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Sample Paper (Based on CBSE CCE SA - 2) (IX) MATHEMATICS [Time allowed: 3 hours] [Maximum marks: 80] General Instructions: 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into 4 sections, section A, B, C, and D. 3. Section A contains 10 multiple choice type questions each carry 1 mark. Section B contains 8 questions of 2 marks each, section C contains 10 questions of 3 marks each and section D con- tains 6 questions of 4 marks each. 4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. Attempt only one of the alternatives in all such questions. SECTION - A Question Numbers 1 to 10 carry 1 mark each. 1. The equation 3x + 5y = 7 has a unique solution, if x, y are (a) natural numbers (b) positive real numbers (c) real numbers (d) rational numbers 2. The quadrilateral formed by joining the mid-points of the sides of quadrilateral LMNO, taken in order, is a rhombus, if (a) LMNO is a rhombus (b) LMNO is a ||gm (c) diagonals of LMNO are perpendicular (d) diagonals of LMNO are equal D C 3. In the adjoining figure, the incorrect statement is m (a) area (∆ADC) = area (∆BDC) E (b) area (∆ABC) = area (∆ABD) l A B (c) area (∆EBC) = area (∆EAD) A (d) area (quad. ABCD) = area (∆ABC) + area (∆ABD) x C 4. In the adjoining figure, O is the centre and A is such that ∠BOA = 120°, 120° O then the value of x is B (a) 120° (b) 30° D (c) 90° (d) 60° C 5. In the adjoining figure, ABCD is a cyclic quadrilateral, ∠CAB is D 50° (a) 30° (b) 50° ° 40 (c) 45° (d) 60° 30° B A AVTE/IX/M/10-11/Jan/SA-2 1 6. The radius of the base of a right circular cone is 6 cm and its height is 8 cm. Slant height of the cone is (a) 14 cm (b) 20 cm (c) 28 cm (d) 10 cm 7. The class marks of a frequency distribution are 15, 20, 25,.... The class corresponding to the class mark 20 is (a) 17.5 - 22.5 (b) 12.5 - 17.5 (c) 18.5 - 21.5 (d) 19.5 - 20.5 8. The mean of 7 observations is 20. If one number is added, the mean becomes 21. The added number is (a) 28 (b) 7 (c) 18 (d) 38 9. The median of 18 items arranged in ascending order is (a) value of 9th item (b) value of 10th item (c) sum of 9th and 10th items (d) mean of 9th and 10th items 10. There are 10 white balls in a bag. A ball is drawn at random from the bag, then probability of it being a black ball is 1 (a) 0 (b) 10 9 (c) (d) 1 10 SECTION - B Question Numbers 11 to 18 carry 2 marks each. 11. Solve the linear equation 5x − 4 = 2 5 + 6 . 12. Which of the following are solutions of the equation x + 3y = 7 and which are not? 7 (2,5), 0, , ( 4 , 3 ) , ( 1 , 2 ) , ( 4 , 1 ) , ( 3 , 1 ) . 3 x y 13. Write four solutions of the equation + =1. 2 3 14. Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other. OR In the square ABCD of side 10 cm. E and F are the mid-points of AD and BC. Find ar(∆APE). A B E F P D C 15. If each diagonal of a quadrilateral divides it into two triangles of equal area, then prove that the quadrilateral is a parallelogram. AVTE/IX/M/10-11/Jan/SA-2 2 16. The surface area of a cuboid is 3328 m2 . Its dimensions are in the ratio 4 : 3 : 2. Find the volume of the cuboid. 17. A hemispherical bowl of internal radius 9 cm, is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottles needed to fill the whole water of the bowl. 18. The median of the following observations, arranged in ascending order is 32. Find the value of p. 12, 14, 15, 27, p + 2, p + 3, 35, 36, 40, 49 SECTION - C Question Numbers 19 to 28 carry 3 marks each. 19. If 500 g of onions cost . 30, draw a graph to give the price of any number of kilograms of onions. From the graph, determine the cost of 5 kg of onions. OR Draw the graph of the equation y + 2x = 7 and determine from the graph whether x = 2, y = 3 is its solution or not. 20. P and Q are points on opposite sides AD and BC of a ||gm ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O. 21. Prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side and is equal to half of it. 22. Construct a ∆PQR in which ∠Q = 60°, ∠R = 45° and perimeter of ∆PQR = 11 cm. 23. How many square metres of canvas are required for a conical tent whose height is 3.5 m and the radius of the base is 12 m? 24. A cylinder is 12 cm high and the circumference of its base is 44 cm. Find its curved surface area and total surface area. OR 2 Find the length of wire of a diameter cm that can be drawn from a solid sphere of radius 9 cm. 5 25. A card is drawn from a deck of well shuffled cards. Find the probability of getting either a club or a queen. OR A letter of English alphabet is chosen at random. Find the probability of getting a letter ‘N’ from the word ‘LONDON’. 26. Below are the marks obtained by 30 students of a class in Maths test, out of 100. Make a frequency distribution table for this data with class interval of size of 10 and draw a histogram to represent the data. 53, 61, 48, 100, 75, 90, 77, 60, 48, 58, 64, 59, 60, 78, 55, 88, 60, 37, 58, 84, 62, 44, 52, 50, 56, 98, 67, 70, 39, 68 27. Two circles with centres O and O’ intersect at two points A and B. A line PQ is drawn parallel to OO’ through A (or B) intersecting the circles at P and Q. Prove that PQ = 2OO’. 28. If BM and CN are perpendiculars drawn on the sides AC and AB of ∆ABC, prove that B, C, M and N are concyclic. AVTE/IX/M/10-11/Jan/SA-2 3 SECTION - D Question Numbers 29 to 34 carry 4 marks each. 29. Linear equation for converting Fahrenheit to Celsius is F = 9 C + 32 5 (i) Draw the graph of the linear equation given above using Celsius on x-axis and Fahrenheit on y-axis. (ii) If the temperature is 35°C, find the temperature in Fahrenheit. (iii) If the temperature is 104°F, what is the temperature in Celsius? 30. In a parallelogram PQRS, PS = 6 cm, MS = 2 cm, NR = 4 cm. Prove that MSNQ is a parallelogram. P Q N M S R 31. The pillars of a temple are cylindrical shaped. If each pillar has a circular base of radius 25 cm and height 10.5 m, then find the quantity of concrete mixture used to build 30 such pillars. Also, find the cost of concrete mixture at the rate of . 250 per m3 . OR The volume of the space inside a right circular conical tent is 138 2 m 3 and its vertical height is 7 4 m. Find the canvas required to make the tent and also, find the cost of the canvas at the rate of ( Rs. 120 per m2 . Take 33 = 5.74 ) 32. A die is thrown 500 times with frequencies for the outcomes 1, 2, 3, 4, 5, 6 as given in the following table. Find the probability of getting an outcome (i) less than 4 (ii) at least 5. Outcomes 1 2 3 4 5 6 Frequency 80 75 90 75 85 95 OR Eleven bags of wheat flour each marked 5 kg, actually contained the following weights of flour: 4.97, 5.05, 5.08, 5.06, 5.00, 5.03, 5.00, 5.08, 5.04, 5.07, 4.98 Find the probability that any of these bags chosen at random contains more than 5 kg of flour. 33. Prove that the parallelograms lying on the same base and between the same parallels are equal in area. 34. ABCD is a parallelogram. The circle through A, B and C intersect CD (produced) at E. Prove that AE = AD. C E D B A For Solutions Email us at avte37@yahoo.co.in AVTE/IX/M/10-11/Jan/SA-2 URL www.avteschool.org 4

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