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MATHEMATICS (Std X) (Two hours and a half) 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. ---------------------------------------------------------------------------------------------------------------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 [ ]. SECTION A (40 Marks) Attempt all questions from this Section Question 1 A. Renu has a cumulative deposit account of 200 per month at 10% per annum. If she gets 6775 at the time of maturity, find the total time for which the account was held. [3] B. Given A= { : 8 < 5 + 2 17, }, = { : 2 7 + 3 < 17, } Represent A and B on two different number lines. Write down the elements of . [3] C. Factorise the expression ( ) = 2 X 7 Y 3 + 18. Hence, find all possible values of for which f( ) = 0. [4] Question 2 2 A. Find the matrix A, if = Z 0 \ 1 [ and Y = + Y 1 B. If , , are in continued proportion and ( ) = 2 , prove that: = [3] Y(`ab) ` [3] C. Find using quadratic formula, the roots of the following quadratic equations, if they exist (i) 3 Y 5 + 2 = 0 (ii) Y + 4 + 5 = 0 [4] Question 3 A. Anil went to a shop to buy a bicycle costing 10620.The rate of CGST is 9%. He asks the shopkeeper to reduce the price of the bicycle to such an extent so that he has to pay 10620 inclusive GST. Find the reduction needed in the price of the bicycle. [3] This Paper consists of 6 pages Std X Preliminary Examination 2020-21 Mathematics- Monday,18th January, 2021 Page1 B. In the given figure, = = , = 38 . Calculate: (i) (ii) [3] C. Find the ratio in which the line joining (6,5) and (4, 3) is divided by the line = 2. Also, find the co-ordinates of the point of intersection. [4] Question 4 A. Prove that klmnoYklmp n Yqrk p noqrkn = [3] B. From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid. [3] C. In the given figure, is a point on such that : = 4: 3 and . (i) Calculate : (ii) If = 90 , = 90 and = 6 , calculate the length of . [4] This Paper consists of 6 pages Std X Preliminary Examination 2020-21 Mathematics- Monday,18th January, 2021 Page2 SECTION B (40 Marks) Attempt any four questions from this section Question 5 A. Find the solution set of 3( 2) < 1, where {1,2,3,4,5,6}. 2 B. If 3Z 1 4 [ + 2 } 0 3 ~=Z 2 15 3 [,find the values of , and . 4 [3] [3] C. Use a graph paper to answer the following questions. Take 1 = 1unit along the axes. Plot the points ( 2,0), (4,0), (1,4) and ( 2,4). (i) Draw the line of symmetry of ABC. Name it 1. (ii) Point is reflected about the line 1 to get the image . Write the co-ordinates of . (iii) Name the figure . (iv) Draw all the lines of symmetry of the figure . [4] Question 6 A. Find the positive value of for which the equations Y + + 64 = 0 and Y 8 + = 0 will have real roots. [3] B. Which term of the . 5,12,19,26,33, ..will be 35 more than its 12 term? [3] C. The following figure shows a parallelogram whose side is parallel to the axis, = 60 and vertex = (7,5). Find the equations of and . [4] Question 7 A. Given that `p aX`b bp aX` b = X Y using the properties of proportion find : . [3] This Paper consists of 6 pages Std X Preliminary Examination 2020-21 Mathematics- Monday,18th January, 2021 Page3 B. If = and = , prove that: ` b = 1 [3] C. An aeroplane travelled a distance of 400km at an average speed of / . On the return journey, the speed was increased by 40 / . Write down an expression for the time taken for: (i) The onward journey (in terms of ). (ii) The return journey. If the return journey took 30 minutes less than the onward journey, write an equation in and find the value of . [4] Question 8 A. Find the equation of a line which has y-intercept 4, and it is parallel to the line 2 3 7 = 0. Find the co-ordinates of the point, where the lines cuts . [3] B. In the adjoining figure, and intersect each other at point . If = 90 , = 5 , = 4 = 9 , Find . [3] C. The histogram given below represents the marks obtained by some candidates in an examination. Using the data in the diagram, calculate the mean marks. [4] This Paper consists of 6 pages Std X Preliminary Examination 2020-21 Mathematics- Monday,18th January, 2021 Page4 Question 9 A. The first term of an AP is 20 and the sum of its first seven terms is 2100; find the 31st term of this AP. [3] B. The angles of depression of two ships A and B as observed from the top of a light house 60m high are 60 and 45 respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number. [3] C. A die has six faces, marked as The die is thrown once. What is the probability of getting : (i) a positive integer (ii) an integer greater than 3 (iii) the smallest integer [4] Question 10 A. The total surface area of a right circular cone of slant height 13 is 90 Y . Calculate (i) It s radius in . (ii) It s volume in cm3 in terms of . [4] B. The monthly income of a group of 320 employees in a company is given below: [6] Monthly income (in ) 6000-7000 7000-8000 8000-9000 9000-10000 10000-11000 11000-12000 12000-13000 Number of employees 20 45 65 95 60 30 5 Draw an ogive of the given distribution on a graph sheet taking 1cm= 1000 on one axis and 1cm= 50 employees on the other axis. From the graph determine: (i) The median wage; (ii) The number of employees whose income is below 8500; This Paper consists of 6 pages Std X Preliminary Examination 2020-21 Mathematics- Monday,18th January, 2021 Page5 (iii) If the salary of a senior employee is above 11500, find the number of senior employees of the company; (iv) The upper quartile. Question 11 A. The angle of elevation of a jet-plane from a point A on the ground is 60 . After a flight of 15 seconds, the angle of elevation changes to 30 . If the jet-plane if flying horizontally at a constant height of 1500 3 m, find the speed of the jet-plane. [3] B. In the given figure below, the diagonals of a cyclic quadrilateral intersect in and the area of the triangle is 24 Y . If = 8 and = 5 , calculate the area of . [3] C. A bag contains 5 black balls, 7 blue balls, 4 white balls and 6 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is (i) Red (ii) Black or white (iii) Not blue (iv) Neither black nor blue [4] JJJJJJJJJAll the bestJJJJJJJJ This Paper consists of 6 pages Std X Preliminary Examination 2020-21 Mathematics- Monday,18th January, 2021 Page6
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