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CBSE Class 10 Pre Board 2020 : Mathematics Basic - Prelim 2 (Kendriya Vidyalaya (KV) Agra)

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KENDRIYA VIDYALAYA SANGATHAN, AGRA REGION II PRE BOARD (SET D) SESSION (2019-20) MATHEMATICS-BASIC (Code 241) TIME: 3 Hours CLASS: X Maximum Marks: 80 General Instructions: 1. All questions are compulsory. 2. The Question Paper consists of 40 questions divided into four sections A, B C and D. 3. Section A contains 20 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 8 questions of 3 marks each and Section D contains 6 questions of 4 marks each. 4. There is no overall choice in the paper. However internal choice is provided in two question of 1 mark, two questions in 2 marks, three questions in 3 marks and three questions of 4 marks. 5. Use of calculators is not permitted. Section-A Q 1- Q 10 are multiple choice questions. Select the most appropriate answer from the given options. 1 1 HCF of 52 x 32 and 35 x 53 is (a) 53 x 35 (c) 53 x 32 2 (b) 5 x 33 (d) 52 x 32 The product of the zeroes of 2x2 +kx +6is 1 (a) 2 (c) -3 3 (b) 3 (d) 4 If 4x2 -6x m is divisible by x-3, the value of m is (a) 18 (c) 20 1 (b) 45 (d) 36 4 The pair of equations 5x 15y = 40 and 3x 9y =24 has 5 (a) one solution (c) infinitely many solutions If the nth term of AP 2n+1 , then the third term of AP is (a) 2 (c) 12 (b) 7 (d) 21 Page 1 of 5 1 (b) two solutions (d) no solution 1 6 If sin = cos , then value of is 1 (a) 300 (c) 600 7 (b) 450 (d) 900 The distance between (0,3) and (4,0) 1 (a) 2 unit (c) 4 unit (b) 3 unit (d) 5 unit 8 A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is : (a) 12 cm (b) 13 cm (c) 8.5 cm (d) 119 cm. 1 9 The length of diagonals of a rhombus are 16 cm. and 12 cm. then the area of Rhombus is 1 (a) 98 cm2 (c) 192 cm2 10 (b) 96 cm2 (d) 28 cm2 The value of sin2200 + sin2700 1 (a) 0 (c) 2 (b) 1 (d) -1 (Q 11- Q 15) Fill in the blanks 11 The mean of first 5 prime number is ................................... 1 12 If the probability of winning a game is 0.3. the probability of losing is.................... 1 13 If the product of two numbers are 2500 and their HCF is 50 , then the LCM is............... 1 OR Express 462 as a product of its Prime factors? 14 If 15 cotA =8 then sinA is ............................... 1 OR If sinA = 3/10 , The value of tanA is ............................ 15 ABC PQR , ar(ABC)= 81cm2 and ar(PQR)=121 cm2 . af altitude AD= 9 cm. then altitude PM= .............. 1 (Q 16- Q 20) Answer the following 16 The radii of two circles are 19 cm and 9 cm respectively.Find the radius of the circle which has circumference equalto the sum of the circumferences of the two circles. Page 2 of 5 1 17 On which axis does the point P(0,2) lie ? 1 18 Without actually performing the long division, state whether the following rationalnumber will have a 13 terminating decimal expansion or a non-terminating repeating decimalexpansion: 1250 1 19 How many face cards are there in well suffled deck of 52 cards. 1 20 Find the mid point of the points (3,4) and (2,8) 1 Section-B 21 Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is 8? A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag.What is the probability that the ball drawn is (i) red ? (ii) not red? OR One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card A quadrilateral ABCD is drawn to circumscribe a circle. Prove thatAB + CD = AD + BC 2 24 Evaluate: 2 tan2 45 + cos2 30 sin2 60 OR Show that : tan 48 tan 23 tan 42 tan 67 = 1 2 25 The length of the minute hand of a clock is 14 cm. Find the area swept by the minutehand in 5 minutes. At the graphs in Fig given below. Each is the graph of y = p(x),where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x). 2 22 23 26 2 2 2 Section-C 27 Divide :3x3 + x2 + 2x + 5 by 1 + 2x + x2. 3 3 Page 3 of 5 28 Draw a triangle ABC with side BC = 7 cm, B = 45 , C = 30 . Then, construct atriangle whose sides 3 are4times the corresponding sides of ABC. OR 29 Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60 . In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use = 3.14) 3 30 Prove that sec A (1 sin A)(sec A + tan A) = 1. 3 OR (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2A 31 Prove that 3 is an irrational. 3 32 Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that PTQ = 2 OPQ. 3 33 In what ratio does the point ( 4, 6) divide the line segment joining the points A( 6, 10) and B(3, 8 3 34 Draw the graphs of the equations x y + 1 = 0 and 3x + 2y 12 = 0. and find the solution. 3 Section-D 35 36 37 The difference of squares of two numbers is 180. The square of the smaller number is 8times the larger 4 number. Find the two numbers. 4 The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is44. Find the first three terms of the AP. OR In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class Iwill plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students? 4 From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30 . A flag is hoisted at the top of the building and the angle of elevationof the top of the flagstaff from P is 45 . Find the length of the flagstaff and the distance of the building from the point P. Page 4 of 5 38 Prove that The ratio of the areas of two similar triangles is equal to the square of the ratio of their Corresponding sides. OR In an Equilateral Triangle, Prove that three times the square of one side is equal to four times the squares of one of its altitudes. 4 39 Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm. into a cubical pond which is 50 m long and 44m wide. In what time will the level of water in the pond rise by 21 cm. 4 OR 40 A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim.When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth ofthe water flows out. Find the number of lead shots dropped in the vessel. 4 Find mean and mode of the following data. Class interval 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 - 100 Frequency 2 5 9 12 17 20 15 9 7 4 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx END OF PAPER XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Page 5 of 5

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