# MATHEMATICSName: __________________ Max Marks: 90Class: IX Duration: 3hrs.General Instructions:i. All questions are compulsory.ii. The question paper consists of 31 questions divided into 4 sections, A, B, C and D. Section A comprisesof 4 questions of 1 mark each. . Section B comprises of 6 questions of 2 marks each.Section C comprises of 10 questions of 3 marks each. Section D comprises of 11 questionsof 4 marks each.iii. Question numbers 1 to 4 in Section A are multiple choice questions, select one correct option outof the given four.iv. Use of calculators is not permitted.SECTION-A(Question numbers 1 to 4 carry 1 mark each.)1. Equation of x-axis is -------------(A) x = 0 (B) x = y (C) y = 0 (D) x + y = 02. The median of a triangle divides it into two(A) triangles of equal area (B) equilateral triangles(C) right triangles (D) isosceles triangles3. In Fig.1, AOB is a diameter of the circle and AC = BC, then CAB is equal to(A) 30o (B) 45o (C) 90o (D) 60oFig. 14. Linear equation of the type y = mx, has---------------(A) infinitely many solutions (B) a unique solution(C) only solution x = 0, y = 0 (D) solution m = 0.SECTION-B(Question numbers 5 to 10 carry 2 marks each)5. D and E are points on sides AB and AC respectively of ABC such that ar (DBC) = ar (EBC).Prove that DE= BC.6. An edge of a cube is increased by 10%. Find the percentage by which the surface area of thecube has increased.7. Find the mode of the following data:5, 7, 6, 5, 9, 8, 6, 7, 11, 10, 5, 7, 6, 8, 6, 9, 10.8. In a cricket match, a batsman hits a boundary 4 times out of 30 balls, he plays. Find theprobability that he did not hit a boundary.9. In Fig.2 , Find the measure of Fig. 210. If the arithmetic mean of 25, 30, 32, x, 43 is 34, then find the value of x.SECTION C(Question numbers 11 to 20 carry 3 marks each)11. Find three different solutions for the equation3x 8y = 2712. Prove that a diagonal of a parallelogram divides it into two congruent triangles.13. Draw a line segment AB = 5cm. From the point A, draw a line segment AD = 6cm making(Use ruler and compass only).14. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. Thediameter of the pencil is 7mm and the diameter of the graphite is 1mm. If the length of the pencil is14cm, find the volume of the wood. (use = 22/7)15. Find mean of the following data:Marks: 10 11 12 13 14 15Number of students: 6 3 4 5 7 516. The points scored by a basket-ball team in a series of matches are as follows:17, 2, 7, 27, 25, 5, 14, 18 , 10, 24, 10, 8, 7, 10Find mean, median and mode for the data.17. Give the geometrical representation of x = -3 as an equation(i) in one variable (ii) in two variables.18. Solve the equation 2x+1 = x3 and represent the solution(s) (i) on the number line (ii) inthe Cartesian plane.19. A heap of wheat is in the form of a cone, the diameter of whose base is 14m and height is3m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find thearea of the canvas required.20. The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped intoit. Find the ratio of surface areas of the balloon in the two cases.SECTION-DQuestion numbers 21 to 31carry 4 marks each.21. Show that the line segments joining the mid points of the opposite sides of a quadrilateralbisect each other.22. Construct a triangle ABC in which BC = 8cm, 23. Draw the graph of linear equation x + 2y = 8. From the graph, check whether (-1, -2) is asolution of this equation.24. A storage tank is in the form of a cube. When it is full of water, the volume of the water is15.625m3. If the present depth of the water is 1.3m, find the volume of water already usedfrom the tank. Write any two reasons to use water wisely.( Value based question)25. In Fig.5, PQ is the diameter of the circle with center O. If PQR = 65o, RPS = 40o and PQM =50o, find QPR, PRS and QPMFig. 526. Construct a triangle PQR in which 27. In Fig.3, ABCD is a parallelogram and E is the mid-point of AD.DL II BE meets AB produced at F. Provethat B is the midpoint of AF and EB =LF.Fig. 328. In Fig.4, ABCD is a trapezium in which AB DC. O is the mid -point of BC. Through the pointO, a line PQ AD has been drawn which intersects AB at Q and DC produced at P. ProveThat ar (ABCD) = ar (AQPD).Fig. 429. A die is thrown 400 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given inthe following table.Outcome: 1 2 3 4 5 6Frequency: 72 65 70 71 63 59Find the probability of(i) getting a number less than 3.(ii) getting an outcome 6.(iii) getting a number more than 4.30. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC).Prove that ABCD is a trapezium.31. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) x ar (CPD)= ar (APD) x ar (BPC)**********

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