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GOKULDHAM HIGH SCHOOL & JUNIOR COLLEGE SECONDARY SECTION (2023-2024) PRELIMINARY EXAMINATION SUBJECT : MATHEMATICS GRADE: 10 MARKS: 80 DATE: 08.01.2024 TIME: 2 hours 30 minutes Answers 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 time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from 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 rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [] Mathematical tables are provided. This paper consists of 9 printed pages and a blank page. SECTION A (Attempt all questions from this section) Question 1 Choose and write the correct answers to the questions from the given options: [15] [Do not copy the question.] (i) The values of p for which the quadratic equation px +4x +1 = 0 has distinct real roots are a) < 4 b) 4 c) >4 d) 4 (ii) A shopkeeper sells an article and paid C.G.S.T. of Rs. 40 on which GST is @16% ,then the profit of shopkeeper is a) Rs.800 b) Rs.600 c) Rs.500 d) Rs.300 (iii) If order of a matrix is 2 x 3 ,then the number of elements are a) 2 b) 3 c) 5 d) 6 1 GRADE 10 (iv) (v) (vi) (vii) (viii) MATHEMATICS The twelfth term from end of A.P. 2, 4, 6, ...., 100 will be a) 80 b) 78 c) 76 d) 74 A 14m long ladder rests at point X on a wall, the foot of the ladder is 7m from the wall, angle of elevation of point X from the foot of the ladder is 1.The ladder is moved closer to the wall and it rests at point Y directly above point X, angle of elevation of point Y from the foot of the ladder is 2. Then a) 1 = 2 b) 1 < 2 c) 1 > 2 d) 1 2 If ABC ~ DBA, then: a) AB = BC DB b) AB = AC BC c) AB = AD BD d) AB = AD AC Mean proportional of 3 and 27 is a) 9 b) 3 c) 27 d) 81 ASSERTION (A) :The interest earned on Rs.1000 in a recurring deposit for 3 years at 8%p.a is equal to Rs.4440 given that maturity value is Rs.40,440. REASON(R):The interest earned in a recurring deposit is given by the formula I =M.V.+ n m.d. where M.V is maturity value, n is time in months, m.d. is monthly deposit a) b) c) d) A is true, R is false A is false, R is true Both A and R are true Both A and R are false 2 GRADE 10 (ix) (x) (xi) (xii) (xiii) MATHEMATICS If a solid right circular cone of height 24 cm and base radius 6cm is melted and recast in the shape of a sphere, the radius of the sphere is a) 4 cm b) 6 cm c) 8 cm d) 10 cm Which of the following cannot be the probability of an event? a) 1.5 b) 3/5 c) 25% d) 0.3 At what price should a 9% Rs.100 share be quoted when the money is worth 6%? a) Rs.100 b) Rs.125 c) Rs.150 d) Rs.175 The slope of a line parallel to the line 3x = 4y + 11 is a) 3/4 b) 3/4 c) 4/3 d) 4/3 In the given figure, O is the centre of a circle and OAB =50 . Then, CDA =? a) b) c) d) (xiv) 25 40 75 50 tan A/(1+tan A) is equal to a) 1-cos A b) 1-sin A c) sec A d) cosec A 3 GRADE 10 (xv) MATHEMATICS The locus of a point equidistant from two fixed points A and B in the same plane is a) a line parallel to AB. b) a line perpendicular to AB at A. c) the perpendicular bisector of AB. d) a circle passing through A and B. Question 2 (i) Fateh deposits a certain sum of money every month in a recurring deposit account for 2years.If the bank pays interest at 10% p.a. and Fateh receives Rs.66,250 as the maturity value, what sum of money did he deposit every month? [4] (ii) The line joining the points A (4, 4 ) and B ( 8 , 8 ) is divided by the x-axis at point P. Find (showing all working/reason): (a)AP: PB (b)co-ordinates of P (c)angle of inclination of AB (iii) Prove the identity: (cosecA sinA)(secA cosA)( tanA + cotA) =1 [4] [4] Question 3 (i) A toy is in the shape of a right circular cylinder with a cone on one side and a hemisphere on the other, all with the same radius 5cm.The length of the cylindrical part is 13cm and the total length of the toy is 30cm. 13cm 30cm If the hemisphere and the cylindrical parts are to be painted in yellow and the conical part in red, calculate the surface area (to the nearest whole number) painted in (a) Yellow (b) Red. [Use = 3.14] [4] 4 GRADE 10 (ii) MATHEMATICS In the given diagram, ABCD is a cyclic quadrilateral and BD is diameter of circle with centre O. TA and TC are tangents. BCT= 20 and LBAT=35 ,find C (a) ADC. 20 (b) AOC. T B (c) DBA (d) ATC O D 35 [4] A (iii) Use a graph paper for this question. Use scale: 2cm = 1unit along both x and y-axes. (a)Plot the points O(0,0), A( 4, 4), B( 4, 0) and C(0, 3) (b) Reflect points A and B in the y-axis, name them as A and B and write their coordinates. (c)Write the geometrical name of the closed figure OABCB A . (d)Name a point on the figure which is invariant under reflection in y-axis, write its coordinates. SECTION B (Attempt any four questions from this section) Question 4 (i) The following bill shows the GST rates and the marked price of articles: Items Almonds Pulses Watch BILL: GENERAL STORE Quantity Rate Rate of GST 1kg 8 kg 1 Rs.800/kg Rs.125/kg Rs.2000 12% 0% 28% Calculate: (a) the total CGST paid to the Government for all the items (b) the total GST paid to the government (c) the total amount to be paid for the above bill. (ii) [5] Solve the following quadratic equation: 1 2x = 7 Give your answer correct to three significant figures. 5 [3] [3] GRADE 10 MATHEMATICS (iii) In the figure given below, AC bisects BAD and AB=16cm, AC = 12cm, AD = 9 cm. A (a) Prove that ABC~ ACD (b)Find area of ABC : area of ACD (c)Find area of ACD : area of quadrilateral ADCB. D 12cm C B [4] Question 5 (i) Find mean of the following distribution by step deviation method:Marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80 (ii) Given A = [ 0 No. of students 4 7 9 12 9 6 3 0 ],B=[ 2 1 [3] 2 ] and C = [ 0 2 2 ]. 2 [3] Find the values of p and q if BA= (iii) Chords AB and CD of a circle intersect externally at point P as given in the diagram below. Calculate the : (a)value of x. C D (b)length of AP. 1 P B A 6 [4] GRADE 10 MATHEMATICS Question 6 (i) Use graph paper for this question. Draw a histogram from the following frequency distribution and estimate the mode from the graph. [Scale 2cm =5 units on one axis and 2cm =2 units on the other ] Class interval Frequency (ii) 0-5 5-10 2 5 10-15 15-20 18 14 20-25 8 25-30 5 [3] The first term of a G.P with positive common ratio is 1.The sum of its 3rd [3] and 5th term is 90. Find the positive common ratio and this G.P. (iii) The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq.cm. If the volume of the tube is 176 cubic cm, Find the inner and outer radii of the tube. [4] Question 7 (i) The monthly income of a group of 320 employees in a company is given below: Monthly income No. of employees 6000 - 7000 7000 - 8000 20 45 8000 - 9000 65 9000 10000 10000 - 11000 95 60 11000 - 12000 30 12000 - 13000 5 Draw an ogive of the given distribution on a graph sheet. [Scale: 2cm=Rs.1000 on one axis and 2cm=50 employees on the other axis.] From the graph, estimate : (a) the median wage. (b) the number of employees whose income is below Rs.8500. (c)If the salary of a senior employee is above Rs.11,500, find the number of senior employees in the company. [5] (d)the upper quartile. 7 GRADE 10 (ii) MATHEMATICS A and B are two points on the co-ordinate axes as shown in the figure. P( 2, 3) is the midpoint of AB. Find the Y (a) coordinates of A and B A (b) slope of AB P( 2, 3) (c)slope of CD ,the perpendicular bisector of AB X B (d)equation of CD X [5] Y Question 8 (i) Solve the following inequation. Write the solution set and represent it on a real number line: 2 + 10x < 13x +10 24 +10x , x Z (ii) [3] In the diagram given below TD is a tangent to the circle with centre O at point D. Secants ABC and DBF intersect at point B on the circle. BCF is an equilateral triangle Find: F (a) ABD (b) DAO (c) TDA D T (iii) The angle of elevation of the top of a building under construction was 30 from a point P on the ground, 120 m away from its base. After its completion when the building was again observed from the same point, angle of elevation of the new top was 60 . How much higher was the building raised, from the time it was first observed? Question 9 (i) a +3ab . If b +3a b. = 172 , fine a:b using properties of proportion. 171 8 [3] [4] [3] GRADE 10 (ii) MATHEMATICS In winter, a train travels a distance of 264 km at a certain speed. In summer, it travels 8km/h faster than in winter and takes 22 minutes less than in winter. [3] Find it's speed in winter. (iii) Use ruler and compass only for answering this question. Construct a ABC with BC = 6cm, ABC= 120 and AB=3.5cm. (a)Find and name the locus of points equidistant from AB and BC. (b)Construct a circle such that all three sides of above ABC are tangents to it. (c)Measure and write the radius of this circle in part (b). (d)Measure and write the length of tangent to this circle from point A in your [4] construction. Question 10 (i) Use factor theorem to factorise the following polynomial completely: [3] 6x + 17x + 4x 12 (ii) Amrita buys 52 shares of nominal value Rs.100 available at Rs.132. (a) What is her investment? (b)If the dividend is 12% what will be her annual income? (c)If she wants to increase her annual income by Rs.240, how many extra shares should she buy? [3] (iii) There are 12 cards each numbered 1 to 12.What is the probability that a card picked up randomly has (a) a prime number (b) a number between 3 and 11 (c) a square number [4] (d) a number divisible by 2 and 3 ***** 9
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