Mathematics - Class IX 2012 - Exam - Set 48, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 48 and more Exams Mathematics in PDF only on Docsity! Page 2 of 11 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) 45002 Page 3 of 11 SECTION–A / Question numbers 1 to 8 carry one 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. Which of the following ordered pairs is a solution of the equation x2y6 ? (A) (2, 4) (B) (0, 3) (C) (4, 1) (D) (4, 1) x2y6 (A) (2, 4) (B) (0, 3) (C) (4, 1) (D) (4, 1) 2. In the figure, ABCD is a parallelogram of area 128 cm2. If CF16 cm, the length of AD is : (A) 8 cm (B) 4 cm (C) 16 cm (D) 10 cm आकृति मं ABCD एक समाॊिर चिभुुजु है जजसका ऺेत्रफऱ 128 सेमी2 है। यदि CF16 सेमी है, िो AD की ऱम्बाई है : (A) 8 सेमी (B) 4 सेमी (C) 16 सेमी (D) 10 सेमी 3. In the figure, if BAC50 and DBC40, then BDC equal. (A) 140 (B) 40 Page 6 of 11 250 (a) 50 (b) 125 (c) 75 (a) (b) 13. Find the length of a chord of a circle which is at a distance of 4 cm from the centre of the circle with radius 5 cm. OR Prove that if chords of congruent circles subtend equal angles at their centres, then they are equal. 5 सेमी त्रत्रज्या वाऱे वतृ्त की उस जीवा की ऱम्बाई ऻाि कीजजए जो वतृ्त के केन्द्र से 4 सेमी की िरूी पर है। अथवा तसद्ध कीजजए दक सवागंसम वतृ्तं की वह जीवाएॉ , जो वतृ्त के केन्द्र पर समान कोण बनािी हं, समान होिी हं। 14. Find the mode of the following data : 1, 3, 5, 7, 3, 5, 4, 7, 2, 6, 7, 12, 10, 11, 3, 7, 8 6, 7, 7, 4, 2, 11, 7, 15 1, 3, 5, 7, 3, 5, 4, 7, 2, 6, 7, 12, 10, 11, 3, 7, 8 6, 7, 7, 4, 2, 11, 7, 15 SECTION-C / Question numbers 15 to 24 carry three marks each. 15. If the point (2, 4) lies on the graph of the equation (a1) y3x6, find four other solutions of this equation. (2, 4) (a1) y3x6 16. Page 7 of 11 In the figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that     1 ar AXS ar PQRS 2  आकृति मं , PQRS िथा ABRS समाॊिर चिभुुजु हं िथा भजुा AB पर एक त्रबॊि ुX जथथि है। िर्ाइुए दक    1ar AXS ar PQRS 2  17. Construct a PQR in which QR6 cm, Q30 and PQPR3 cm PQR QR6 Q30 PQPR3 18. Find the volume of the largest right circular cone that can be cut out from a cube whose edge is 14 cm (use  22 7 ) 14  22 7 OR A bag of grain contains 2.8 m3 of grain. How many bags of grain are needed to fill a right circular cylindrical drum of radius 4.2 m and height 5 m ? 2.8 m3 4.2 5 19. Find the mean of the following data : Page 8 of 11 x : 10 12 20 25 35 f : 3 10 15 7 5 x : 10 12 20 25 35 f : 3 10 15 7 5 OR The following observations are arranged in increasing order : 17, 19, 20, 24, x, x2, 28, 31, 34, 36 If the median of the observations is 26, find the value of x If each observation is increased by 2, what is the new median ? 17, 19, 20, 24, x, x2, 28, 31, 34, 36 26 x 20. Write the equations of any three lines passing through the point (2, 3). (2, 3) OR Find the value of k if x2, y1 is a solution of the equations 2x3yk and 3xyk. x2, y1 2x3yk 3xyk k 21. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around it to a width of 5 m to form an embankment. Find the height of the embankment. 10 14 5 22. Diagonals AC and BD of quadrilateral ABCD intersect each other at O in such a way that ar (AOD)  ar (BOC). Prove that ABCD is a trapezium. ABCD AC BD ar (AOD)  ar (BOC) ABCD 23. Show that the diagonals of a rhombus are perpendicular to each other. 24. At a hospital, a doctor compiled the following data about 400 patients whom he could cure of