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CBSE Class 10 Pre Board 2020 : Mathematics Standard (Kendriya Vidyalaya (KV), Lucknow Region)

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Set 1 Total Pages : 2 KENDRIYA VIDYALAYA RRC FATEHGARH PREBOARD-I (2019-20) SUB: Mathematics Advance Time : 3 hour Q.1. CLASS : Max. Marks : General Instruction: 1. All questions are compulsory 2. The question paper consists of 40 questions divided into 4 sections, A, B, C, and D, section A comprises of 20 questions of Multiple choice questions of 1marks each. Section B comprises of 6 questions of 2marks each. Section C comprises of 8 questions of 3marks each and Section D comprises of 6 questions of 4 marks each. 3. Use of calculator is not permitted. SECTION A The product of HCF and LCM of 18 and 16 is (a) 240 (b) 144 ( c) 288 (d) 230 Q.2. Q.3. Show that x = - 4 is a solution of 3x2 + 13x + 4 = 0 Q.4. The value of 1 + tan2 A is equal to (a) 2 (b) sec2 A ( c) 1 (d) cot2 A How many tangents can a circle have____________ If a pair of linear equations is consistent, then the lines will be____________ A line intersecting a circle in two points is called a _____________ The graph of a polynomial P(x) cuts the x axis at two places and touches it at three places. Number of zeroes of P(x) is ____________ For what value of k, do the equation 3x y + 8 = 0 and 6x ky = - 16 represent coincident lines? Q.5. Q.6. Q.7. Q.8. Q.9. 1 2 Given sin A = and cos B = , then A + B is 900 . Write True or False. (a) Q.10. Q.12. Q.13 Q.15 Q.16 Q.17 Q.18 Q.19 Q.20 Q.21 Q.22 (b) 1 2 ( c) 2 3 2 (b) 3 2 (c) 2 3 (b) 2 1M 1M 1M 1M 1M 1M 1M 1M 1M (d) 2 1M (d) -2 The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is (a) 4.2 (b) 2.1 (c) 8.2 (d) 1.05 Ratio of volume of two cylinders with equal height is: (a) H : h (b) R : r (c) R2 : r2 (d) None of these If the area of a square is same as the area of a circle, then the ratio of their perimeters in terms of is: (a) Q.14 1 2 The sum of zeroes of polynomial is 2x2 3x + 4 is (a) Q.11. 1 2 X 80 (c) 2 (d) 1M 1m 1M 3 If the radius of a circle is decreased by 50%. Then its area will be decrease by: (a) 25% (b) 50% (c) 75% (d) 60% Distance of the point P( 3, -4 ) from the origin is : (a) 10 (b) 3 (c) 34 (d) None of these If the distance between the points ( 3, 2 ) and ( -1, x ) is 5. Then x = ? (a) 3 (b) 4 (c) 6 (d) 5 th If the n term of an AP is ( 2n + 1 ), then the sum of its first three term is : (a) 6n +3 (b) 15 (c) 12 (d) 21 th 15 term of the AP, x 7, x 2, x + 3, . is : (a) x + 63 (b) x + 73 (c) x + 83 (d) x + 53 A boy goes 12 m due North and 5 m due West. How far is he from the starting point? (a) 17 m (b) 7 m (c) 13 m (d) 25 m If height of an equilateral triangle is 6 cm. then side of an equilateral triangle is : (a) 4 cm (b) 5 cm (c) 4 3 cm (d) 3 2 cm SECTION B Prove that the tangents, drawn at the ends of a diameter of a circle, are parallel. If tangents AB and AC, inclined to each other at an angle of 1200 are drawn to a circle with centre O of radius 6 cm, then find the length of each tangent. 1M 1M 1M 1M 1M 1M 1M 3M 3M Q.23. 3M In Fig. DE || OQ and DF || OR. Show that EF || QR. Q.24 Q.25 If Cot A = 17 , 18 (1+ )(1 ) evaluate (1+ )(1 ) . One year ago, a man was 8 times as old as his son. At present, his age is equal to the square of his son s age (in years). Find their present ages. 3M 3M Q.26 Without performing the long division, state whether 13 will 3125 have a terminating or non-terminating repeating 3M decimal expansion. Q.27 SECTION C In fig l and m are two parallel tangents at A and B. the tangent at C makes an intercept DE between l and m. Prove 3M that DOE = 900 2 2 Q.28. If cos + sin = 1 and sin - cos = 1, prove that 2 + 2 = 2 3M 29 An umbrella has 8 ribs which are equally spaced (see Fig.) Assuming umbrella to be a flat circle of radius 45 cm, 3M Q.30 find the area between the two consecutive ribs of the umbrella. Find the roots of the following equation : 3M 1 +4 - 1 7 = 11 30 Q.31 A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure .if the height of the cylinder is 10cm, and its base is of radius 3.5 cm,find the total surface area of the article. 3M Q.32 Q.33 State and prove Pythagoras theorem. 3M 3M Obtain all the zeros of 3x + 6x3 -2x2 -10x -5 if you know that two of its zeros are 5 3 and 5 . 3 Use Euclid s division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or 9m+8 where m is some integer. SECTION D Determine graphically the coordinates of the vertices of a triangle formed by the equation 2x 3y + 6 = 0 and 2x + 3y 18 = 0; and the y-axis. Also, find the area of this triangle. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains A container shaped like a right circular cylinder having diameter 12cm and height 15cm is full of ice-cream. The ice-cream is to be filled into cone of height 12cm and diameter 6cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row? 3M Q.39. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. 4M Q.40. From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45 , respectively. If the bridge is at a height of 3 m from the banks, find the width of the river. 4M Q.34 Q.35. Q.36. Q.37. Q.38. 4M 4M 4M 4M KENDRIYA VIDYALAYA R.R.C FATEHGARH (U.P.) BLUE PRINT FIRST PRE-BOARD CLASS X Maths (Standard) NAME OF CHAPTER REAL NUMBERS 1(MCQ) 2(SAI) 3 (SAII) 4(VLA) Q(marks) 1(1) 2(1) 3(1) ... 6(3) POLYNOMIALS 2(2) .... .... .... 2(2) QUADRATIC EQUATION 1(1) 2(1) 3(1) 4(1) 10(4) EQUATION IN TWO VARIABLES 2(2) .... 3(1) .... 5(3) ARITHEMATIC PROGRESSIONS 2(2) ..... ... 4(1) 6(3) TRIANGLES 2(2) 2(1) 3(1) .... 7(4) CO-ORDINATE GEOMETERY 2(2) .... ... 4(1) 6(3) 2(1) 3(1) .... 7(4) .... .... 4(1) 4(1) INTRODUCTION TO 2(2) TRIGONOMETERY APPLICATION OF ..... TRIGONOMETRY CIRCLE 2(2) 2(1) 3(1) .... 7(4) CONSTRUCTIONS .... .... .... 4(1) 4(1) 2(2) 2(1) 3(1) .... 7(4) 2(2) ... 3(1) 4(1) 9(4) 20(20) 12(6) 24(8) 24(6) 80(40) AREA RELATED TO CIRCLE VOLUME AND SURFACE AREA TOTAL No. of question (s) are given within brackets and marks outside the brackets Marking scheme of first pre-board 2019-20 Class X Subject Mathematics (Standard) SECTION A Ans 1 Ans 2 Ans 3 Ans 4 Ans 5 Ans 6 Ans7 Ans 8 Ans 9 Ans 10 Ans 11 Ans 12 Ans13 Ans14 Ans15 Ans16 Ans17 Ans18 Ans19 Ans20 Ans 21 Ans 22 Ans 23 Ans 24 Ans 25 (c) 288 Full marks for correct answer True (b) sec2A Infinite Intersecting / co-incident Secant 5 (c) 2 (a) 3/2 (b) 2.1 (c) R2/r2 (c) (c)75% (d) None of these (d)5 (b)15 (a)X+63 (c)13 (c)4 3 SECTION B marks for diagram marks for given, to prove 1 marks for correct proof for diagram 1 marks for calculation marks for correct answer (2 3) Full marks for correct proof On solving the value of expression is 289/324 Present age of son = x and age father = y First condition (y-1) =8(x-1) M Second condition Y2 = x2 M On solving x=7 and y = 49 1M Ans 26 Denominator has only 5 as factors, Hence it is terminating decimals. Ans 27 Ans 28 full marks for correct proof Squaring and adding both equations And using identities sin2 A + cos2 A = 1. Angle of sector = 3600/ 8 = 450 Ans 29 r2 Ans 30 Ans 31 Ans 32 Ans 33 Ans 34 Ans 35 Area = M 2 = 795.53 cm 2M On solving given expression, Equations becomes x2 3x + 2 = 0 on solving x = 1, x = 2 Surface area of article =2 rh + 2 r2+ 2 r2 On putting values, surface area = 374 cm2. 1 M for statement 1 M for given, to Prove, and construction and diagram 1 M for correct proof. 1/2 Mark for finding divisor 1 mark for correct division and quotient 1 mark for finding the zeroes, x = -1, -1 Full marks for correct explanation with all three steps 1 mark for denoting first equation on graph 1 mark for denoting first equation on graph M Ans 36 Ans 37 Ans 38 Ans 39 Ans 40 1 mark for denoting bounded area. 1 mark for finding area, and area = 6 square unit. Let the speed of express train be x km/h Speed of passenger train be (x 11)km/h According to equation 132/(x 11) = 132/x + 1 On solving, x2 11 1452 = 0 On solving x = 44,-33 Hence speed of express train is 44km/h and passenger train is 33km/h 1 mark for volume of container 1 mark for volume of ice cream in cone( volume of cone + volume of hemisphere) I marks for no. of cones = volume of container / volume of ice cream in cone 1 mark for correct answer, n = 10 2 mark for forming correct equation AP n2 41 n +400 = 0 1 marks for correct explanation of no. of logs n = 16 1 marks for no. of logs in top most row = 5 2 marks for drawing parental triangle. 1 marks for similar triangle 1 marks for writing steps 2 marks for framing both equations 1 mark for finding the values of angles 1 mark for correct answer i.e width of river is 8.19 m

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