CBSE Class X Mathematics Sample Paper 04 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 Which term of the progression 4, 9, 14, 19, is 109? 2 Find the sum of the zeroes of the quadratic polynomial 3 If and, then what is the value of cot a? 4 A die is thrown once What is the probability of getting a composite number? 5 Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, 3) and B is (1, 4) 6 In fig-1, AQ, AR and BC are the tangents If AQ = 10 cm, find the perimeter of DABC SECTION B 7 Determine an AP whose 3 rd term is 16 and difference of 7 th term and 5 th term is 12 1 / 15
8 Find the coordinates of the points of trisection of the line segment joining points (4, 1) and B( 2, 3) 9 Find two consecutive positive integers, sum of whose squares is 365 10 In Fig 2, and AB = 6 cm Find the length of DC 11 In fig-3, from an outside point P, PA is a tangent to a circle whose centre is at C A is the point of contact If PC = 10 cm and PA= 8 cm Find the diameter of the circle 12 2 cubes each of volume are joined end to end Find the surface area of the resulting cuboid SECTION C 13 Find two consecutive odd positive integers, sum of whose squares is 970 14 How many terms of the sequence 18, 16, 14, should be taken so that their sum is zero? 15 In fig-4, DE BH and EF HC Show that, DF BC 16 Show that the points (1, 7), (4, 2), ( 1, 1) and ( 4, 4) are the vertices of a square Find the area of the rhombus, if its vertices are (3,0), (4,5), (-1,4) and (-2,-1) taken in order 17 The ages of workers in a factory are given below : Age (in years) 20-30 30-40 40-50 50-60 60-70 Number of workers 5 26 78 104 98 2 / 15
Find the modal age of workers Compute the Median for the given data Class interval 100-110 110-120 120-130 130-140 140-150 150-160 Frequency 6 35 48 72 100 4 18 Two dice one blue and one grey, are thrown at the same time What is the probability that the sum of the two numbers appearing on the top of the dice is 6? 19 Show that is irrational Use Euclid s division algorithm to find the HCF of 4052 and 12576 20 Prove that, 21 In fig 5 ABCD is a quadrant of a circle with radius 28 cm and a semicircle BEDB is drawn with BD as diameter Find the area of the shaded region The radius of a radius of a circle is 20cm Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area Find the radius of the largest of the three concentric circle 22 Find the HCF of 96 and 404 by the prime factorization method Hence, find their LCM SECTION D 23 Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm 24 Five years hence, the age of Anubhab will be three times that of his son Five years ago, Anubhab s age was seven times that of his son What are their present ages? 3 / 15
25 Prove that: If a cosθ b sin θ = c prove that 26 The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled A card is drawn from the remaining cards Find the probability of getting a card of (i) heart (ii) king (iii) club 27 In fig-6, AB and CD are two diameters of a circle with center at O OD is the diameter of the smaller circlegiven that, OA = 7 cm, find the area of the shaded region 28 From the top of a building 100 m high, the angles of depression of the top and bottom of a tower are observed to be 45 o and 60 o respectively Find the height of the tower Also find the distance between the foot of the building and the bottom of the tower 29 A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in fig-7 If the height of the cylinder is 10 cm and its base is of radius 3 5 cm, find the total surface area of the article 30 The sum of first six terms of an AP is 42 The ratio of its 10 th term to its 30 th term is 1 : 3 Find the 1 st term and the 13 th term of the AP For what values of n nth term of the series 3, 10, 17And 63, 65, 67Are equal 4 / 15