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AMITY INTERNATIONAL SCHOOL NOIDA Pre Board Class- X Session- 2020-21 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 three 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. Internal choice is provided in 2 questions of 2 marks, Question Part-A Marks No. allocated Section-I Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 1 2 Express positive integer 540 as the product of its prime factors or Can 72 and 20 respectively be the LCM and HCF of two numbers? Write the reason. Find the zeroes of the polynomial x2-5 x. 1 1 3 For which values of p does the pair of equations given below has unique solution? 4x + py + 8 = 0 2x + 2y + 2 = 0 1 4. How many solutions The following system of equations has? y = x; y = 2x 1 5. Show that -3, 0,3, 6,9, .. is an AP. OR 6. In an Arithmetic Progression, if d= - 4, n=7,an=4, then find a. Check whether the given polynomial is a quadratic equation or not x3- 4x2- x +1= ( x-2) 3. 7. Find the nature of the roots of the equation: 3x2 17x + 20 = 0 1 1 1 OR Check if x = 3 is a solution of the equation 3x2 +13x+ 14 = 0 8. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80 , then find POA. 1 9. In the given figure, AB is a chord of the circle with centre O and PQ is a tangent at point B of the circle. If AOB=110 , then find ABQ. 1 OR If two tangents inclined at an angle of 600 are drawn to a circle of radius 3 cm,then find the length of each tangent. 10. In Fig., two chords AB and CD intersect each other at the point P. Prove that : AP.PB=CP.DP 1 1 11. Given below is the construction done by a student to divide line segment AB into certain ratio. Find the ratio in which AB is divided. 12. If A + B = 900 and tan A = 3 / 4 ,what is the value of cot B 1 13. If sec2x ( 1 + sin x ) (1 sin x) = k. Find the value of K. 1 14. In a circle of radius 21 cm, an arc subtends an angle of 600 at the centre, then find the length of arc. 1 15. A spherical ball of iron has been melted and recast into smaller balls is one fourth of the radius of the original one. How many such balls can be made? 1 16. Find the probability of having 53 Tuesdays in a year. 1 OR Cards marked numbers 2 to 101 are kept in a box and mixed thoroughly. One card is with drawn at random, find the probability that the number of card is a prime number less than 20. Section-II Case study based questions are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark 17. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 60 flower pots have been placed at a distance of 1 m from each other along AD, as shown in Fig. Yamini runs th of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th of the distance AD on the eighth line and posts a red flag. (a) Find the position of red and yellow flags i) (2,25) , (8, 20) ii) (2, 15) , (8.12) iii) (2, 12) , (8, 15) iv) (2, 20) , (2, 25) (b) ( c) (d) 1 1 If Rashmi has to post a blue flag exactly halfway between the line segment joining 1 the two flags, where should she post her flag? i) (5, 37/2) ii) (5, 22) iii) (7, 22.5) iv) (5, 23) Coordinates of the points which divides the line segment AB in the ratio 1:2 i) (4,14) ii) (4, 35) iii) (4, 70/3) iv) (4, 70) 1 (e) 1 18. Reshma is fly fishing in a stream. The tip of her fishing rod is 1.8 m about the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. (a) , ? (b) (c) (d) (e) i) . ii) . iii) . iv) Find the tangent of angle subtended by the rod to the horizontal i) 2/3 ii) 3/4 iii) 1/2 iv) 3/2 Find the area of triangle formed in question (a) i) 2.16 sq m ii) 2.30 sq m iii) 2.90 sq m iv) 3.20 sq m If she pulls the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 second? i) 2.79 m ii) 2.97 m iii) 2.70 m iv) 2.65 m If we decrease the width of the triangle, then length of hypotenuse will i) Decrease ii) Increase iii) cannot say anything iv) None of the above Q19 CASE STUDY 3 In a class four students Anil, Jay, Richa and Suresh were asked to draw the graph of p(x) = ax2+bx +c. following graphs are drawn by the students Richa (a) (b) (c) (d) Suresh How many students have done the graph correctly? (i) 1 (ii) 2 (iii) 3 (iv) 4 Which type of polynomial be represented by Jay s graph (i) Linear (ii) Parabola (iii) Zig-zag (iv) None of these How many zeroes are there for Richa s graph? (i) 1 (ii) 2 (iii) 3 (iv) 4 If p(x)=ax2+bx+c and a+b+c =0 , then one zero is (i) -b/a (ii) (iii) (iv) c/a b/c -c/a (e) If shape of the curve is represented by x2 7x + 12 ,then its zeros are (i) 4, -5 (ii) 2, -3 (iii) 3, 4 (iv) 3,-5 20. Case Study 4 Every year the hazard of pollution raises its ugly head around the year, but we can keep the check on this pollution in a natural way by planting air purifying plants. The health of a plant can be tested by its leaf length also. Here is the data showing the lengths of 40 leaves of a plant : (a) (b) (c) What is the frequency of the median class ? (i) 9 (ii) 12 (iii)5 (iv)17 What will be the lower limit of the modal class ? (i) 140 (ii) 148 (iii) 164 (iv) 132 What is the class mark of the third class interval (i)136 (ii)128 (iii)140 (iv)148 (d) (e) If mean of a data is 140, and median is 138 the mode will be (i)135 (ii)134 (iii)120 (iv)140 How many leaves have length more than or equal to 148 mm? (i) 5 (ii) 9 (iii) 11 (iv) 4 Part B All questions are compulsory. In case of internal choices, attempt any one. 21. HCF and LCM of two numbers is 4 and 9696 respectively. If one number is 96 find the other number. 2 22. The vertices of a rectangle are (3, 4) ,( -1, 2) and ( 2, -4) what are the coordinates of the fourth vertex? 2 OR Show that P(5, -3) is one of the two point of trisection of the line segments joining the points A(7, -2) and B ( 1, -5) 23. Find a quadratic polynomial , whose zeros are reciprocal of the zeroes of the polynomial x2 - x 6 . 2 24. Draw a pair of tangents to a circle of radius 6cm, from a point 10 cm away from its centre. Construct a pair of tangents to the circle and measure their lengths. 2 25. 2 OR If A 300 and B 600 ,verify that sin(A + B) = sinA cosB + cosA sinB In the given figure, the sides AB, BC and CA of a triangle ABC touch a circle 2 at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, find the length of BC (in cm) 26. . 27 If HCF of 144 and 180 is expressed in the form 13m 3, find the value of m. 3 28. Solve for x : + 3 = , x 0, -1,2 or Solve for x: 4x2 4ax + (a2 b2) = 0 29. 3 Find the area of the shaded region in Fig., if AC = 24 cm, BC = 10 cm and O is the center of the circle. 30. 3 In triangle PQR, PS is the bisector of angle QPR where S QS PQ lies on QR. Prove that . SR PR OR In right angled Triangle ABC if D and E trisect BC then prove that 8 AE2 = 3 AC2 + 5AD2 31. The following distribution represents the age of 36 females: Age( Below Below Below Below Below years) 15 30 45 60 75 No. of 3 15 20 25 28 femal es 3 Below 90 36 Find the median age of the females. 32. 3 An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 450. Find The height of the chimney. Section V The mean of the following data is 472. Find the missing frequencies x and 5 y. Inco 200 - 300 - 400 - 500 - 600 - 700 - 800 - Total me ( 300 400 500 600 700 800 900 Rs.) No. 5 x y 16 9 6 4 100 of worke rs 33. The angle of elevation of a jet plane from a point A on the ground is 600. After a flight of 30 seconds, the angle of elevation changes to 300. If the jet plane is flying at a constant height of 3600 3 meter find the speed of the jet plane. 34. 5 2 OR There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angle of depression of the top and the foot of the other temple are 300 and 600 respectively. Find the width of the river and the height of the other temple. 35. 36. 5 A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with a shape of right circular cone mounted on a hemisphere of radius 3 cm. If the total height of the toy is 12 cm, find the number of toys so formed. A number consists of two digits. When the number is divided by the sum of 5 its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number.
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