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Class 10 CBSE Pre Board 2015 : Mathematics 3 (Kendriya Vidyalaya (KV) No. 2, Raipur)

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KENDRIYA VIDYALAYA SANGATHAN.RAIPUR REGION SUMMATIVE ASSESMENT- II (2014-2015) CLASS X (MATHEMATICS) Time: 3 Hrs Max. Marks: 90 Marking scheme Q. No. 01 02 03 04 05 Solutions 4 45 5 D=0 324 4 = 9 = 3 , = 5 , = 78 78 = 3 + ( 1)5 n = 16th term 21 = 2 ( )2 = 06 07 . = 08 09 10 11 12 13 14 15 3000 7 Radius of sphere 2 4 22 7 7 7 = 3 7 2 2 2 539 3 3 OP |PT , OQ |QT (with Reason ) = 45 formula for slant height of frustum = 20 , = 11 , = 40 = 41 11 ,13, 15 99 = 11 , = 2, = 99 = 45 45 = 2475 9 9 = 2 3 18 20 2 3 + 2 = 0 = 2 = 1 For correct step I For correct step II For correct required answer For correct diagram For correct steps Height = 129.75m 7 ( ) = 24 5 ( ) = 24 Marks 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 5 6 Area of triangle = 0, Condition for the three points to be collinear For correct steps =4 ( , ) For correct steps Required point (0,0) Area of the minor sector = 52.38 2 Area of major sector = 261.90 2 Area of square Area of quadrant Area of shaded region = 10.5 2 . . = . for correct answer = 20 Correct diagram For correct steps Distance between ships = 1200 3 3 ( ) = 49 3 ( ) = 49 23 ( ) = 49 10 ( ) = 49 y using section formula For correct steps = 1 & = 3 2 + 2 = 10 OA = AQ = OQ midpoint of hyp. Of right triangle is equidistant from the vertices is an equilateral triangle = 2 = 60 , = For correct answer ( ) = 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300 300 = / , =2 +5 For correct steps Required answer 25 / = 235.5 3 202.79 3 concept used is volume of solid figures value depicted by Niraj is honesty , = 25 , = 24 = 550 2 = 308 2 = 858 2 = , = 8 1 1 8 + = 8 15 For correct steps Correct answer 3 and 5 Correct diagram 01 01 01 01 01 01 01 1 1 01 01 01 1+1 01 01 1+1 01 01 01 01 01 01 01 01 01 01 01 01 01 02 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 30 31 Using Pythagoras theorem finding the length of semi-chord For correct step Correct answer 8cm For correct construction For correct steps + ( + 2 ) + ( + 16 ) = 216 13 936 -------X------- 01 01 01 1+1 1+1 01 1+1 01 Time: 3 Hrs KENDRIYA VIDYALAYA SANGATHAN.RAIPUR REGION SUMMATIVE ASSESMENT- II (2014-2015) CLASS X (MATHEMATICS) Max. Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections- A, B, C and D. 3. Section A contains 4 questions of 1 mark each ,section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each, and section D contains 11 question of 4 marks each. 4. Use of calculator is not permitted. SECTION (A) 1. In an A.P., if a = -10, n = 6 and an =10, then find the common difference. 2. A die is thrown once .What is the probability of getting an even number? 3. If the height and length of the shadow of a man are the same, then find the angle of elevation of the sun. 4. Find the perpendicular distance of A(5,12) from Y-axis. Section- (B ) 5. For what value of K, the roots of the quadratic equation 3 +2kx+ 27 = 0 are real and equal? 6. Which term of the A.P., 3, 8, 13, 18, .is 78. 7. The diameter of a cycle wheel is 21cm.How many revolutions will it make to travel 1.98km? 8. The largest sphere is cut out of a cube of side 7 cm .Find the volume of the sphere. 9. In figure, TP and TQ are the two tangents to a circle with centre O such that <POQ=1350, then find <PTQ. 10.The radii of the ends of frustum of a cone 40cm height are 20cm and 11cm. Find its slant height. Section- (C ) 11.Find the sum of all two digit odd positive numbers. 12.Find the roots of the following equation: - = ; x -3, 6 13.A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB +CD = AD + BC D R C S Q A P B 14. The string of a kite is 150 m long and it makes an angle of 60 with the horizontal. Find the height of the kite from the ground. 15. A bag contains 5 red balls ,8 white balls ,4 green balls and 7 black balls. If one ball is drawn at random, then find the probability that it is : a) black b) red c) not green 16. Find the value of K for which the points with coordinates (7,-2), (5, 1) and (3, k) are collinear. 17.Find a point on x axis which is equidistant from (-3,-4) and (4,-3). 18.Find the area of the sector of a circle with radius 10 cm and of central angle 60 0. Also find the area of the corresponding major sector. 19.In the given figure, OABC is a square of side 7cm.If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. (Take 20.A hemispherical bowl of internal diameter of 30 cm contains some liquid .This liquid is to be filled into cylindrical shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl. ) Section- (D ) 21. A pilot flying an aero plane at an altitude of 1800 m observes that two ships are sailing towards it in the opposite directions. The angles of depressions of the ships as observed from the aero plane are 60 0 and 300 respectively. Find the distance between the two ships? 22. All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is drawn at random from the remaining pack. Find the probability of getting: a) a black face card b) a queen c) a black card d) a spade 23. If P (9a-2,-b) divides line segment joining A (3a+1,-3) and B (8a,5) in the ratio 3:1, then find the value of a and b. Also determine the value of a2 +b2. 24.In the given figure, OP is equal to diameter of the circle. Prove that ABP is an equilateral triangle. 25.A train takes 2 hrs less for a journey of 300 km, if its speed is increased by 5km/hrs from its usual speed. Find the usual speed of the train. 26. In the figure, Neeraj a juice seller has set up his juice shop where he has three types of glasses of inner diameter 5 cm to serve the customers. The height of the glasses are 12 cm (Take = 3.14). He decided to serve the customer in A type of glasses. I. Find the volume of glass of type A II. Which glass has the minimum capacity? III. IV. Which mathematical concept is used in above problem? By choosing a glass of type A, which value is depicted by juice seller Neeraj? 27.A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm .The total height of the toy is 31 cm .Find the total surface area of the toy. 28. The sum of two numbers is 8. Determine the numbers if the sum of their reciprocal is 8/15. 29. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. 30.Draw a triangle ABC with side BC= 6 cm, AB =5 cm and <ABC=600. Then construct a triangle whose sides are of the corresponding sides of the triangle ABC. Also write the steps of construction. 31.The sum of first, third and seventeenth terms of an AP is 216.Find the sum of the first 13 terms of the AP.

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