the angle of clevation of the top of light |3+3+4] speed of the boat.u 5 black and 6 white balls. One ball is Question 7. (a) A box consists of4 red, ( ) red that the ball drawn is: () black, drawn out at random. Find the probability or white. (b) Prove the identity: sinA cOsec A- cot A. in an external point to a circie are cqun! (c) Prove that two tangents drawn from (3+3+4| length. CD is the diameter Question 8.\aTn the given figure, chord AB at P such that of the circle which meets the find the radius of the circle. AP BP 12 cm. If DP m8 cm, ahd the l5th term is 66. Find the first term 0 brThe 4th term of an AP is 22 and sum of the series to 8 terms. difference. Hence, find the common 3 the the following frequency distribution is 30, find (3+3+4| of that the mean (C) Given 1 rissing frequency ' 3030- 4o 20T 2010 Class nterval 0-10 10 6 40- 50 S0 - 60 6 Frequency 16176. If the monthly Ro, is of a RD. Account time of the R.D. Questlon 9. (al The aturity value of interest is 8%; find the Ithe rate installment is Rs 400 Aceount. the a circle is inscribed in () In the following fgure,BC 38 cm, QB 27 cm, teral ABCD. II perpendicular to DC, Hote is C 25 cm and that AD circle. the radius of lind the and SR produced meet at is a cyelic quadrilateral. PQ RO 4 cm and TR 6 cm. ORS el In tho given ligure, TRO: (b) Find SPif TP 18 cm, 4 T. (a) Prove a TPS 3+3+4] Ouestion 10. (a) Show that (2x +3) is a factor of 6x? + 17x2 +4%- 12. Hence, factorise the given polynomial conpletely. (b) Find the sum ofthe sequence- /3, 1, -3, 9, ...... upto 10 terms. (c) Ashok and Sandcep invest 18000 cach in buying shares of two different companies. Ashok buys 7.5 % 100 shares at a discount of 20%, whereas Sandeep buys 7 50 shares at a premium of 20 %. If both receive equal dividend at the end of [3+3+4] the year, find the rate of dividend received by Sandeep. 4
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