CBSE Class X Mathematics Sample Paper 03 Time Allowed: 3 Hours Max Marks: 80 General Instructions: i All questions are compulsory ii The question paper consists of 30 questions divided into four sections A, B, C and D iii Section A contains 6 questions of 1 mark each Section B contains 6 questions of 2 marks each Section C contains 10 questions of 3 marks each Section D contains 8 questions of 4 marks each iv There is no overall choice However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each You have to attempt only one of the alternatives in all such questions v Use of calculators is not permitted SECTION - A 1 Find the zeroes of the quadratic polynomial 2 Write the sum of the first fifteen natural numbers 3 Find the coordinate of the mid-point of the line segment joining the points whose coordinates are and 4 In fig-1, centre of the circle is O From outside point P, two tangents PA and PB are drawn to touch the circle Given ÐAPB = 60 o Find ÐAOB 5 A ladder of length 4 m makes an angle of 45 o with the ground when placed against an electric post Determine the distance between the feet of the ladder and the electric post 6 Captain of Indian cricket team tosses two different coins, one of 1 and other of 2 simultaneously What is the probability that he gets at least one head? 1 / 16
SECTION - B 7 Find the discriminant of the equation and hence find the nature its roots 8 If the 10 th term of an AP is 47 and its 1 st term is 2, find the sum of its first 15 terms 9 Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5) 10 In fig-2, and Prove that, is isosceles 11 Two concentric circles are of radius 5 cm and 3 cm Find the length of the chord of the larger circle which touches the smaller circle 12 The height and base diameter of a solid cylinder are 210 m and 24 cm respectively Find the volume of the cylinder SECTION - C 13 The taxi charges in a city consist of a fixed charge together with the charge for the distance covered For a distance of 10 km, the charge paid is 200 and for a journey of 15 km, the charge paid is 275 What are the fixed charges and the charge per km? How much a person has to pay for travelling a distance of 25 km? 14 Show that is irrational 15 Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer 16 The 4 th term of an AP is equal to three times the 1 st term & the 7 th term exceeds twice the 3 rd term by 1 Find the 1 st term and common difference The first and the last terms of an AP are 17 and 350 respectively If the common difference is 9, how many terms are there and what is their sum? 2 / 16
17 If A(-5, 7), B(- 4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area Find the coordinates of the points which divide the line-segment joining the points (-4, 0) and (0, 6) in four equal parts 18 Prove that the sum of the squares of the sides of a rhombus is equal to sum of the squares on its diagonals 19 Prove that, the lengths of tangents drawn from an external point to a circle are equal In fig-3, PQ and RS are two parallel tangents to a circle with centre O and another tangent EF with point of contact C intersecting PQ at E and RS at F Prove that EOF = 90 20 Evaluate: 21 A box contains 90 discs which are numbered from 1 to 90 If one disc is drawn at random from the box, find the probability that it bears a perfect square number Two horses are considered for a race The probability of selection of the first horse is 1/4 and that of second is 1/3 What is the probability that : a both of them will be selected b only one of them will be selected c none of them will be selected 22 A box contains 5 red marbles, 8 white marbles and 4 green marbles One marble is taken out of the box at random What is the probability that the marble taken out will be i) white ii) not green? 3 / 16
SECTION - D 23 Two water taps together can fill a tank in hours The tap of larger diameter takes 10 hrs less than the smaller one to fill the tank separately Find the time in which each tap can separately fill the tank A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more Find the original speed of the train 24 Find the sum of all three-digit numbers which leaves the remainder 3 when divided by 5 25 Construct a triangle similar to triangle ABC with its side equal to of the corresponding sides of the triangle ABC Construct an isosceles triangle whose base is 7cm and altitude 5 cm and then construct another triangle whose sides are times the corresponding sides of the isosceles triangle 26 Prove that: 27 In fig-3, of ABC is a right angle and AB = 3 units, AC = 4 units Semicircles are drawn on AB, AC and BC as diameters Also a circle circumscribing the area of the shaded region ABC is drawn Find the 28 Two ships are sailing in the sea on either side of a light-house The angles of depression of two ships as observed from the top of the light-house are 60 o and 45 o respectively If the distance between the ships is meters, find the height of the light-house 29 A person connects a pipe of internal diameter 20m from a canal into a empty cylindrical tank in his field which is 10 m in diameter and 2 m deep If the rate of flow of water 4 / 16
through the pipe is 6km/hr, then after how much time the flow of water should be stopped to avoid over flow of water from the tank? What value we have from the problem? 30 The median of the following frequency distribution is 35 Find the value of x Class Interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 2 3 5 6 x 3 2 Compute the mode for the following frequency distribution Size of items: 0-4 4-8 8-12 12-16 16-20 20-40 24-28 28-32 32-36 36-40 Frequency: 5 7 9 17 12 10 6 3 1 0 5 / 16