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L.R. & S.M. Vissanji Academy Secondary Section Second Priliminary Examination 2021 SUBJECT : Mathematics Grade : 10 Date : 22 / 03 /21 Marks : 80 Time: hrs INSTRUCTIONS: Answers to this paper must be written on the paper provided separately. You will not be allowed to write during the 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. This paper has_5_ printed pages. The intended marks for the questions or parts of questions are given alongside the questions. Section I [40] Attempt all questions in this section. Question 1 1 i) Find 5 numbers in AP, whose sum is 12 and ratio of first to last term is 2:3. [3] 2 4 1 ii) Given M = [ ]. Find k if M2 6M + kI = Null Matrix, [3] 1 2 where I is an identity matrix of order 2 x 2 . iii)There are two dice, one red and the other black. Both are rolled. [4] Simultaneously .Calculate the probability that (a) the number on the red dice is 3. (b) each dice shows 5 (c) the number on the black dice is either 2 or 4 (d) the product of two numbers is odd. Question 2 i) Solve 2 +1 2 + 2(3 ) 7, . Also graph the solution set on the number line.[3] i) solve the quadratic equation x2 -3(x+ 3) = 0; give your answer correct to two significant figures. [3] iii) If 2x3 + ax2 + bx- 2 has a factor ( x+ 2) and leaves a remainder 7 when divided by 2x -3 , find the value of a and b.with these values of a and b, factorise the given polynomial completely. [4] Question 3 i) If a , b , c and d are in proportion , prove that : [3] 3 2 +8 2 = 3 2 +8 2 . ii)T he numbers 6, 8, 10 ,12 ,13 and x are arranged in an ascending order .if the mean of the observation is equal to the median, find the value of x. [3] iii)In the given figure ,AP and BP are tangents to the circle with centre o . If CBP = 250 and CAP ,= 40O [4] Find (i) ADB (ii) AOB (iii) ACB (iv) APB . Question 4 i) Find the equation of the line passing through the point ( 0 ,-2) and the point of intersection of the lines 4x + 3y = 1 and 3x y + 9 =0. [3] ii) The radius and height of a cylinder are in the ratio 2 :7 . If the volume of the cylinder is 704cm 3 , find the total surface area of the cylinder. [3] iii) Puneet has a recurring deposit account in a bank and deposits Rs 400 per month. If he receives Rs 10100 at the time of maturity,find the time for which the account is held if the rate of interest is 5% p.a. [4] Section II [40] Attempt any four questions in this section Question 5 i) Use graph paper for this question. The point P (3 , 4) is reflected to P in the x-axis and O is the image of O(origin) in the line PP . Find: (a) the coordinates of P and O (b) the length of segments PP and OO . [3] ii) A two digit number contains the smaller of two digits in the unit s place .The product of the digits is 24 and the difference between the digits is 5 .Find the [3] number. iii) Using step deviation method . Calculate the mean marks of the following distribution . State the modal class. [4] Class 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 intervals Frequency 5 20 10 10 9 6 12 8 Question 6 i) The king ,queen and jack of clubs are removed from a deck of 52 playing cards and well shuffled . one card is selected from the remaining cards. Find the probability of getting .(a) a heart (b) a king ( c) a club (d) the 10 of hearts. [3] ii) Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9cm. [3] iii) Determine the ratio in which the point (-6 ,a) divides the join of A( -3 ,1) and B(-8 ,9). Also , find the value of a. [4] Question 7 i) If -5 is a root of the quadratic equation 2x2 + px -15 = 0 and the quadratic equation p( x2 + x) + k = 0 has equal roots , find the value of k . [3] ii)The angles of elevation of the top of a rock from the top and foot of a 100m high tower are respectively 30o and 45o . find the height of the rock. [3] iii) If p= 4 + , Using properties of proportion find the value of +2 +2 + 2 [4] 2 Question 8 i) Prove 1 tan + 2 = + . ii) In the given figure ,PQRS is a cyclic quadrilateral Given QPS = 730 , PQS =550 and PSR =820 , Calculate : QRS , RQS and PRQ . [3] [3] iii) In , AB = 8cm , AC = 10cm and = 90 . P and Q are points on the sides AB and AC respectively such that PQ = 2cm and = 90 , find : (a) Area of (b) Area of quadrilateral PBCQ : Area of . [4] Question 9 a) Find two numbers such that the mean proportion between them is 9 and the third proportional to them is 243. [3] b) The 4th term of an A.P. is 22 and 15 th term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms. [3] c) A hollow metallic tube has an internal radius of 3cm and height 21cm. The thickness of the tube is 0.5cm. The tube is melted and cast into a right circular cone of height 7cm. Find the radius of the cone correct to one decimal place. [4] Question 10 i) A manufacturer sells a refrigerator to a wholesaler for Rs 30000. The wholesaler sells it to a retailer at a profit of Rs 2000. The retailer sells it to a customer and makes a profit of Rs. 3000. If GST charged is 18%, find: a) The GST deposited by the wholesaler with government. b) The total amount of GST received by the government on sale of refrigerator. c) The amount paid by the customer for it. [3] ii) Use graph paper for this question. Plot P (2 , 4 ), Q ( 2 , 1 ) and R ( 5 , 0 ). Reflect P and Q in x-axis to get P and Q . [3] a) Write co-ordinates of P and Q b) Write geometrical name to figure PQQ P R c) Find area of the figure so formed. iii) In the adjoining figure, P and Q are points on AB and AC respectively [4] such that PQ BC. Prove: a) APQ ~ ABC b) If AP : PB = 4 : 3, find PQ if BC = 21 cm c) Find area APQ : area ABC Question 11 i) A plane travels a distance of 1600 km at an average speed of x km/hr. On the return journey, due to bad weather, as the speed was reduced by 40 km/hr, it took 1 hour 20 minutes more than onward journey. Find x. [4] ii)Draw an ogive for the following distribution: Monthly income (in Rs) 600700 700800 800900 9001000 10001100 11001200 12001300 No of employees Hence (1) The (2) The (3) The 40 68 86 120 90 40 26 determine: median income numer of employees whose income exceeds Rs 1180 lower and upper quartiles. [6] ************************************************************************************************
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