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HUTCHINGS HIGH 8CHOOL AND JUNIOR COLLEGE PRELIMINARY EXAMINATION 2022-2023 MATHEMATICS CLABS X TIME: 2 HOURS 30 MIN MAX MARKS:80 Total number of printed sides: 5 Answers to this paper must be written on the paper provided separately. You will not be allowved to write during the first 15 minutes. Thus time is to be spent in reading the question paper. The tune given at the head of this paper is the time allowed for uwriting the answers. Attempt all questions from Section A and angy four 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 work will result in loss of marks. The intended marks for questions or parts of questions are given in brackets[ Mathematical tables are provide SECTION A (Attempt all questions from this section) QUESTION 1 Choose the correct answers to the questions from the given options: ( Which of the (a) 0.7 15 following cannot be the probability of an event? (b) 23 c-1.5 d 15% 023 (ii) In triangles ABC and DEF, LB = LE,LF = LC and AB 3DE, then the two triangles are (a congruent but not similar (c) neither congruent nor similar (ii fb) similar but not congruent congruent and similar (d Voiume of a hemispherical ball of diameter 10.5cm can hold? tal 0303lit bj 3.03lit(0.030lit (d) 30.3lit (iv) Which ofthe following points is invariant with respect to the line y =-2 a) (3,2) b)(3,-2) (v ) (2,3) (d) (-2, 3) The 21st term of an A.P whose first two terms are -3 and 4, is (a) 17 (b) 137 (c) 143 (d) -143 (vi) If the cost of an article is Rs. 25,000, and CGST paid by the customer is Rs. 2250, the rate of GST is (a) 9% (viyttY (b) 10% (c) 15% and 2X+Y-L thenX is Pg 1 (d) 18% 2x is the root of the equation kx 2 (viii la) is (d) 2 -V2 (b- 0, then the valuc of k 4 o st (ix Two direct common tangentsexist il (a) the two circles do not touch cach other (b) the two circles touch cach other externally (c) the two circles touch each other internally 1d) the two circles intersect each other The set from which values of the variable involved in the incquation are chosen 1s called (a) empty set (xi) (b} solution set (c) null set (d) replacement set The sum of last 10 terms ofA.P 8, 10, 12, . . . . 2 6 1 (a)-40 xii (b) 1170 (c) 400 (d) 1710 The remainder when 2x- 5x + 1is divided by (x+3) (a) 34 (xii (b) 4 Consider the Class 0-5 Frequency 13 (c) 43 (d) -32 following frequency distribution 6- 11 12-17 10 5 18-23 24 29 11 The upper limit of the median class i_ (a) 17 (b) 17.5 (c) 18 d)18.5 (xiv) The point which divides the line segment joiningthe points (7, 6) and (3,4) in the ratio 1:2 internally lies in (ayI quadrant (zv) If M = (b) II quadr nt and -L then (c) II quadrant (d) IV quadrant M+ 2N is la QUESTION 2 () Sonia has a recurring deposit account in a bank. She deposits Rs. for 2 years. If she gets Rs. 66250 at the time of maturity, find (a) interestpaid by the bank () If 7x- 15y 4x + (b) rate of interest y, find the value ot (a 59x+5y filled with water. If the sphere cylindrical vessel rises by 3. 4 3x+2y2 D2-2y2 14 Sin 6 tan 6 (ii) Prove the following identity QUESTION 3 () A sphere of diameter 12cm 2500 per month 1-cos6 I + sec 6 is dropped in is completely right circular cylindrical vessel, partly submerged in water, the water level in the a Find the diameter (ii) Find the equation of the line passing through intersection of the lines 4x + 3y 1 and 3x = of the cylindrical vessel. -y +9 Pg 2 4 the = 0 points (0,-2) and the 14] point of 14 (1HiUse graph shect for this Take 1 em =I unit along both question. and a x y axis. (a) Plot the following points: A(0,5) D Rellect the points B,C and D on B(3,0), C(1,0) , the respectively. c Write down the coordinates of B', C', (d) Join the points A,, figure ABCDD'CB B. C, D, D', C", B', y-axis and and D{1,-5) name and D' A in order and them give a as B, C, D name to the cosed 5 SECTION B (Attempt any four questions from this section QUESTION 4 (4) A retailer buys a TV from a manufacturer for Rs. 25000. He marks the TV 20% above his cost price. If the sales are price and sclls it to a consumer at 10% discount intra-state and the ratc of GST is 12%, find (a) Consumers cost price of TV inclusive of tax(under GST) (b) GST paid by the retailer to the Central and State Governments. (1) Solve the quadratic price of the on the marked 3 equation and give your answer correct to 2 decimat places 7x2+2x -2 =0 3 (iii) Drawa histogram for Class 20 30 the following 30 40 frequency.distribution and calculate the mode. 40 50 Frequency 50 60 60 70 18 70 80 8 41 QUESTION 5 (4) 1f X = showthat 6X-X = 9fwhere I is the unit matrix. 131 (ii) In the given figure, AB is.a diameter of a ircle with centre O and AT is a tangent. If LAOQ = 58, find LATQ. B 13 (ii Given that (x +2) and (x +3) are factors of 2x + ax +7x - b. Determine the values of a and b 4 QUESTION 6 () Find the equation of the right bisector of the line segment joining the points A(3, -4) and B(5, -6). 3 (i) Find 0, if Cos0-3cos9+2 Sin0 131 Pg 3 The sum (,t of first five terms and the sum of first seven terms of the same A.P Is the sum offirst ten tems of this A.P is 235, find the sum of its first twenty 14 term QUESTION 7 (A game of umbers has cards marked with 11. 12. 13, . ...40. A card is drawn at random. Find the probability that the number on the card is : (a) a perfect sequare 4 be 131 (b) divisible by 7 ind the least numnber of coins of diameter 2.5 cm and height 3 mm which are to melted to form a solid eylinder of radius 3 cm and height 3 5 cm (4) In the adjoining figure. AC is a diamcter of the circlc. If AB = BC and AED 1 18", then find: (a)LDEc 4 (b} DAB E QUESTION 8 (i)Solve the following inequation, write the solution set and represent it on the number line , 3 (li) Find the mean for the following frequenc diatribution by step deviation method Class Intervals. Frequency 8490 8 90 96 12 96 - 102 15 102 108 108 114 10 3 (iii) In the adjoining figure AD = 4cm, BD = 11cm, AE = 6cm and EC = 4cm. (a) Prove that A ADE A ACB (b) If LABC = 40 , find LAED (c) If DE =7cm, find BC B 4 C QUESTION 9 () The table below shows the distribution of thhe scores obtained by 120 students in a shooting competition. Using a graph sheet, draw an ogive for the distribution (Use scale 2cm = 10 units Score obtained 10 No. of 5 10 20 9 on both axes) 50 2030 30 40 40 50 60 16 22 26 18 70 80 60 70 11 80 90 90 100 3 shootcrs Use your ogive to estimate (a) The median (b) the interquartile range more than 75% scores the number of who shooters obtained (c) 6 ( ) Sonal can row a boat at a speed of 5km/hr. Ifit takes her 1hr more to row the boat 5.25km upstream, than to return downstream, find the speed of the stream. QUESTION 10 () Ir (4a + 5b) (4c - 5d)= (4a - 5b) (4c + 5d), prove that a, b,dd are in proportion. (ii) Draw a line AQ = 7cm. Mark a point P on AQ such compasses only, construct (a) A circle with AP as diameter (b) Two tangents to the above circle from point Q 4 3 that AP 4cmn. Usingruler and = * 3 (iii) A boy 1.7m is standing 20m away fr m a flagstaff on the same level ground. He observes that the angle of elevation of the top of the flagstaff is 24 Calculate the height of the flagstaff. 4
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