Mathematics - Class IX 2012 - Exam - Set 45, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 45 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) 45007 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. The graph of the linear equation 2x3y6 cuts the y-axis at the point. (A) (2, 0) (B) (0, 3) (C) (3, 0) (D) (0, 2) 2x3y6 y- (A) (2, 0) (B) (0, 3) (C) (3, 0) (D) (0, 2) 2. In the given figure, D is the midpoint of side BC of ABC and E is the midpoint of AC. If ar (DEC)6 sq. units, then ar (ABC) (in sq. units) is equal to : (A) 12 (B) 18 (C) 24 (D) 36 ABC BC D AC E ar (DEC) 6 ar ABC) (A) 12 (B) 18 (C) 24 (D) 36 3. In the given figure, AOB90 and ABC30, then CAB is equal to : (A) 30 (B) 105 (C) 90 (D) 60 AOB90 ABC30 CAB Page 6 of 11 O ADB30 ABC40 CAB OR Prove that the chords of a circle which are equidistant from the centre are of equal length. 14. Find the mode of the observations : 3, 5, 7, 4, 7, 8, 3, 6, 7, 4, 7, 3. If 5 is added to each observation, what will be the new mode ? प्रेक्षणं : 3, 5, 7, 4, 7, 8, 3, 6, 7, 4, 7, 3. का बहुैऱक ज्ञात कीजजए। यदद प्रत्येक प्रेक्षण मं 5 जोड़ो ददया जाए तो िया बहुैऱक क्या हैोगा ? SECTION-C / Question numbers 15 to 24 carry three marks each. 15. Draw the graph of the equation 2x3y60 on the graph paper. 2x3y60 16. In given figure, ABCD is a parallelogram. Show that PQ divides the parallelogram into two parts of equal areas. ABCD PQ 17. Construct a right triangle ABC, right angled at B, in which BC4 cm and ACAB8 cm. ABC B BC4 cm ACAB8 cm 18. The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone Page 7 of 11 of radius 4 cm. Find the height of the cone. 5 4 5 OR Find the volume of a sphere whose surface area is 154 cm2 (use  22 7 ). 154 2 19. For the data 3, 21, 25, 17, (x3), 19, (x4) if mean is 18, find the value of x, and hence, find the mode of the data. OR Find the mean of first ten prime numbers. यदद आॉकड़ों 3, 21, 25, 17, (x3), 19, (x4) का माध्य 18 हैै, तो x का माि ज्ञात कीजजए। अतः आॉकड़ों का बहुैऱक ज्ञात कीजजए। अथवा प्रथम दस अभाज्य सॊख्याओॊ का माध्य ज्ञात कीजजए। 20. The fixed fare for first kilometer is Rs. 5 and for the consecutive kilometers it is Rs. 2. Taking distance covered as x and total fare as Rs. y, write a linear equation, representing the above situation. 5 2 x y OR If x2 2 and y 2 satisfy the linear equation 3xky4 2 find the value of k. Can there be more than one value of k ? x2 2 y 2 3xky4 2 k k 21. Ten cylindrical pillars of a building have to be painted. If the diameter of each pillar is 50 cm and height 3.5 m, find the total area (in m2) to be painted and the cost of painting 10 pillars at the rate of Rs. 20 per m2. (Use  22 7 ). 10 50 3.5 2 10 20 / 2  22 7 22. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a square. दर्ााइए दक यदद दकसी चतभुुाज के ववकणा एक दसूरे को समकोण पर समदिभाजजत करते हंै, तो चतभुुाज एक वगा हैै। Page 8 of 11 23. In a triangle ABC, E is the midpoint of the median AD. Show that एक ABC मं, माजध्यका AD का मध्य वबन्द ुE हैै। दर्ााइए दक 24. Three coins are tossed simultaneously 1000 times and the following observations are made. Three Heads216 times, two heads384 times, 1 head270 times, No heads130 times. If coins are tossed once again, find the probability of (a) non occurrence of exactly 2 heads (b) 3 heads (c) no heads 1000 216 , 384 , 270 , 130 (a) 2 (b) 3 (c) SECTION-D / Question numbers 25 to 34 carry four marks each. 25. ABCDE is a pentagon. A line through B parallel to AC meets DC produced to F. Show that (i) ar (ACB)  ar (ACF) (ii) ar (AEDF)  ar (ABCDE) 1 ar ( BED) ar ( ABC) 4    1 ar ( BED) ar ( ABC) 4   