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CBSE Class 10 Board Exam 2018 : Mathematics

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Munni Singh
K R Mangalam World School, South Delhi
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Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online CLASS X (2020-21) MATHEMATICS STANDARD (041) SAMPLE PAPER-09 Time : 3 Hours Maximum Marks : 80 General Instructions : 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part A : 1. It consists of two sections- I and II. 2. Section I has 16 questions. Internal choice is provided in 5 questions. 3. Section II has four case study-based questions. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part B : 1. Question no. 21 to 26 are very short answer type questions of 2 mark each. 2. Question no. 27 to 33 are short answer type questions of 3 marks each. 3. Question no. 34 to 36 are long answer type questions of 5 marks each. 4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks. Part - A Section - I Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. Q1. Write whether rational number decimal. 7 75 will have terminating decimal expansion or a non-terminating O Find HCF of the numbers given below: k, 2k, 3k, 4k and 5k, , where k is a positive integer. Q2. A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. What is the numerator of the given fraction ? Q3. TABC AD ? Q4. If the point P (k, 0) divides the line segment joining the points A (2, - 2) and B (- 7, 4) in the ratio 1 : 2, then what is the value of k ? is an equilateral triangle with each side of length 2p . If AD = BC then what is the value of O Find the coordinates of a point A on y -axis, at a distance of 4 units from x -axis and below it. Q5. If sin + cos = 2 cos , ( ! 90c) then what is the value of tan ? Q6. q cos q m . If 4 tan = 3 , then find c 44 sin sin q + cos q To Get 20 Solved Paper Free PDF by whatsapp add +91 89056 29969/9530143210/9461443210 in your class Group Page 1 Mathematics Standard X Sample Paper 09 Unsolved Q7. www.cbse.online An observer, 1.5 m tall is 20.5 away from a tower 22 m high, then what is the angle of elevation of the top of the tower from the eye of observer? O A 6 m high tree cast a 4 m long shadow. At the same time, a flag pole cast a shadow 50 m long. How long is the flag pole? Q8. Two concentric circles of radii a and b where a > b, Find the length of a chord of the larger circle which touches the other circle. O In the given figure, a circle touches all the four sides of quadrilateral ABCD with AB = 6 cm , BC = 7 cm and CD = 4 cm , then what is the length of AD ? Q9. To divide a line segment AB in the ratio 2: 5 , a ray AX is drawn such that +BAX is acute. Then points are marked at equal intervals on AX . What is the minimum number of these points ? O To divide the line segment AB in the ratio 2 | 3 , a ray AX is drawn such that +BAX is acute, AX is then marked at equal intervals. Find minimum number of these marks. Q10. In the given figure, AB is the diameter where AP = 12 cm and PB = 16 cm. Taking the value of as 3, find the perimeter of the shaded region. Q11. Find the area (in cm2 ) of the circle that can be inscribed in a square of side 8 cm. Q12. Consider the following frequency distribution of the heights of 60 students of a class Height (in cm) 150-155 Number of students 15 155-160 160-165 165-170 170-175 175-180 13 10 8 9 5 What is the upper limit of the median class in the given data? Q13. If xi s are the mid-points of the class intervals of grouped data, f i s are the corresponding frequencies and x is the mean, then find / (f i xi - x ). Q14. Out of one digit prime numbers, one number is selected at random. What is the probability of selecting an even number? Download 20 Solved Sample Papers PDF from www.cbse.online Page 2 Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online Q15. Find the probability of an impossible event. Q16. A number is selected at random from 1 to 30. Find the probability that it is a prime number. Section II Case study-based questions are compulsory. Attempt any 4 sub parts from each question. Each question carries 1 mark. Q17. For a jewellery metal box to satisfy certain requirements, its length must be three meter greater than the width, and its height must be two meter less than the width. (i) If width is taken as x , which of the following polynomial represent volume of box ? (a) x2 - 5x - 6 (b) x3 + x2 6x (c) x3 - 6x2 - 6x (d) x2 + x 6 (ii) Which of the following polynomial represent the area of metal sheet used to make box ? (a) x2 - 5x - 6 (b) 6x2 + 4x 12 (c) x3 - 6x2 - 6x (d) 6x2 + 3x 4 (iii) If it must have a volume of 18 in3 , what must be its length ? (a) 6 in (b) 3 in (c) 4 in (d) 2 in (iv) At a volume of 18 in3 , what must be its height ? (a) 1 in (b) 3 in (c) 2 in (d) 4 in (v) If box is made of a metal sheet which cost is 10 rs per in2 , what is the cost of metal ? (a) Rs 540 (b) Rs 1080 (c) Rs 270 (d) Rs 340 Q18. Raju and his classmates planned a picnic in zoo. The total budget for picnic was Rs 2000 but 5 students failed to attend the picnic and thus the contribution for each student was increased by Rs 20. To Get 20 Solved Paper Free PDF by whatsapp add +91 89056 29969/9530143210/9461443210 in your class Group Page 3 Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online The expanse of different item was as follows. S. No. Article Cost per student 1 Entry ticket Rs 5 2 Coffee Rs 10 3 Food Rs 25 4 Travelling cost Rs 50 5 Ice-cream Rs 15 (i) If x is the number of students planned for picnic, which is the correct quadratic equation that describe the situation. (a) x2 5x 500 = 0 (b) x2 + 4x 400 = 0 (c) x2 + 5x 500 = 0 (d) x2 4x + 400 = 0 (ii) What is the number of students planned for picnic ? (a) 30 (b) 40 (c) 25 (d) 20 (iii) What is the number of students who attended the picnic? (a) 20 (b) 40 (c) 15 (d) 25 (iv) What is the total expanse for this picnic ? (a) Rs 1500 (b) Rs 2000 (c) Rs 1000 (d) Rs 2100 (v) How much money they spent for travelling ? (a) Rs 500 (b) Rs 1000 (c) Rs 800 (d) Rs 3750 Q19. Resident Welfare Association (RWA) of a Gulmohar Society in Delhi have installed three electric poles A, B and C in a society s common park. Despite these three poles, some parts of the park are still in dark. So, RWA decides to have one more electric pole D in the park. The park can be modelled as a coordinate systems given below. Download 20 Solved Sample Papers PDF from www.cbse.online Page 4 Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online On the basis of the above information, answer any four of the following questions: (i) What is the position of the pole C ? (a) (4, 5) (c) (6, 5) (b) (5, 4) (d) (5, 6) (ii) What is the distance of the pole B from the corner O of the park ? (b) 3 2 units (a) 6 2 units (c) 6 3 units (d) 3 3 units (iii) Find the position of the fourth pole D so that four points A, B C and D form a parallelogram. (a) (5, 2) (b) (1, 5) (c) (1, 4) (d) (2, 5) (iv) What is the distance between poles A and C ? (a) 6 2 units (b) 3 2 units (c) 6 3 units (d) 3 3 units (v) What is the distance between poles B and D ? (a) 2 3 units (b) 28 units (c) 6 3 units (d) 26 units Q20. The boiler is essentially a closed vessel inside which water is stored. Fuel is burnt in a furnace and hot gasses are produced. These hot gasses come in contact with water vessel where the heat of these hot gases transfer to the water and consequently steam is produced in the boiler. Then this steam is piped to the turbine of thermal power plant. There are many different types of boiler utilized for different purposes like running a production unit, sanitizing some area, sterilizing equipment, to warm up the surroundings etc. To Get 20 Solved Paper Free PDF by whatsapp add +91 89056 29969/9530143210/9461443210 in your class Group Page 5 Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online Rajesh has been given the task of designing a boiler for NTPC. Boiler consist of a cylindrical part in middle and two hemispherical part at its both end. The cross section of boiler is given below. Length of cylindrical part is the 3 times of radius of hemispherical part. (i) Which of the following is correct expression for the surface area of cylindrical part of boiler? (a) 2 r2 (b) 6 r2 (c) 4 r2 (d) 8 r2 (ii) Which of the following is correct expression for the total surface area of boiler? (a) 22 r2 (b) 11 r2 3 3 (c) 6 r2 (d) 10 r2 (iii) Which of the following is correct expression for the volume of boiler? (a) 15 r3 (b) 19 r3 3 4 (c) 13 r3 (d) 17 r3 3 4 (iv) What is the ratio of volume to the surface area? (a) 13 r (b) 3 r 30 10 (c) 10 r (d) 3 r 3 10 (v) If r = 3 m , what is the volume of boiler? (a) 117 m3 (b) 125 m3 (c) 231 m3 (d) 238 m3 Part - B All questions are compulsory. In case of internal choices, attempt anyone. Q21. Show that 5 6 is an irrational number. O m n Write the denominator of the rational number 257 500 in the form 2 5 , where m and n are nonnegative integers. Hence write its decimal expansion without actual division. Q22. In the figure, ABCDE is a pentagon with BE z CD and BC z DE . BC is perpendicular to CD. AB = 5 cm, AE = 5 cm, BE = 7 cm, BC = x y and CD = x + y. If the perimeter of ABCDE is 27 cm. Find the value of x and y , given x , y ! 0 . Download 20 Solved Sample Papers PDF from www.cbse.online Page 6 Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online O Find the values of and for which the following pair of linear equations has infinite number of solutions : 2x + 3y = 7; 2 x + ^ + hy = 28 . Q23. Find the roots of the quadratic equation 4x2 4px + ^p2 q2h = 0 Q24. In an equilateral triangle ABC, AD is drawn perpendicular to BC meeting BC in D. Prove that AD2 = 3BD2 . A sin A = cos A sin A Q25. Prove that : 1 +costan A 1 + cot A Q26. Find the mode of the following distribution : Classes 25-30 30-35 35-40 40-45 45-50 50-55 Frequency 25 34 50 42 38 14 Q27. Prove that 3 is an irrational number. Q28. Solve the following pair of equations for x and y : a2 - b2 = 0, a2 b + b2 a = a + b , x ! 0; y ! 0 . x y x y O Solve for x and y : ax + by = a + b 2 3x + 5y = 4 Q29. TABC is right angled at C. If p is the length of the perpendicular from C to AB and a, b, c are the lengths of the sides opposite +A, +B and +C respectively, then prove that 12 = 12 + 12 . p O a b In TABC, DE || BC. If AD = x + 2, DB = 3x + 16, AE = x and EC = 3x + 5, them find x. Q30. Prove that : 2 (sin6 + cos6 ) 3 (sin4 + cos4 ) + 1 = 0 Q31. Draw a circle of radius 3 cm. From a point P , 7 cm away from centre draw two tangents to the circle. Measure the length of each tangent. Q32. A wire when bent in the form of an equilateral triangle encloses an area of 121 3 cm2. If the wire is bent in the form of a circle, find the area enclosed by the circle. Use = 227 . Q33. Compute the median from the following data : Mid-values 115 125 135 145 155 165 175 185 195 Frequency 6 25 48 72 116 60 38 22 3 Q34. If the sum of first n term of an AP is given by Sn = 3n2 + 4n. Determine the AP and the nth term. O The sum of the 3 and 7 terms of an AP is 6 and their product is 8. Find the sum of first 20 terms of the AP. rd th To Get 20 Solved Paper Free PDF by whatsapp add +91 89056 29969/9530143210/9461443210 in your class Group Page 7 Mathematics Standard X Sample Paper 09 Unsolved www.cbse.online Q35. If A (- 2, 1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram ABCD , find the values of a and b . Hence find the lengths of its sides. Q36. Distance between two ships is 73.2 m. From the top of tower, 100 m high, a man observes two cars on the opposite sides of the tower with the angles of depression 30c and 45c respectively. Find the distance between the cars. (Use 3 = 1.73 ) Download solved version of this paper from www.cbse.online ********** Download 20 Solved Sample Papers PDF from www.cbse.online Page 8

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