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arnniwas Bajaj engish bigh school Ramniwas Bajaj English High School First Preliminary Examination 2022 2023 Mathematics Max. Marks: 80 Grade: 10 30 min Time Allowed: 2 hour Date: 25/11/22 INSTRUCTIONS: Answers to this paper must be written on the paper separately. the first 10 minutes. Y o u will not be allowed to write during Question Paper. T h i s time is to be spent in reading the the answers. this paper is the time allowed for writing T h e time given at the head of B. Section Section A and any four questions from on Attempt all questions from done be clearly shown, and must be All working, including rough work, must the same sheet as the rest of the answer Omission of essential The intended marks working will result in loss of marks. for questions or parts ofquestions are given in brackets []. Section A (40 Marks) (Attempt all questions from this Section.) Question1 Choose the correct answers to the questions from the given options: 15 When Mr. Desai stayed in a hotel for 2 days, he had to pay 7080 hotel for a unit of including 18% GST. What is the tariff ofthe accommodation? b.3250 d3540 The solution set for the given inequation is a. 3500 C.3000 (i) 18 4x -2,xEI b. {1,2,3,4,5} d. {-5,-4,-3,-2,-1,0,1,2,3,4,53 a. 15} (ii) (iv) C5,6,7,8.. 30x+ 225 = 0 are The nature of roots for the equation:x b. Imaginary a. Rational and unequal d. Irrational and unequal cReal and equal The product of two consecutive natural numbers which are multiples of 3, is equal to 810. Find the two numbers a. 81,10 b. 27,30 C. 18,45 d. 270,3 6 Write the order of the matrix 7 () (vi) 1 2 and classify it 8 b Rectangular Matrix 3 x 2 a. Column Matrix 2 x 3 C. Null Matrix 3 x 2 d. Square Matrix2 x3 Find the value of x, given that A2 = B A- and B=l0 Page 1 off6 english highschooi UNIEASE YOUR POTENTIA b (vii) difference C. 28 If the first term of d. 42 an 5 t ( 2 - 1 4 AP is-27 and the common 5+2 which difference is 3 term is 0? C. 12th term AB is diameter of a b. 10th term d. 1st term circle with centre C (-2,5). If A is (4,-3), 5-34 5-3 the ( coordinates of point B are b. (13,8) a. (2,-2) C. (6,-8) (x Is b. 35 29 a. 8th term ix) common 4 is a (vii) 36 a. 144 d. 24 C. 48 term is 5 and AP whose first The 7th term of an d(-8,13) 0+3 ,- Point P(a,b) becomes P(-a,-b) when reflection is in a) x axis b) y axis origin d) Invariant (xi) In the figure given below, AB || DE, AC = 3 cm, CE = 7.5 cm and BD = 14 cm. Calculate DC. B E 5 cm C. 4 cm xii) The value of che a 1 0 cm d. 8 cm x in the given figure is 35 P 800 60 xii) 'a' is the mean of 5,10,15,20,20 b. 70 d. 750 then the value of a is Page 2 of 6 Ramniwas Bajaj english high school UNLEASH YOUR PGTENTIAL (xiv) a. 20 b. 25 14 d. 16 A dice is thrown once, the probability of getting a number greater than 2 is a. b. 6 d. If the radius of a cylinder is 14 cm and height is 10 cm, then its curved (xv) surface area is b. 6160 cm3 d. 6160 cm2 a880cm2 C. 880 cm3 Question 2 [4 a Mr. Britto opened a Recurring deposit account in a bank and deposited 800 per month for 1 4 years. If he received 15,084 at thetime of maturity find the rate of interest per annum. 6 Using properties of proportion find x : y,given: [41 x2+2xy*3y23 3y+9 2x+4 cProve that: (1+ cot0 - cosec@)(1 + tan6 + sec@) = 2 41 Question3 4 a) From a solid wooden cylinder of height 28 cm and diameter 6cm, two conical cavities are hollowed out. The diameter of the 10.5 cm. Take r cones are also of 6cm and find the volume = height of the remaining solid. 25. 52 m b) ABC is a triangle and G(4,3) is the centroid of the triangle. If A(1,3) ,B=(4,b) and C=(a,1) , find a and b. Find the length ofside BC. 5 c)Use graph paper to answer the following questions. and Q(0,5). Reflect Q in the origin to get () (i) Plot ii) (iv) (v) Reflect P and R in x-axis to get P and R P(3,1) 4 5] Q Reflect P in y-axis to get R GIve a name to figure PQRR'QP' e e Find its perimeter. 4 n Page 3 of 6 Ramniwas Bajai english high schoof UNLEASEH YOUR POTENTIAL SECTIONB (40 Marks) Attempt any four questions from this Section Question 4 a) Ms. Anjali visits the market and buys the following articles: 13 Medicines costing950, SGST @2.5% A pair of shoes costing 3000, SGST @9% A Laptop bag costing 1000 with a discount of 30% , GST Calculate () the total amount of GST paid. (i) The total bill amount including GST paid by b) Solve and give your answer to correct to 3 (x- 1)2 - Ms. 0-50 significant figures 50-100 (in Rupees) No. of students On a 10 graph paper, draw a histogram Anjali. 13 3x +4 = 0 c) The daily pocket expenses of some students in Pocket expenses @ 18%. for the the mode. a class are given below. 4] 100-150 150-200 200-250 24 18 6 given distribution and estimate Question5 a) IfA= find the value of 54 - A [3 b) In the given figure, AC is the 31 diameter of the circle with centre O. Chords BA and CD are extended meet at point P. If angle P = 35 and angle ACB 20 , calculate: (i) angle 2 BDC (i) angle ABD and (ii) angle = AOB. o o 203 c) When the polynomials axs + 5 x - 11x-14 and 3x3+ax2-4x+ 20 are divided by (x + 2), the remainders are same. Find the value of a. 14] 2 Question 6 a) Find the equation of a line through P(5,-2) and perpendicular to the line [3 Page 4 of6 Ramniwas Bajaj english high school NLEASH 2x-7y1. If(k,k +2) lies that line, find the value of K. 31 (cosA-sin A)(1+tanA)= secA DProvethat 2 cos2A-1 of an APis 22 and c) The 4th tem common on YoUR rOTNTAL term 15th tem is 66. Find the first and the 4) the series to 8 terms. difference. Hence find the sum of Question 7 a) A box contains selecting a white balls some green, The probability of 13] yellow and white tennis balls. yellow ball is 1/3. If the box contains 10 in the box (b) probability of then find: (a) total number of balls and green ball is selecting a white ball. b) height 21cm is melted down and recast into spheres of radius 3.5 cm. Calculate the number of spheres that cylinder of A solid metal radius 14 cm and 131 can be made. c) In the given figure below, AD is a 4 diameter O is the centre of the circle. AD is parallel to BC and zCBD = 32 Find () 20BD (i) AOB 32 ii) 2BED Question 8 a Solve for x and write the solution set for the following inequation and represent 13 it on the number line. 3x+ 14 -2 4< 22x-4,x ER 3 b) Find the mean of the following distribution by step deviation method: Class 20-30 30-40 10 6 40-50 50-60 60-70 12 5 131 70-80 interval Frequency 41. Page 5 of6 Ramniwas Bajaj english high school UNLEASH YOUR POTENTIAL c) In the given diagram, ABC is a triangle 4] and BCFD is a parallelogram. AD:DB = 4:5 and EF = 15cm. 15 cm Find: (a) AE: EC (b) DE and (c) BC 4 F Question9 a) Some students planned eight of them failed to a picnic. join the The budget for the food was party, the 480. As [41 cost of the food for each member increased by R10. Find how many students went for the picnic. 2 * b) The following table shows a record from a hospital of 84 number of casualties due to accidents of different age groups. Age (in years) 5-15 No. of 15-25 25-35 35-45 45-55 10 15 13 25 6 casualties Taking a scale of 2cm = 10 years the other. Draw an ogive on one 55-65 65-75 10 causalities on /+ (i) The upper quartile 5 , 1 (Gii) The number of a) Using = and estimate e median. 4 Question 10 axis and 2 cm 6] casualties above age 57 years properties of proportion, solve for x. 2.x + V4x 2 - Given that x is positive. [31 1 - b) Construct a triangle ABC in which base BC =6cm, AB 5.5cm, angle ABC circumscribing the triangle ABC. Measure and write down the radius of the circle. n 120 . Construct = c) 2x V4x2-1 A a = circle observes the angle of elevation of the top of the building to be 30 . He walks towards it in horizontal line through its base. On covering 60m, the angle of elevation changes to 60. Find the height of the building to the 13] man nearest metre. 4] tt ****** Page 6 of 6
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