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CBSE Class 10 Pre Board 2020 : Mathematics Basic - Prelim 1 (Kendriya Vidyalaya (KV) Agra)

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KENDRIYA VIDYALAYA SANGATHAN, AGRA REGION PRE BOARD SESSION (2019-20) MATHEMATICS (Basic) SET D 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 to 10 are multiple choice questions. Select the most appropriate answer from the given options. 1 The decimal expansion of 63 72 175 is a) terminating b) non terminating c) non terminating and repeating d) an irrational number 2 The weight of 40 eggs were recorded as below: Weight (gms) 85 - 90 90 - 95 95-100 100-105 105-110 No. of eggs 7 12 15 4 2 The lower limit of the modal class in the given data is a) 95 b) 90 c) 94.5 d) 100 3 The HCF of smallest two-digit composite number and smallest composite number is a) 40 b) 2 c) 10 d) 14 Page 1 of 7 4 For which value(s) of K , will the lines represented by the following pair of linear equations will have infinitely many solutions? 4x-y-5=0 8x-2y-k=0 a) all real values except 10 b) 10 c) 5/2 d) 5 The value of sin2 300 + sin2 600 is a) 0 b) 1 c) 2 3 d) not defined 6 If 15 tan A = 8, then find the value of sec A. a) 17 15 8 b) 15 15 c) 17 d) 7 8 17 If sin 2A = 2 sin A is true, then the value of A is a) 00 b) 900 c) 600 d)300 8 The mid point of a line segment with end points (-3, 4) and (10, -5) is a) (-13, -9) b) (-6.5, -4.5) c) (3.5, - 0.5) 9 The distance of the point (-3 , -4 ) from the x-axis (in units) is a) 3 b) -3 c) 4 d) 5 10 If the distance between the points (8, p)and (4, 3) is 5, then the value of p is: Page 2 of 7 d) None of these a) 6 b) 0 c) both (a) and (b) d) None of these Fill in the blanks: 11 If the numerical values of volume and surface area of a sphere are equal, then the diameter of the sphere is .. 12 If and are the zeroes of the polynomial x2 -6x -5, then the value of + is ............................... OR If and are the zeroes of the polynomial 2x2 - x -2, then the value of is ............................... 13 The sides of two similar triangles ABC and PQR are 7cm. and 9 cm. respectively, then the ratio of the areas of these two triangles is .......................................... 14 If a, a-2 and 3a are in A.P. then the value of a is ......................................... 15 When a dice is thrown , the probability of getting prime numbers is................................ Answer the following: 16 Write one rational and one irrational number between 2 and 3. 17 In figure, PT = 2 cm, TR=4 cm, ST||QR. Find the ratios of area of PST & PQR. 18 If the angle between two tangents drawn from an external point P to a circle of radius r and centre O is 600, then find the length of OP. OR If the radii of two concentric circles are 4 cm and 5 cm, then find the length of each chord of one circle which is tangent to the other circle. 19 Which term of the AP : 21, 18, 15, . . . is 81? 20 Find the discriminant of the quadratic equation 2x2 4x + 3 = 0 Section-B 21 Find the sum of odd numbers between 0 and 50. Page 3 of 7 22 Find the angle of elevation of the sun when the shadow of a pole h metres high is 3 h metres long. 23 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. find the length of PQ . 24 If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how much water flows out of the cylindrical cup? 25 A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is11/20 and that of blue ball is1/5, Find the number of black balls . OR Two coins are tossed simultaneously. What is the probability of getting at most one head . 26 Let ABC ~ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF =15.4 cm, find BC. OR Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD. Section-C 27 Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients. 28 Find the area of a triangle whose vertices are (1, 1), ( 4, 6) and ( 3, 5). 29 Prove that: 1 +1 = 1 + tan + cot OR Prove that (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A 30 ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region. Page 4 of 7 31 Determine the A P and 12th term if the sum of the first term of an A P is given by = 3 2 4 . 32 The following distribution gives the daily income of 50 workers of a factory : Daily incone (in Rs.) 100-120 120-140 140-160 160-180 180-200 No. of Workers 12 14 8 6 10 Find the mean. 33 The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is 105 and for a journey of 15 km, the charge paid is 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of25 km? OR From a bus stand in Bangalore, if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is 46; but if we buy 3 tickets to Malleswaramand 5 tickets to Yeshwanthpur the total cost is 74. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur. 34 There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point? OR Prove that 3 is an irrational number. Section-D 35 A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. OR The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field. 36 A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 600 and from the same point the angle of elevation of the top of the pedestal is 450. Find the height of the pedestal. Page 5 of 7 37 In an equilateral triangle ABC, D is a point on side BC such that BD =3 BC. Prove that9AD2 =7AB2 38 Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle 3 whose sides are 2 times the corresponding sides of the isosceles triangle. OR 1 Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. 39 A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take = 3.14) OR Ajay made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take =22/7) Page 6 of 7 40 The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f. Daily pocket allowance Number of children 11 - 13 7 13 - 15 15 17 6 9 17 19 13 END OF PAPER Page 7 of 7 19 - 21 f 21 23 5 23 - 25 4

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