Mathematics - Class IX 2012 - Exam - Set 36, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 36 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) 45004 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 equation of the line passing through the origin is : (A) y3 (B) x4 (C) x3y (D) x4y5 उस रेखा का समीकरण जो मऱू बबन्दय से होकर जाती है, है : (A) y3 (B) x4 (C) x3y (D) x4y5 2. The area of ABC is 400 cm2. If AD is a median of ABC, then the area of ABD (in cm2) is : (A) 800 (B) 400 (C) 200 (D) 150 400 2 AD ABC ABD 2 (A) 800 (B) 400 (C) 200 (D) 150 3. In the adjoining figure, O is the centre of the circle and P, Q and R are points on the circle such that  PQR100, then OPR equals : (A) 80 (B) 10 (C) 100 (D) 60 O P, Q R  PQR100 OPR (A) 80 (B) 10 (C) 100 (D) 60 4. The equation y4x7 has : (A) no solution (B) unique solution Page 6 of 11 DBC. O BAC60 DCB100 , DBC 14. If the mean of x, x2, x4, x6, x8 is 24, find the value of x. x, x2, x4, x6 x8 24 x SECTION-C / Question numbers 15 to 24 carry three marks each. 15. Find three different solutions for the equation 2xy3. समीकरण 2xy3 के तीन बिभभन्न हऱ ऻात कीमजए। 16. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB)ar (BQC). ABCD DC AD P Q ar (APB)ar (BQC). 17. Construct a PQR with Q90, QR6 cm, R60. Construct angle bisector of angle P. एक PQR की रचना कीमजए मजसमं Q90, QR6 सेमी, R60 है । P का कोण समद्विभाजक खींभचए। 18. The radius and height of a right circular cylinder are in the ratio of 2 : 3. If the volume of the cylinder is 1617 cm3, then find the radius and height of the cylinder. 2 : 3 1617 3 Page 7 of 11 OR A heap of wheat is in the form of a right circular cone whose base diameter is 10.5 m and of height 3 m. Find the volume of wheat in it. If the heap is to be covered by canvas to protect it from rain, find the area of canvas required. 10.5 3 19. If the observations of 6, 7, x2, x, 17, 20 are written in ascending order and their median is 16. Find the value of ‘x’. Using the value of x, also find mean of given numbers. 6, 7, x2, x, 17, 20 16 x OR Find the mode of the following data. 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 52, 60 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 52, 60 20. Plot 2xy4 on a graph paper. ग्राफ पेपर पर 2xy4 का आऱेख खींभचए। OR/अथिा The cost of a pen is four times the cost of a pencil. Express the statement as a linear equation in two variables and plot the equation on a graph paper. एक पनै का मलू्य एक पभंसऱ के मलू्य का चार गयना है। इस कथन को दो चरं िाऱे एक रैमखक समीकरण के रूप मं व्यक्त कीमजए तथा उस समीकरण का ग्राफ पेपर पर आऱेख खींभचए। 21. A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup. 28 22. If diagonals of a parallelogram are perpendicular to each other ; then show that it is a rhombus. 23. Diagonal AC of a parallelogram ABCD bisects A. Show that : (i) it bisects C also (ii) ABCD is a rhombus Page 8 of 11 ABCD AC, A (i) C (ii) ABCD 24. A die is thrown 500 times. The frequencies of the outcomes are recorded in the following frequency distribution table : Outcome 1 2 3 4 5 6 Frequency 120 50 65 70 80 115 Find the probability of the occurrence of (a) a number between 3 and 6 (b) an even number (c) an odd number 500 1 2 3 4 5 6 120 50 65 70 80 115 (a) 3 6 (b) (c) SECTION-D / Question numbers 25 to 34 carry four marks each. 25. In the given figure, PQRS is a parallelogram. B and D are midpoints of the sides QR and PS respectively. Show that ABCD is a parallelogram. ABCD QR PS B D ABCD