Mathematics - Class IX 2012 - Exam - Set 37, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 37 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) 45003 Page 3 of 10 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. If the point (1, 1) lies on the graph of the equation 3y(a1) x7, then value of a is : (A) 3 (B) 3 (C) 5 (D) 5 (1, 1) 3y(a1) x7 a (A) 3 (B) 3 (C) 5 (D) 5 2. A triangle ABC and a parallelogram ABCD have a common base BC and lie between the same parallels. If the area of triangle ABC is 34 cm2, what is the area of the parallelogram ABCD ? (A) 17 cm2 (B) 68 cm2 (C) 34 cm2 (D) 8.5 cm2 ABC ABCD BC ABC 34 2 ABCD (A) 17 2 (B) 68 2 (C) 34 2 (D) 8.5 2 3. Given a circle with centre O and smallest chord AB is of length 6 cm and the largest chord CD of the circle is of length 10 cm, then the radius of the circle is. (A) 1.5 cm (B) 6 cm (C) 5 cm (D) 3.5 cm O केन्द्र वाऱे वतृ्त की एक छोटी जीवा की ऱम्बाई 6 सेमी तथा उसकी सबसे बड़ी जीवा की ऱम्बाई 10 सेमी है, तो वतृ्त की त्रिज्या है : (A) 1.5 सेमी (B) 6 सेमी (C) 5 सेमी (D) 3.5 सेमी 4. Which of the following is the equation of a line parallel to y-axis ? (A) y0 (B) xyz (C) yx (D) xa y- (A) y0 (B) xyz (C) yx (D) xa 5. If the mean of the data, 2, x1, 9, x2 is 4 then the value of x is : (A) 2 (B) 3 (C) 4 (D) 5 2, x1, 9, x2 4 x (A) 2 (B) 3 (C) 4 (D) 5 6. The radius of a sphere is 2r, then its volume will be : Page 6 of 10 17. Construct a triangle ABC with AB4 cm, BC6 cm and CA7.5 cm. Construct the perpendicular bisector of CA. त्रिभजु ABC की रचना कीजजए जजसमं AB4 सेमी, BC6 सेमी तथा CA7.5 सेमी है। CA ऩर ऱॊब समदिभाजक खीॊनचए। 18. A toy is in the form of a cone mounted on a hemisphere of base radius 3.5 cm. If the total height of the toy is 15.5 cm, find its total surface area of the toy 22 Use 7        . 3.5 15.5 22 7        . OR The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water it can hold ? 3 22 Use and 1000 cm 1 litres 7        . 132 25 322 1000 1 7        . 19. The mean age of 10 students of a class is 15 years, A student of age 14 years leaves the class and in his place age of their teacher is counted. This increased the mean age of group to 16 years. Find the age of the teacher. 10 15 14 16 OR The following observations have been arranged in ascending order. 29, 32, 48, 50, x, x2, 72, 78, 84, 95 If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x2, 72, 78, 84, 95 63 x 20. Give the geometrical interpretation of 2x40 as an equation : (a) in one variable (b) in two variables 2x40 (a) (b) OR/ Draw the graph of the equation 2x3y6. Also, find two points on the graph of this equation. Page 7 of 10 2x3y6 21. The floor of a rectangular hall has a perimeter of 250 m and its length and breadth are in the ratio of 13 : 12. If the cost of painting the four walls and ceiling at the rate of Rs. 5 per m2 is Rs. 27000, find the height of the hall. 250 13 : 12 5 2 27000 22. Prove that the diagonals of a parallelogram divide it into four triangles of equal area. 23. If non-parallel sides of a trapezium are equal then prove that it is cyclic. 24. If the mean of the following data is 6, find the value of p. xi 2 4 6 10 p5 fi 3 2 3 1 2 6 p xi 2 4 6 10 p5 fi 3 2 3 1 2 SECTION-D / Question numbers 25 to 34 carry four marks each. 25. ABC is an isosceles triangle in which ABAC. AD bisects PAC and CDAB. Show that (i) DACBCA (ii) ABCD is a parallelogram. ABC ABAC AD, PAC CDAB (i) DACBCA (ii) ABCD Page 8 of 10 26. Construct a triangle PQR in which QR7 cm Q45, and PQPR2.5 cm. OR Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm. एक त्रिभजु PQR की रचना कीजजए जजसमं QR7 सेमी, Q45तथा PQPR2.5 सेमी है। अथवा एक समकोण त्रिभजु की रचना कीजजए जजसका आधार 12 सेमी तथा कणण तथा अन्द्य भजुा का योग 18 सेमी है। 27. The coordinates of points given in the following table represent some of the solutions of the equation, y5 x2 xi 1   2 2  yi  17 3   3 Find the missing values. Also find the coordinates of the points where the line cuts x-axis and y-axis. y5 x2 xi 1   2 2  yi  17 3   3 x- y- 28. Find the volume of a sphere whose surface area is 154 cm2. Also, find the cost of polishing its surface @ Rs. 5 per cm2 154 2 5 2 29. If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, then prove that the chords are equal. यदद एक वतृ्त की दो प्रनतच्छेदी जीवाऍ ॊ, प्रनतच्छेद त्रबन्द्द ुसे होकर जाने वाऱे व्यास के साथ समान कोण बनाती हं, तो नसद्ध दकजजए दक जीवाएॉ समान हं। 30. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisects each other. OR ABC is the right – angled triangle right angled at B ; and P is the mid-point of AC. Prove that PAPB 1 2 AC.