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

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KENDRIYA VIDYALAYA SANGATHAN , AGRA REGION II PRE BOARD EXAM- 2019-20 (SET D) CLASS: X SUB: MATHEMATICS STANDARD(041) MM: 80 GENERAL INSTRUCTIONS: 1. All the questions are compulsory. 2. The question paper consists of 40 questions divided into 4 sections A, B, C, D. 3. Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of marks each. 4. There is no overall choice. However an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, three questions of 3 marks each, and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. 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 : Q1. If ( 9 3 7 7 9 2x-6 ) (49 ) = ( ) ; the value of x is : 81 9 (a)12 (b) 9 (c) 8 (1) (d) 6 Q2. The ratio in which x-axis divides the line segment joining the points (5,4) and (2,-3) is : (1) (a)5:2 (b)3:4 (c)2:5 (d)4:3 Q3. If two positive integers a and b can be expressed as a=x3 y2 and b=x2 y3, where x and y are prime numbers , then their HCF is : (a) xy (1) (b)x2 y2 (c)x3 y3 Page 1 of 7 (d)none of these Q4. If one of the zeroes of the polynomial f(x)=(k2+4)x2+13x+4k is reciprocal of the other then k= ? (1) (a)2 (b)1 (c)-1 (d)-2 OR The graph of polynomial p(x)=x3-2x2-x+2 intersect x-axis at (a)no point (b)1 point (c)2 points (d)3points Q5.The value of tan 48 tan 23 tan 42 tan 67 is : (a) 1 (1) (b)9 (c)8 (d)0 Q6. If and are the roots of quadratic equation 4x2+3x+7=0 , then find the value of 1 1 + : (1) 7 (a)3 7 (b)-3 3 (c)7 3 (d)-7 Q7. The sum of first n odd natural number is : (a) n2 (b)n2-1 (1) (c)n2+1 (d)2n+1 Q8. The lines represented by pair of linear equations in two variables x 3=0 and y +-3=0 are : (a) parallel (c) coincident (b)perpendicular (1) (d)can t say Q9. The fourth vertex of the rectangle whose three vertices taken in order are (4,1), (7, 4), (13, 2) is : (1) (a) (10, 5) (b) (10, 5) (c) (8, 3) (d) (8, 3) Q10. If origin is the mid point of line segment joining point A(x,y) and b(2,3) then the value of x and y is : (1) (a)(2,-3) (b)(2,3) (c)(-2,3) (d)(-2,-3) (Q 11- Q 15) Fill in the blanks : Q11. If p divides k2 , then p also divides k . This statement is true if and only if p is a __________ number . (1) Page 2 of 7 Q12.The mean of first five prime numbers is ________ (1) Q13. Seventh term of AP is 40 . The sum of its first 13 terms is ____. (1) Q14. The ratio of areas of two similar triangles is 49:64 . The ratio of their respective medians is ______. (1) Q15. All __________ triangles are similar . (1) (Q 16- Q 20 ) Answer the following questions : Q16. In adjoining figure , line segment DE is parallel to side BC of triangle ABC . Also AD = 2 cm , BD = 3 cm , DE = 4 cm . Find the value of BC . (1) Q17. A chord of a circle is equal to the radius of the circle .Find the angle subtended by the chord at a point on minor arc . (1) OR The length of a tangent from a point A at a distance 5 cm from the Centre of the circle is 4 cm . Find the radius of the circle . Q18. Base radius of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Find the ratio of their volumes . (1) Q19. If sin 5A = cos 4A where both 5A and 4A are acute angles then what is the value of A . Q20.If P(E)= 0.05 than what is the probability of not E ? Page 3 of 7 (1) (1) SECTION B Q21. Which term of AP 72 , 63 , 54 , .. is 0 ? (2) Q22.If the angles of elevation of a tower from two points at a distance a and b (a>b) from its foot and in the same straight line from it are complementary. What is the height of the tower ? (2) Q23. The length of the diagonals of a rhombus is 16 cm and 12 cm respectively then find the side of rhombus . (2) OR Determine whether the triangle having sides (a-1) cm , 2 cm and (a+1) cm is a right angled triangle . Q24.Two tangents PA and PB are drawn to the circle with center O, such that APB = 1200. Prove that OP = 2AP . (2) Q25.How many spherical lead shots each having diameter 3 cm can be made from a solid cuboid made up of lead of dimensions 9 cm 11 cm 12 cm ? (2) Q26. Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly . One card is drawn from this box . Find the probability that the number on the card is : (i) a multiple of 7 (ii) a perfect square number (2) OR All kings and queens are removed from a pack 52 of playing cards .There remaining cards are well shuffled and then a card is drawn at random . Find the probability that this card is a (i) A red face card (ii) A black card SECTION C Q27. Show that 3 is an irrational number . (3) OR Find the largest positive integer that will divide 398 ,436 and 542 leaving remainder 7 , 11 and 15 respectively. Q28. Two zeroes of the cubic polynomial ax3+3x2-bx-6 are -1 and -2. Find the values of a and b. Page 4 of 7 (3) Q29. Find the value of k if the points A(8,1) ; B(k ,-4) and C(2,12k) are collinear . (3) Q30. For what values of k , does the following pair of linear equations has infinitely many solutions : (k-3)x + 3y =k kx + ky = 12 (3) OR 2 men and 5 boys can do a piece of work in 4 days. The same work is done by 3 men and 6 boys in 3 days. . Find the time taken by 1 man alone and by 1 boy alone to finish thework. Q31. If pth ,qth and rth terms of an AP are a ,b and c respectively then show that a(q-r) + b(r-p) + c(p-q) = 0 . Q32. If cos cos = m and cos sin (3) = n then show that (m2+n2)cos2 = n2. OR . Q33. In the figure given below, ABC is right angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3cm and AC = 4cm. Find the area of the shaded region. Page 5 of 7 (3) Q34. The table given below shows the frequency distribution of the scores obtained by 200 candidates in a BCA examination : Score (3) 200-250 Frequency 30 250-300 300-350 350-400 400-450 450-500 500-550 550-600 15 45 20 25 40 10 15 Draw less than type cumulative frequency curve. SECTION D 2 1 Q35. Solve for x : 2( +3 ) 3( +3 2 1 ) = 5 ; where x 3, 12 . (4) OR A shopkeeper buys a number of books for Rs. 80 . If he had bought four more books for the same amount , each book would have cost Re. 1 less . How many books did he buy ? Q36. The mean of the following frequency distribution is 53. But the frequencies a and b in the classes 20-40 and 60-80 are missing. Find the missing frequencies . (4) 80 0 - 20 Age (in years) Number of people 15 20 - 40 40 - 60 a 60 - 80 21 b 100 Total 17 100 Q37. A man in a boat rowing away from lighthouse 100 m high takes 2 minutes to changes the angle of elevation of the top of light house from 600 to 450. Find the speed of the boat . (4) Q38.Construct an isosceles triangle whose base is 7 cm and altitude 4 cm and then construct another similar 3 triangle whose sides are 4 times the corresponding sides of the isosceles triangle . (4) OR Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 120 . Page 6 of 7 Q39. The rain water from a roof of dimensions 22 m by 20 m drains into a cylindrical vessel having Diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm . (4) OR An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. Q40. In the below figure A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC IIQR . (4) xxxxxxxxxxxxxxxxxEND OF PAPER xxxxxxxxxxxxxxxxxxxxxx Page 7 of 7

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