MATHS - X (PA-B)

CHETTINAD VIDYASHRAM R.A. PURAM, CH-28 DATE : 02/12/2020 PA-B (2020 - 21) CLASS: X TIME:3HOURS SUBJECT: MATHEMATICS General Instructions: MARKS: 80 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 of I mark each. Intemal 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. It consists ofthree sections II, IV and V. 2. In section II1, Question Nos. 21 to 26 are Very Short Answer Type questions of 2 marks cach. 3. In section IV, Question Nos. 27 to 33 are Short Answer Type questions of3 marks cach. 4. In scction V, Qucstion Nos. 34 to 36 are Long Answer Type qucstions of 5 marks cach. 5. Internal choice is provided in 2 questions of2 marks, 1 question of 3 marks and I question of 5 marks. Part-A Section- 1 Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 1. Write down the decimal cxpansion of 1169 without actual division. 3125 OR Write in decimal form. 8 2. The graph ofy =plx) is given below for some polynomial p(x). Find the number of zeroes of plx). 1 3. Ifthe linc given by 3x +2ky = 2 and 2r + 5y+ 1 =0 are parallel, then find the value of k. 1 1

4. In the given figure, ABCD is a rectangle. Find the values of x and y. D x+y C 14 cm 30 cm B 5. Determine the 10th term from the end of the AP: 4, 9, 14,. 254 OR If 18, a, b, - 3 are in A.P., thena+b=? 6. Ifthe sum ofroots ofthe cquation -(k+6)x +2 (2k-1)= 0is equal tohalf oftheirproduct, then find the value of k. 7. If 3 is a solution of 3x+(k- 1)x+9=0, then k = ? 1 OR When x i s a solution of3x2 +2kr-3 =0, find k. 8. If the graph of a polynomial intersects the x-axis at exactly two points, is it necessarily a quadratic polynomial? 1 9. Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle. 1 OR In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If 4QPT = 60°, find PRQ. 10. ABC is an isosceles triangle right-angled at C. Find AB. 1 11. Is it possible to construct a pair of tangents from point P to 1 circle of radius 5 cm situated at a distance of 4.9 cm from the centre? 12. If 2 sin 20 = v3, then find 0. 1 13. If 1S cot 6= 8, then find the value of Sin6)(+ sin) (1+ cos6)(l-cose) 14. If two tangents inclined at an angle 60° are drawn to a circle of radius 5 cm, then find the length of each tangent. 1 15. A metallic spherical shell of internal and external diameters 4 cm and 8 cm respectively is melted and recast into the form ofa cone of base diameter 8 cm. Find the height ofthe cone. 1 16. Two dice are thrown together. Find the probabilityof getting the same number on both dicc. 1 OR Two different dice are tossed together. Find the probability that the product ofthe two numbers on the top of the dice is 6.

Section-I Case Study based questions are compulsory. Attempt any four sub-parts of each question. Each sub-part carries 1 mark. 17. Case Study Based-1 Kerala Kerala is a statc in Southern India. The state is known as a tropical paradise of waving palms and wide sandy beaches. This map of the Indian province of Kerala shows its area can be approximated using a simple straight-sided shape. The shape has two parallel sides 561 km and 216 km long. The other sides are 180 km and 211 km long. Is parallel sides are 100 km apart. Shreya observed the shape formed by four straight lines and explored it on her notcbook in diffcrent ways shown below. B E QR cD BC EF Shape I Shape Il Refer to Shape I (a) Let ABCD is a trapezium with AB || DC, E and F are points on non-parallel sides AD and AE 1 BC respectively such that EF is parallel to AB. Then ED BF AB (ii) B (iv) None of these. ) CD (ii) CD FC (6) Here, AB || CD. IfDO= 3x- 19, OB = r-5, CO = x-3 and AO =3, the valuc ofr is 1 () 5 or 8 (i) 8 or 9 iin) 10 or 12 (iv) None of these. (c) Again AB||CD. IfDO = 3r-1, OB =Sx-3,AO = 6x-5 and OC = 2x+1, then the value ofr is 1 (i) 1 (ii) 2 (iv) 3 Refer to Shape II (d) In AABC, PQ || BC.IfAP = 2.4 cm, AQ =2 cm, QC = 3 cm and BC= 6 cm, AB and PQ are respectively 1 () AB=6 cm, PQ = 2.4 cm (ii) AB= 4.8 cm, PQ= 8.2 cm (ii) AB = 4 cm, PQ =5.3 cm (iv) AB =84 cm, PQ =2.8 cm (e) In ADEF, if RS|| EF, DR =4x - 3, DS =8r-7, ER 3x - I and FS 5x -3,then the value ofr is ii) 2 (iin) 8 () 10

18. Case Study Based-2 Saving Money Saving money is a good habit for cveryone. It helps you in the event of financial emergency. Some children of Class X decided to save their pocket moncy. The following distribution shows their daily pocket allowance. Daily Pocker 100-120 120-140 140-160 160-180 180-200 8 6 10 allowance (in ) Numberofchildren 12 14 (a) The class-mark of class 140-160 is () 140 (i) 160 (iii) 150 (iv) 20 b) The median class is () 120-140 (i) 140-160 (iii) 160-180 (v) 180-200 (c) The mean daily pocket allowance is 1 () 150 (ii) 142.50 ii) 135,.70 (iv) 145.20 () The uppcr limit of modal class is () 120 (i) 140 (iii) 180 (iv) 200 (e) The modal daily pocket allowance is ()125 (ii) 140 (ii) 135 (iv) 160 19. Case Study Based-3 Aquarium An aquarium is a transparent tank of water in which live fish and other water creatures and plants are kept. The diagrams below show the plans for an aquarium. It will be built in hexagonaB shape. It will be made using six rectangular shapcd clear glasses. one regular hexagon clear glass for roof. D H Top View Front View Notto scaBe

Refer to Top View (a) The value ofx for which the distance betweenthepoints F(2,-3) and Cx, 5) is 10, is 1 () 8 or-4 (i) 4 or 8 ii) 5 or-10 (iv) 5 or 10 (6) The mid-point ofthe line segmentjoining the points E(8, 11) and B(1, 15) is ) 6, 10) ( )(ii) (iv) Refer to Front View (c) The distance of a point F(8, 6) from origin is ) 12 units (i) 16 units (ii) 14 units (iv) 10 units (d)The perimeter ofsquare EFHI where E(-2,0), F(3, 0), H(3,5) and I(-2,5) is ( 8V5 units (i) 40 units (ii) 20 units (iv) None of these. (e) The coordinates of the point which divides segment joining the point A(4, 5) and D(6, 3) in the ratios 3:2 internally is 1 (0,8) un () (iv) 20. Case Study Based-4 A Brooch A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs ofsome brooch are shown below. Observe them carefully. wwww B Design A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm. The wire used for making 4 diameters which divide the circle into 8 equal sectors. Design B: Brooch B is made in two colours-Gold and Silver. Outer part is made with gold. The circumference of silver part is 44 mm and the gold part is 3 mm wide everywhere. Refer to Design A (a) The total length of the silver wire required is (i) 180 mm (i) 200 mm ii) 250 mm (iv) 280 mm (b) The area of cach sector of the brooch is (i) 44 mm2 ii) 52 mm (ii) 77 mm2 (iv) 68 mm2

Refer to Design B (c) The circumference of outer part (golden) is () 48.49 mm (i) 82.2 mm (iti) 72.50 mm (iv) 62.86 mm (d) The difference of areas of golden and silver parts is () 18T (ii) 447 (iin) SIn (iv) 64T (e) A boy is playing with the brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 807 mm? () 2 (i) 3 (it) 4 (iv) 5 PART-B All questions are compulsory. In case of internal choices, attempt any one. Section-l 21. A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. He wants to sell the oil by filling the three kinds of oil in tins of cqual capacity. What should be the greatest capacity of such a tin? 2 22. Detemine the ratio in which the line 3r +y - 9 = 0 divides the line segmcnt joining the points(1, 3) and (2, 7). 2 OR IfA(4,3), B(-1,y) and C(3, 4) are the vertices of right triangle ABC, right-angled at A, then find the value ofy. 23. Samridhi was trying to understand the concept ofzeroes on the basis of the following graphs given below. If the figures shown in the graph is parabola in different situations, then find 2 Fig.(a) Fig. (b) )The number of zeroes in graph given in fig (a) (ti) The number of zeroes in graph given in fig (6). 24. Drawa line segment AB of length 7 cm. Using ruler and compass find a point P on AB such thatA P 3 2 AB

25. Prove that sin -cos 6 +sin+cos 2 sin+cos6 sin-cose 2sin*0-1 OR Prove that 1+sin -sin 2 sec 6 2 sin V1+sin 26. In the given figurc, PQ and RS are two parallel tangents to a circle with centre O and another tangent XY, with point ofcontact C which intersccts PQ at A and RS at B. Prove that ZAOB = 90°. x M C R NB Section-IV 27. The LCM of two numbers is 182 and their HCF is 13. If one of the numbers is 26, find the other. 3 28. Solve for x: 12abr? - (9a2-862)x - 6ab =0. 29. Ifa and ß are the zeroes ofthe polynomial 4x3+3r + 7, find the value of 30. Prove that ifa line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in same ratio. 3 OR Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares ofits diagonals, i.e. AB- + BC +CD + AD' = AC: + BD- (see figure).

31. The mean of the following frequency distribution is 63.3 and the sum of all the frcquencies is 50. Compute the missing frequcncies and. 3 Class 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 5 10 7 8 32. Find the angle of depression from the top of l12m high tower ofan objcctlyingat a point 12m away from the base of the tower. 3 33. The students of a school were askcd to collcct money from a colony for the welfare of the poor and necdy children by performing the Drama in the colony related to subjcct \"clcanlincss. They performed together and the collection is as under. Find the mean and modc of the given data. 3 Collection 1000-1500|1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500 4500-5000 in No. of 24 40 33 28 30 22 16 7families Section-V 34. From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h nmetres and the line joining the ships passes through the foot of the lighthouse, show that the distancc betwecn the ships is v h metres. 5 OR From the top of a building, 15 m high, the angle of clevation of the top of a tower is found to be 30°. From the bottom of the samc building the angle of clevation of the top of the tower is found to be 60°. Find the height ofthe tower and the distance between the tower and building. 35. Jay Pravesh, a juice seller has set-up his juice shop. He has three types ofglasses ofinner diamcter 5 cm to serve the customers. The height of the glasses is 10 cm. (Use t 3.14) 5 TypeA Type B Type C (A glass with conical (A glass with a (A glass with raised bottom of plane bottom) hemispherical height 1.5 cm) raised base) He decided to serve the customers in 'A' type of glasses. ()Find the volume ofglass of type A. (i) Which glass has the minimum capacity and how much? 36. Atul sold a television set and a mobile phone for 10,500, thereby making a profit of 10% on the television set and 25% on the mobile phone. If he had taken a profit of 25% on the television set and 10% on the mobile phone, he would have got 7 10,650. Find the cost price of cach item.