MATHEMATICS - CLS 10_59a5f96b145f0a00d27baec8455deb56

WEST CHENNAI SAHODAYA CLUSTER COMMON EXAMINATION 2020 Class- X Subject- Mathematics Time Allowed: 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 two sections- I and II. 2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 4 questions on case study. 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 Question Part-A Marks No. allocated Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 1. 51 1 State whether the rational number 1700 will have a terminating decimal expansion or a non-terminating repeating decimal expansion. Justify. (OR) Given that LCM (26,169) =338, find HCF (26,169). 2. What should be added to the polynomial x2 − 5x + 4 so that 3 is a zero of 1 this polynomial? 3. Find the value of p for which the equations x + 2y = 5 and 3x + py +15 = 0 1 are inconsistent. 4. Find the point of intersection of line − 3x + 7y = 3 with x - axis 1 5. Determine the 10th term from the end of the A.P:4, 9,14……..254 1 (OR) Write the value of x for which x + 2, 2x, 2x + 3 are three consecutive 1 terms of an A.P 1 6. Find the nature of roots of the quadratic equation 2x2 – 3x + 5 = 0. 7. Find the value of cosec²30°- sin²45°- sec²60° Page 1 of 7

8. 1 5 1 If is a root of the equation x2 + kx − = 0, then find the value of k. 1 2 4 (OR) If the discriminant of the equation 5x2 – ax + 4 = 0 is 1, then find a (a > 0) 9. In the given figure, AOB is a diameter of the circle with center O and AC is a tangent to the circle at A. If ∟ BOC = 1300, then find ∟ACO. 10. In the figure, AB and CD are common tangents to circles which touch each 1 other at D. If AB = 8 cm, find the length of CD. (OR) The chord of a circle of radius 1 cm subtends a right angle at its centre. Find the length of minor arc AB (in cm). 11. If the ratio of corresponding sides of two similar triangles is 2 : 3, then what 1 is the ratio of their corresponding heights 1 12. To draw a pair of tangents to a circle which are inclined to each other at an 1 angle of 60°, it is required to draw tangents at the end points of those two 1 radii of the circle. What should be the angle between the radii? 1 13. If 3 tan A = cot A and A is an acute angle, find ∠ A 14. The perimeter of a semi-circular protractor is 36 cm. Find its diameter. 15. What is the radius of a cylinder whose volume and curved surface area are numerically equal Page 2 of 7

16. Two dice are thrown once. What is the probability of getting a doublet? 1 4 (OR) A letter is chosen at random from the word ‘APPRECIABLE’. Find the probability of getting a consonant. Section-II Case study based questions are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark 17. Case Study based-1 Taj Mahal is located on the right bank of the Yamuna river in a vas Mughal garden that encompasses nearly 17 hectares, in the Agra District. It is one of the world’s wonders and one amongst the UNESCO World Heritage sites. (i) If 10 hectares = 100000 m2, then what is the measure of Mughal Garden (approximately) in square metres. a) 1700000 b) 17000000 c) 170000 d) 1700 (ii) The main building stands on a platform having a height of 50 meters and base area 169000 m2 (approximately) find volume of the platform. a) 3380000 cm3 b) 8450000 m3 c) 845000 m3 d) 3380 m3 (iii) Find the cloth required to cover its central inner hemispherical dome if the radius of its base is 14 m approximately. (Take π = 22) 7 a) 1232 m2 b) 1324 m2 c) 1434 m2 d) 1136 m2 (iv) If one minaret volume is 132 m3 and volume of 1 brick is 11 cm3, find the number of bricks used for one minaret. a) 11000000 b) 12000000 c) 13000000 d) 132000000 (v) If dimension of the pool in front of a model Taj Mahal is 18cm X 7cm X6cm, then LSA of the pool is _________ a) 250 cm2 b) 300 cm2 c) 150 cm2 d) 756 cm2 Page 3 of 7

18. Case Study Based- 2 4 A tree in a garden breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 300 with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. (i) What is the length (in metres) of the unbroken part? a) 1 b) 2 c) 5 d) 8 √3 √3 √3 √3 (ii) What is the length (in metres) of the broken part? a) 10 b) 12 c) 14 d) 16 √3 √3 √3 √3 (iii) Find the total height of the tree (in metres). a) 5√3 b) 8√3 c) 10√3 d) 16√3 (iv) What is the area of the right angle triangle formed (in sq.metres)? a) 8 b) 32 c) 56 d) 35 √3 √3 √3 √3 (v) What is measure of ∟ABC? a) 450 b) 600 c) 900 d) 150 19. Case Study Based- 3 4 Rama chooses a date at random in February for get together party. Refer the above calendar and answer the following questions. (i) What is the probability that she chooses Saturday or Sunday? 5 b) 15 c) 9 d) 4 a) 29 29 29 9 (ii) What is the probability that the selected date is a prime number? 10 11 9 8 b) 29 c) 29 d) 29 a) 29 Page 4 of 7

(iii) Probability that the selected date is a multiple of 3 and 4 is ________ 16 b) 2 c) 15 d) 4 a) 29 29 29 29 (iv) What is the probability that the selected date is a Composite number and Saturday? b) 2 c) 3 d) 4 29 29 29 1 a) 29 (v) Probability that the selected date is ≤ 13 and Thursday is _____ 13 b) 12 c) 2 d) 3 a) 29 29 29 29 20. Case Study Based- 4 4 To conduct Sports Day activities, in a rectangular shaped school ground ABCD, tracks in the form of lines have been marked at a distance of 1 m each. 150 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. Shreya runs 1/5th distance on 3rd track and posts the flag and Vini runs 1/3rd distance on the 8th track and posts the flag. (i) Find the coordinates where Shreya posts the flag. 2 a) (30, 3) b) (3, 50) c) (3, 30) d) (2, 50) 2 (ii) Coordinates where Vini posts the flag is ____ a) (50, 8) b) (8, 50), c) (30, 8) d) (8, 30) (iii) Distance between the two flags is _______ a) √470 units b) √115 units c) √425 units d) √125 units (iv) If Rajini has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? a) (5.5, 35) b) (11, 35) c) (5.5, 40) d) (11, 70) (v) How much distance Vini ran more than Shreya? a) 125 m b) 20 m c) 11 m d) 10 m Part –B Section III: All questions are compulsory. In case of internal choices, attempt any one. 21. If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then determine the values of a and b. 22. Check whether 12n can end with the digit 0 for any natural number n. Page 5 of 7

23. The coordinates of the points A and B are respectively (4, - 3) and (- 1, 7). 2 Find the abscissa of a point C on the line segment AB such that AC : CB = 3 : 2. 2 2 (OR) If Q (0,1) is equidistant from P(5, − 3) and R(x, 6), then find the value of x. 24. Divide a line segment AB of length 6.8 cm internally in the ratio 3 : 5. 25. If two towers of height h1 and h2 subtend angles of 600 and 300 respectively at the mid-point of the line joining their feet, then find h1 : h2 26. In the given figure, PA and PB are the tangents to the circle with centre 2 O. ∠APB = 800 find the ∠AMB (OR) Two tangents PA and PB are drawn to the circle with centre O such that ∠APB = 1200, P is an external point, show that OP =2 AP. Section IV 3 27. Prove that √2 is an irrational number 3 28. Solve for x: 1− 1 = 11 , x ≠ −4, 7 3 x−7 x+4 30 (OR) Solve 1 = 1+1+ 1 , a ≠ b ≠ 0, x ≠0,x ≠ −(a + b) x for x: a + b + x ab 29. All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a : i) Face card ii) King iii) Red card Page 6 of 7

30. In the figure, three sectors of a circle of radius 7 cm, making angles of 600, 3 800 and 400 at the centre are shaded. Find the area of the shaded region. 31. Prove that in a right-angled triangle, the square of the hypotenuse is equal 3 to the sum of squares of the other two sides. 3 3 (OR) 5 Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the 5 same ratio. 5 32. Prove that: tan θ + cot θ = 1 + sec θ cosec θ 1−tan θ 1−cotθ 33. The weights (in kg) of 50 wrestlers are recorded in the following table Weight 100 - 110 110 – 120 120 – 130 130 – 140 140 - 150 (in kg) 4 14 21 8 3 Number of Wrestlers Find the mean weight of the wrestlers Section V 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 flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P. (Take √3 = 1.732) (OR) The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 300 and 450 respectively. Find the height of the multi-storeyed building and the distance between the two buildings (Take √3 = 1.7). 35. Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44m wide. Find the time in which the level of water in the tank will rise by 21 cm 36. Find the value of p if x = - 2 is a root of the equation 3x2 + 7x + p = 0. Also find the values of k so that the roots of the equation x2 + k (4x + k – 1) + p = 0 are equal.   ************* Page 7 of 7