Important Instructions for the School Principal. (Not to be printed with the question paper) Note:

Transcription

1 Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for the use in School Based Summative Assessment- II, March-2012 only. This question paper is not to be used for any other purpose except mentioned above under any circumstances. 2) The intellectual material contained in the question paper is the exclusive property of Central Board of Secondary Education and no one including the user school is allowed to publish, print or convey (by any means) to any person not authorised by the Board in this regard. 3) The School Principal is responsible for the safe custody of the question paper or any other material sent by the Central Board of Secondary Education in connection with School based SA-II, March-2012, in any form including the print-outs, compact-disc or any other electronic form. 4) Any violation of the terms and conditions mentioned above may result in the action criminal or civil under the applicable laws/byelaws against the offenders/defaulters. Note: Please ensure that these instructions are not printed with the question paper being administered to the examinees. Page 1 of 9

2 SUMMATIVE ASSESSMENT II, MATHEMATICS / II, 2012 Class X / X Time allowed : 3 hours Maximum Marks : 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 10 questions of 1 mark each, Section-B comprises of 8 questions of 2 marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 6 questions of 4 marks each. (iii) Question numbers 1 to 10 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) (iii) 1 10 (iv) 2 3 (v) Page 2 of 9

3 SECTION A / Question numbers 1 to 10 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice The discriminant of the quadratic equation 7 3 x 2 10x 3 0 is : 10 (A) 142 (B) (C) 184 (D) x 2 10x 3 0 (A) 142 (B) (C) 184 (D) Which of the following is not an AP : (A) 5 3 3,, 2, (B) 0.3, 0.33, (C) 3, 12, 27, 48,. (D) p, 2p1, 3p2, 4p3. AP (A) 5 3 3,, 2, (B) 0.3, 0.33, (C) 3, 12, 27, 48,. (D) p, 2p1, 3p2, 4p3. 3. The length of the tangent drawn from a point 8 cm away from the centre of a circle of radius 6 cm is : (A) 7 cm (B) 2 7 cm (C) 10 cm (D) 5 cm 6 cm 8 cm (A) 7 cm (B) 2 7 cm (C) 10 cm (D) 5 cm 4. If the angle between two radii of a circle is 130, then the angle between the tangents at the end points of radii at their point of intersection is : (A) 90 (B) 50 (C) 70 (D) (A) 90 (B) 50 (C) 70 (D) If four sides of a quadrilateral ABCD are tangential to the circle as shown in the fig, then : (A) ACADBDCD (B) ABCDBCAD (C) ACADBCBD (D) ABCDACBC ABCD Page 3 of 9

4 (A) ACADBDCD (B) ABCDBCAD (C) ACADBCBD (D) ABCDACBC 6. To divide a line segment internally in the ratio 3 : 5, the number of arcs to be drawn on a ray inclined to the line segment is : (A) 3 (B) 5 (C) 8 (D) 15 3 : 5 (A) 3 (B) 5 (C) 8 (D) If the area of three adjacent faces of a cuboid are X, Y and Z respectively, then the volume of cuboid is : (A) XYZ (B) 3XYZ (C) XYZ (D) 3XYZ X, Y Z (A) XYZ (B) 3XYZ (C) XYZ (D) 3XYZ 8. If the perimeter of a circle is equal to that of a square, then the ratio of these areas is : (A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11 : 14 (A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11 : 14 9 A pole 6 m high casts a shadow 2 3 m long on the ground, then the sun s elevation is : (A) 60 (B) 45 (C) 30 (D) m (A) 60 (B) 45 (C) 30 (D) If the probability of an event is 0.65, then the probability of not happening of that event is : (A) 0.35 (B) (C) 1.25 (D) (A) 0.35 (B) (C) 1.25 (D) 3 SECTION-B / Question numbers 11 to 18 carry two marks each Find the roots of the quadratic equation 6x 2 x20 by factorisation. 6x 2 x Find the 6th term from the end of the A.P. : 5, 2, 1, 4,., 31 AP 5, 2, 1, 4,., ABC is an isosceles triangle in which ABAC which is circumscribed about a circle as shown in the figure. Show that BC is bisected at the point of contact. Page 4 of 9

5 ABC ABAC BC 14. Two cubes have their volumes in the ratio 8 : 125. What is the ratio of their surface areas? 8 : A sphere of maximum volume is cut out from a solid hemisphere of radius 6 cm. What is the volume of the cut out sphere? 6 cm 16 The segment AB is divided into 4 equal parts. C is nearer to A and E is nearer to B. Find the co ordinates of A and B, if the co ordinates of C, D and E are 5 1 2, 2, (3, 0) and 7 1 2, 2 respectively. AB C A E B A B C, D E (3, 0) 7, 1,, Prove that the points (a, 0), (0, b) and (1, 1) lie on the same straight line if a b 1 1 (a, 0), (0, b) (1, 1) 1 a b 18 A die is thrown twice. What is the Probability that 4 will not appear on either time? 4 A coin is tossed two times. Find the probability of getting at least one tail. SECTION-C / Question numbers 19 to 28 carry three marks each Solve x 2 31 x 3 0 by the method of completing the square. x 2 31 x 3 0 Page 5 of 9

6 For what value of k does the quadratic equation (k5) x 2 2 (k5) x20 have equal roots? k (k5) x 2 2 (k5) x The sum of first n terms of an A.P. : is given by n 2 8 n. Find its 12 th term. AP n n 2 8 n Prove that the intercept of a tangent between a pair of parallel tangents to a circle subtend a right angle at the centre of the circle. OR / Two tangents TP and TQ are drawn to a circle with centre O, from an external point T. Prove that PTQ2 OPQ T O TP TQ PTQ2 OPQ 22. Construct a triangle similar to a given triangle ABC, in which AB4 cm, BC6 cm and 5 ABC60, such that each side of the new triangle is 7 of the corresponding side of ABC. ABC AB4 cm BC6 cm ABC60 5 ABC The radius of a solid sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire. 9 cm 2 mm th In the figure O is the centre of the bigger circle and AC is its diameter. Another circle with AB as diameter is drawn. If AC54 cm and BC10 cm, find the area of the shaded region. AC54 cm O AC AB BC10 cm 24. From a solid cylinder of height 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is hollowed out. Find the total surface area of remaining solid. Page 6 of 9

7 12 cm 10 cm A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm. If the height of toy is 12 cm, find the number of toys so formed. 12 cm 15 cm 3 cm 12 cm 25 The angle of elevation of the top of a tower from certain point is 30. If the observer moves 20 meters towards the tower, the angle of elevation of the top increases by 15. Find the height of the tower. use, m 26 If the points A(2, k), B(3, 4) and C(7, 10) are the vertices of a right angled isosceles triangle. Find the value of k and hence find the area of the ABC, given that A90. A(2, k), B(3, 4) C(7, 10) k ABC A90 27 Prove that the points A(0, 1), B(1, 4), C(4, 3) and D(3, 0) are the vertices of a square ABCD. A(0, 1), B(1, 4), C(4, 3) D(3, 0) ABCD 28 One card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is either a red card or a king? 52 SECTION-D / Question numbers 29 to 34 carry four marks each A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed km 250 km/hr Seven years ago Varun s age was five times the square of Swati s age. Three years hence Swati s age will be two fifth of Varun s age. Find their present ages Find the sum of n terms of the AP a, ad, a2 d, a (n1) d Page 7 of 9

8 AP n a, ad, a2 d,, a (n1) d 31. Prove that the tangent to a circle is perpendicular to the radius through the point of contact. 32. A right circular cylinder container of base radius 6 cm and height 20 cm is full of ice cream. The ice cream is to be filled in cones of height 10 cm and base radius 3 cm, having a semispherical top. Find the number of cones needed to empty the container. 6 cm 20 cm 10 cm 3 cm Water is flowing at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time the level of water in pond rise by 21 cm? 14 cm 15 km/hr 50 m 44 m 21 cm 33. A friction cluth is in the form of a frustum of a cone as shown in figure. The diameter of top and bottom base are 20 cm and 32 cm. Its height is 8 cm. Find its lateral surface and volume. 20 cm 32 cm 8 cm 34. From a point P on the ground the angle of elevation of the top of a 10 m. tall building is 30. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag staff from P is 45. Find the length of the flag staff and the distance of the building from the point P. (use ) P Page 8 of 9

9 P 45 P o 0 o - Page 9 of 9