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CBSE Class 10 Board Exam 2020 : Mathematics Basic (Series 3)

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CBSE 10
Kendriya Vidyalaya (KV), Kamla Nehru Nagar, Ghaziabad

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SET 1 Series : JBB/3 . Code No. . 430/3/1 - - Roll No. Candidates must write the Code on the title page of the answer-book. (I) (II) - (I) 15 - (II) - - NOTE Please check that this question paper contains 15 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (III) Please check that this question paper contains 40 questions. - 40 (IV) (IV) Please write down the Serial Number of the question in the , (III) (V) - 15 (V) - 10.15 10.15 10.30 - - answer-book before attempting it. 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. ( ) MATHEMATICS (BASIC) {ZYm [aV g : 3 K Q>o A{YH$V A H$ Time allowed : 3 hours .430/3/1. 103A : 80 Maximum Marks : 80 1 P.T.O. : (i) - , , - 40 1. (ii) - 1 20 20 (iii) - 21 26 6 (iv) - 27 34 8 (v) - 35 40 6 (vi) - - , - , - , - (vii) , , (viii) 1 10 - , 1 , 245 1029 5 (a) 15 2. (b) 16 (c) 9 (d) 5 1 (d) 35 1 : 0-5 5-10 10-15 15-20 20-25 10 15 12 20 9 (a) 15 .430/3/1. (b) 25 (c) 30 2 General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper comprises four sections A, B, C and D. This question paper carries 40 questions. All questions are compulsory. (ii) Section A Question no. 1 to 20 comprises of 20 questions of one mark each. (iii) Section B Question no. 21 to 26 comprises of 6 questions of two marks each. (iv) Section C Question no. 27 to 34 comprises of 8 questions of three marks each. (v) Section D Question no. 35 to 40 comprises of 6 questions of four marks each. (vi) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of one mark, 2 questions of two marks, 3 questions of three marks and 3 questions of four marks. You have to attempt only one of the choices in such questions. (vii) In addition to this, separate instructions are given with each section and question, wherever necessary. (viii) Use of calculators is not permitted. Section A Question numbers 1 to 10 are multiple choice questions of 1 mark each. Select the correct choice. 1. 2. What is the largest number that divides 245 and 1029, leaving remainder 5 in each ? (a) 15 (b) 16 (c) 9 (d) 5 1 Consider the following distribution : Class 0-5 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 The sum of lower limits of the median class and the modal class is (a) 15 (b) 25 (c) 30 (d) 35 .430/3/1. 3 1 P.T.O. 3. 60 3 . . , : (a) 3 4. 1095 1168 (a) 5. (b) 3 26 (d) 6 1 25 26 (c) 13 16 (d) 15 16 1 (b) 1 52 (c) 1 13 3 52 1 4 3 1 (d) 1625 462 1 (d) 9 2 1 (d) 5 4 (b) 5 4 (c) 4 3 (d) ? 124 165 (b) 131 30 (c) 2027 625 (2x2 + 5x 9) , (a) 9. (c) 3 3 (k 1) x2 + kx + 1 4 k : (a) 8. 17 26 (a) 7. 3 3 2 52 ? (a) 6. (b) 5 2 (b) 5 2 (c) 9 2 (0, 4), (0, 0) (3, 0) : (a) 7 + .430/3/1. 5 (b) 5 (c) 10 4 (d) 12 1 3. If the two tangents inclined at an angle of 60 are drawn to a circle of radius 3 cm, then the length of each tangent is : (a) 3 cm 4. The simplest form of (a) 5. 17 26 1 25 26 (c) 13 16 (d) 15 16 1 (b) 1 52 (c) 1 13 (d) 3 52 1 5 4 (b) 5 4 (c) 4 3 (d) 4 3 1 Which of the following rational numbers is expressible as a terminating decimal ? 124 165 (b) 131 30 (c) 2027 625 (d) 1625 462 1 9 2 1 If and are the zeros of (2x2 + 5x 9), then the value of is (a) 9. (d) 6 cm If one zero of the quadratic polynomial, (k 1) x2 + kx + 1 is 4 then the value of k is (a) 8. (c) 3 3 cm 1095 is 1168 (b) 3 26 (a) 7. 3 3 cm 2 One card is drawn at random from a well shuffled deck of 52 cards. What is the probability of getting a Jack ? (a) 6. (b) 5 2 (b) 5 2 (c) 9 2 (d) The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is (a) 7 + .430/3/1. 5 (b) 5 (c) 10 5 (d) 12 1 P.T.O. 10. A( 3, b) B(1, b + 4) P( 1, 1) , b (a) 1 (b) 1 (c) 2 (d) 0 1 11 15 : 11. (a, b) (a, b) ________ 12. k 1 x + 2y = 3 5x + ky = 7 , ________. 1 13. (cos2 45 + cot2 45 ) ________ 1 14. (tan 27 cot 63 ) ________ 1 15. 2 : 3 , ________ 1 16-20 : 16. 25 sec = 7 , cot 3 sin + 2 cos 3 tan = 4 , 3 sin 2 cos 68 1 1 17. 14 1 39.6 .430/3/1. 6 1 10. If P( 1, 1) is the midpoint of the line segment joining A( 3, b) and B(1, b + 4), then b is equal to (a) 1 (b) 1 (c) 2 (d) 0 1 In Question numbers 11 to 15, fill in the blanks : 11. Distance between (a, b) and (a, b) is ________. 1 12. The value of k for which system of equations x + 2y = 3 and 5x + ky = 7 has no solution is ________. 1 13. The value of (cos2 45 + cot2 45 ) is ________. 1 14. The value of (tan 27 cot 63 ) is ________. 1 15. If ratio of the corresponding sides of two similar triangles is 2:3, then ratio of their perimeters is _________. 1 Answer the following questions, Question numbers 16 to 20. 16. If sec = 25 , then find the value of cot . 7 1 OR 3 sin + 2 cos If 3 tan = 4, then find the value of 3 sin 2 cos 1 17. The perimeter of a sector of a circle of radius 14 cm is 68 cm. Find the area of the sector. 1 OR The circumference of a circle is 39.6 cm. Find its area. .430/3/1. 7 1 P.T.O. 18. 19. , 1 1 , ABC AB AC D E DE || BC AD = 3.6 , AB = 10 AE = 4.5 , EC AC 1 1 20. 3y 1, 3y + 5 5y + 1 , y 1 21 26 21. 22. 5 , 8 7 (i) (ii) 2 2 9 .430/3/1. 8 2 18. A letter of English alphabet is chosen at random. Determine the probability that chosen letter is a consonant. 1 19. In Fig. 1, D and E are points on sides AB and AC respectively of a ABC such that DE || BC. If AD = 3.6 cm, AB = 10 cm and AE =4.5 cm, find EC and AC. 1 Fig. 1 20. If 3y 1, 3y + 5 and 5y + 1 are three consecutive terms of an A.P., then find the value of y. 1 Section B Question numbers 21 to 26 carry 2 marks each. 21. A bag contains 5 red, 8 white and 7 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is (i) red or white (ii) not a white ball 2 22. Two dice are thrown at the same time. Find the probability of getting different numbers on the two dice. 2 OR Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 9. .430/3/1. 9 2 P.T.O. 23. 2 ABC BC, CA AB P, Q R AB = 10 , AQ = 7 CQ = 5 BC 2 2 24. sec2 + cosec2 = tan + cot sin 1 cos = (cosec + cot ) 25. 2 2 , 216 , 2 x2 2px + 1 = 0 2 26. p 27 34 3 27. 1 2, (x3 4x2 7x + 10) , 3 28. 3 7 3 8 3 : 4 .430/3/1. 10 3 23. In Fig. 2, a circle is inscribed in a ABC, touching BC, CA and AB at P, Q and R respectively. If AB = 10 cm, AQ = 7 cm and CQ = 5 cm then find the length of BC. 2 Fig. 2 24. Prove that : sec2 + cosec2 = tan + cot 2 OR Prove that : sin = (cosec + cot ) 1 cos 2 25. Three cubes each of volume 216 cm3 are joined end to end to form a cuboid. Find the total surface area of resulting cuboid. 2 26. Find the values of p for which the quadratic equation x2 2px + 1 = 0 has no real roots. 2 Section C Question numbers 27 to 34 carry 3 marks each. 27. If 1 and 2 are the zeroes of the polynomial (x3 4x2 7x + 10), find its third zero. 3 28. Draw a circle of radius 3 cm. From a point 7 cm away from its centre, construct a pair of tangents to the circle. 3 OR Draw a line segment of 8 cm and divide it in the ratio 3 : 4. .430/3/1. 11 3 P.T.O. 29. 30. 121 3 , ? cos sin (1 tan ) + (1 cot ) = (cos + sin ) 3 3 (sin + cosec )2 + (cos + sec )2 = 7 + tan2 + cot2 . 3 2 , (7 2 2) 44, 96 404 . . (HCF) . . (LCM) 3 32. 3 33. 3 (desks) , A, B C : (i) (ii) A, B C B, AC 3 31. 3 -3 34. 10 18 .430/3/1. 12 3 29. A wire when bent in the form of an equilateral triangle encloses an area of 121 3 cm2. If the same wire is bent into the form of a circle, what will be the radius of the circle ? 30. Prove that cos sin + = (cos + sin ) (1 tan ) (1 cot ) 3 3 OR Prove that (sin + cosec )2 + (cos + sec )2 = 7 + tan2 + cot2 . 3 31. If 2 is given as an irrational number, then prove that (7 2 2) is an irrational number. OR Find HCF of 44, 96 and 404 by prime factorization method. Hence find their LCM. 3 32. Prove that the parallelogram circumscribing a circle is a rhombus. 3 33. In Fig. 3, arrangement of desks in a classroom is shown. Ashima, Bharti and Asha are seated at A, B and C respectively. Answer the following : (i) Find whether the girls are sitting in a line. (ii) If A, B and C are collinear, find the ratio in which point B divides the line segment joining A and C. 3 3 Fig.-3 34. A number consists of two digits whose sum is 10. If 18 is subtracted from the number, its digit are reversed. Find the number. .430/3/1. 13 3 P.T.O. 35 40 4 35. ` 2,000 5 ` 20 ? 36. 6 42 10 30 1 : 3 13 100 300 60 45 ( 3 = 1.732 ) 4 4 4 37. 7 . 38. 39. 40. 21 . . , 12 . . 15 . . 12 4 4 4 4 4 : 0-10 10-20 20-30 30-40 40-50 50-60 60-70 .430/3/1. 5 10 18 30 ____________ 14 20 12 5 4 Section D Question Nos. 35 to 40 carry 4 marks each. 35. Some students planned a picnic. The total budget for food was ` 2,000 but 5 students failed to attend the picnic and thus the cost for food for each member increased by ` 20. How many students attended the picnic and how much did each student pay for the food ? 36. The sum of first 6 terms of an A.P. is 42. The ratio of its 10th term to 30th term is 1:3. Find the first and the 13th term of the A.P. OR Find the sum of all odd numbers between 100 and 300. 37. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60 , and the angle of depression of its foot is 45 . Find the height of the tower. Given that 3 = 1.732. 38. In a right triangle, prove that the square of the hypotenuse is equal to sum of squares of the other two sides. OR Prove that the tangents drawn from an external point to a circle are equal in length. 39. A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to edge of the cube. Determine the volume of the remaining block. OR A solid metallic cylinder of diameter 12 cm and height 15 cm is melted and recast into 12 toys in the shape of a right circular cone mounted on a hemisphere of same radius. Find the radius of the hemisphere and total height of the toy, if the height of the cone is 3 times the radius. 4 4 4 4 4 4 4 4 40. Find the mean of the following data : Class Frequency .430/3/1. 0-10 10-20 20-30 30-40 40-50 50-60 60-70 5 10 18 30 20 12 5 ____________ 15 4 P.T.O. .430/3/1. 16

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