141 [X Maths]SAMPLE QUESTION PAPER - IMATHEMATICS (SA - 1I)Time allowed : 3 hours Maximum Marks : 90General Instructions1. All questions are compulsory.2. 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. SectionB comprises of 6 questions of 2 marks each. Section C comprises of 10questions of 3 marks each and Section D comprises of 10 questions of4 marks each.3. Question numbers 1 to 8 in Section A are multiple choice questionswhere you are to select one correct option out of the given four.4. There is no overall choice.5. Use of calculator is not permitted.SECTION B9. If the equation kx2 2kx + 6 = 0 has equal roots, then find the value of k.10. Which term of the arithmetic progression 3, 10, 17, .... will be 84 morethan its 13th term ?11. Prove that in two concentric circles, the chord of the larger circle, whichtouches the smaller circle is bisected at the point of contact.12. In the given figure, BOA is a diameter of a circle and the tangent at apoint P meets BA produced at T. If PBO = 30, what is the measure ofPTA?PB A T30O13. An integer is chosen between 0 and 100. Find the probability that thenumber is dividible by 3 and 5 both.14. If the perimeter of a protractor is 72 cm, calculate its area.22Take7     SECTION C15. Solve for x :1 1 1 1;a b x a b x    where a  0, b  0, x  0 and a + b + x  0.16. The first and the last terms of an A.P. are 8 and 350 respectively. If itscommon difference is 9, how many terms are there and what is theirsum?17. Draw a triangle ABC in which BC = 6.5 cm, AB = 4.5 cm and ABC =60. Also construct a triangle similar to this triangle whose sides are34of the corresponding sides of the triangle ABC.18. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal lineat a height of 88.2 m from the ground. The angle of elevation of theballoon from the eye of the girl at any instant is 60. After sometimes the144 [X Maths]angle of elevation reduces at 30. Find the distance travelled by balloonduring the interval (Take 3 = 1.7).19. Find a point on the y-axis which is equidistant from the points A(6, 5) andB(4, 3).20. In what ratio does the point (½, 6) divide the line segment joint the point(3, 5) and (7, 9).21. A chord 10 cm long is drawn in a circle whose radius is 50 cm. Find thearea of segments.22. Find the area of the shaded region in the given figure, if PQ = 24 cm,PR = 7 cm and O is the centre of the circle.QR PO23. The largest sphere is curved out of a cube of side 7 cm. Find the volumeof sphere.24. A glass cylinder with diameter 20 cm has water to a height of 9 cm. Ametal cube of 8 cm edge is immersed in it completely. Calculate theheight by which water will rise in the cylinder.22Use7      .SECTION D25. 6500 were divided equally among a certain number of persons. Hadthere been 15 more persons, each would have got 30 less. Find theoriginal number of persons.26. In a school, students thought of planting trees in and around the schoolto reduce air pollution. It was decided that the number of trees that eachsection of each class will plant, will be the same as the class in whichthey are studying, e.g., a section of class I will plant one tree, a sectionof class II will plant two trees and so on till class XII. There are threesections of each class. Find :(a) How many trees will be planted by the students?145 [X Maths](b) Which mathematical concept is used in above problem?(c) Which value is depicted in this problem?27. The sum of 5th and 9th terms of A.P. is 72, and the sum of 7th and 12thterms is 97. Find the A.P.28. Prove that the length of tangents drawn from an external point to a circleare equal.29. Prove that the intercept of a tangent between a pair of parallel tangentsto a circle subtend a right angle at the centre of the circle. (Figure is given).O30. There is a small island in the middle of a 100 meter wide river and a talltree stands on the island. P and Q are points directly opposite to eachother on two banks and in line with the tree. If the angles of elevation ofthe top of the tree from P and Q are respectively 30 and 45, find theheight of the tree.31. All the three face cards of spades are removed from a well shuffled packof 52 cards. A card is drawn at random from the remaining pack. Find theprobability of getting :(a) a black-faced card (b) a queen.(c) a black card (d) a spade32. Find the value of K, if the points A (2, 3), B (4, K) and C (6, 3) arecollinear.33. A cylinderical bucket, 32 cm high and with radius of base 18cm, is filledwith sand. This bucket is emptied on the gound and a conical heap ofsand is formed. If the height of the conical heap is 24 cm, find the radiusand slant height of the heap.34. A cap is shaped like the frustum of a cone. If its radius on the open sideis 10 cm, and radius at the upper base is 4 cm and its slant height is 15cm, find the area of cloth used for making it.