Mathematics - Class IX 2012 - Exam - Set 35, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 35 and more Exams Mathematics in PDF only on Docsity! Page 2 of 10 SUMMATIVE ASSESSMENT – II, 2012 II, 2012 MATHEMATICS / Class – IX / IX Time allowed : 3 hours Maximum Marks : 90 3 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section-A comprises of 8 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 and Section-D comprises of 10 questions of 4 marks each. (iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are to select one correct option out of the given four. (iv) There is no overall choice. However, internal choices have been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculator is not permitted. (i) (ii) 34 8 1 6 2 10 3 10 4 (iii) 1 8 (iv) 2 3 3 4 2 (v) MA 1070 Page 3 of 10 SECTION – A / Question numbers 1 to 8 carry 1 mark each. For each questions, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1 8 1 1. x2, y5 is solution of the linear equation : (A) x2y7 (B) 5x2y7 (C) xy7 (D) 5xy7 x2, y5 (A) x2y7 (B) 5x2y7 (C) xy7 (D) 5xy7 2. If a triangle and a rhombus are on the same base and between the same parallels then ratio of area of triangle and area of rhombus are in the ratio : (A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 (A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 2 : 1 3. In the figure, O is the centre of a circle and AOC130. ABC will be : (A) 120 (B) 115 (C) 90 (D) 65 O AOC130 ABC (A) 120 (B) 115 (C) 90 (D) 65 4. Graph of x2y3 will intersect x-axis at the point : (A) (3, 0) (B) (0, 3) (C) (3, 0) (D) (0, 3) x2y3 x- (A) (3, 0) (B) (0, 3) (C) (3, 0) (D) (0, 3) 5. Mode of the data 4, 6, 5, 4, 6, 4, 5, 7, 8, 9, 4, 10 is : (A) 4 (B) 5 (C) 6 (D) 10 4, 6, 5, 4, 6, 4, 5, 7, 8, 9, 4, 10 (A) 4 (B) 5 (C) 6 (D) 10 Page 6 of 10 P and Q are any two points lying on the sides DC and AD resp. of a parallelogram ABCD. Show that ar (APB)ar (BQC). DC AD P Q ar(APB) ar (BQC). 17. Construct a triangle ABC in which B45, C60 and ABBCCA12 cm. ABC B45, C60 ABBCCA12 18. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. 7 24 10 19. The following data gives the number (in thousands) of applicants registered with an Employment Exchange during 20052010. Year 2005 2006 2007 2008 2009 2010 No. of applicants registered (in thousands) 19 21 23 30 32 36 Construct a bar graph to represent the above data. 20052010 2005 2006 2007 2008 2009 2010 19 21 23 30 32 36 20. Express y in terms of x, it being given that 3xy90. Check whether the point (3, 0) and (2, 2) lie on the equation. 3xy90 y x (3, 0) (2, 2) 21. A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. 0.25 5 OR/ A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much ? (Take  22 7 ) (soft drink) (i) 5 4 15 (ii) 7 10  22 7 Page 7 of 10 22. Prove that a diagonal of a parallelogram divides it into two congruent triangles. 23. ABCD is a parallelogram and AP, CQ are perpendiculars from vertices A and C on diagonal BD (see fig) Show that (i) APB  CQD (ii) APCQ. ABCD A C BD AP CQ (i) APB  CQD (ii) APCQ. OR/ ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see fig.) AC is a diagonal. Show that (i) SRAC and SR 1 2 AC (ii) PQSR (iii) PQRS is a parallelogram. ABCD P, Q, R S AB, BC, CD DA AC (i) SRAC SR 1 2 AC (ii) PQSR (iii) PQRS Page 8 of 10 24. In a box, there are 9 red, 8 white and 3 black balls. One ball is taken out of the bag. Find the probability that it is : (i) white, (ii) red or black (iii) not-red 9 8 3 (i) (ii) (iii) SECTION – D / Question numbers 25 to 34 carry 4 marks each. 25 34 4 25. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD res P. (see fig.). Show that the line segment AF and EC trisect the diagonal BD. ABCD E F AB CD AF EC BD 26. Construct a triangle ABC in which BC7 cm, B75 and ABBC13 cm. ABC BC7 B75 ABBC13 OR/ Construct a triangle ABC in which BC8 cm, B60 and ABAC2.5 cm. ABC BC8 B60 ABAC2.5 27. Draw a graph of the line x2y3. From the graph, find the coordinates of the point. When (i) x5, (ii) y0. x2y3 (i) x5, (ii) y0. 28. The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of leveling this ground at the rate of 50 paise per square metre. 84 1.5 100 50 OR/ The cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. d.m. is Rs. 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places.