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CBSE Board Exam Class 10 2016 : Mathematics

15 pages, 31 questions, 0 questions with responses, 0 total responses,

CBSE 10
Kendriya Vidyalaya (KV), Kamla Nehru Nagar, Ghaziabad

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SET-1 Series JSR U . Code No. U . 30/1 U U U- S - c U U Roll No. Candidates must write the Code on the title page of the answer-book. U - c U 15 - U U U U U- S - c U U U - 31 U M U , - 15 U - U q 10.15 10.15 10.30 U - U U - S U U Please check that this question paper contains 15 printed pages. Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. Please check that this question paper contains 31 questions. Please write down the Serial Number of the question before attempting it. 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. U - II SUMMATIVE ASSESSMENT - II MATHEMATICS U 3 U Time allowed : 3 hours 30/1 90 Maximum Marks : 90 1 P.T.O. (i) (ii) - (iii) U - 4 U 6 2 U 10 - U 11 4 31 U U - , , U (iv) U U General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions divided into four sections A, B, C and D. (iii) Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each. (iv) Use of calculators is not permitted. 30/1 2 U - SECTION - A 1 4 1 Question numbers 1 to 4 carry 1 mark each. 1. 1 O C U PQ S U CAB5308 , PCA AB 1 In fig.1, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and CAB5308, find PCA. Figure 1 2. k k19, 2k21 2k17 U ? For what value of k will k19, 2k21 and 2k17 are the consecutive terms of an A.P. ? 3. U 608 U 2.5 . U U , A ladder, leaning against a wall, makes an angle of 608 with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder. 30/1 3 P.T.O. 4. U U U a U U U $ 52 A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen. U - SECTION - B 5 10 2 Question numbers 5 to 10 carry 2 marks each. 5. m U 2x21px21550 25 m U p(x21x)1k50 , k If 25 is a root of the quadratic equation 2x21px21550 and the quadratic equation p(x21x)1k50 has equal roots, find the value of k. 6. P Q, A(2, 22) B(27, 4) U U U U P, A P Q Let P and Q be the points of trisection of the line segment joining the points A(2, 22) and B(27, 4) such that P is nearer to A. Find the coordinates of P and Q. 7. 2 ABCD, O U U AB, BC, CD DA P, Q, R S U S U h AB1CD5BC1DA 30/1 2 4 In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that. AB1CD5BC1DA. Figure 2 8. h (3, 0), (6, 4) (21, 3) m Prove that the points (3, 0), (6, 4) and (21, 3) are the vertices of a right angled isosceles triangle. 9. U h 25 , 11 The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term. 10. 3 s P , O r U S U PT PS OP52r , OTS5 OST5308 30/1 3 5 P.T.O. In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP52r, show that OTS5 OST5308. Figure 3 U - SECTION - C 11 20 3 Question numbers 11 to 20 carry 3 marks each. 11. 4 O AB513 AC512 U ( p53.14 ) BC 4 In fig.4, O is the centre of a circle such that diameter AB513 cm and AC512 cm. BC is joined. Find the area of the shaded region. (Take p53.14) Figure 4 30/1 6 12. 5 U U U U U 2.1 . 3 . U U U 2.8 . U U , ` 500 (p5 22 7 ) 5 In fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of ` 500/sq.metre. (Use p5 22 ) 7 Figure 5 30/1 7 P.T.O. 13. P(x, y) bx5ay. A(a1b, b2a) B(a2b, a1b) US , h If the point P(x, y) is equidistant from the points A(a1b, b2a) and B(a2b, a1b). Prove that bx5ay. 14. 6 , , U 7 AOC5408 14 , U (p5 22 7 ) 6 In fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where AOC5408. (Use p5 22 ) 7 Figure 6 15. U n m (7n11) : (4n127) , If the ratio of the sum of first n terms of two A.P s is (7n11) : (4n127), find the ratio of their mth terms. 30/1 8 16. x Solve for x : 17. 1 ( x 21)( x 22 ) 1 ( x 21)( x 22 ) 1 1 1 ( x 22 )( x 23 ) 1 ( x 22 )( x 23 ) 5 5 2 , x 1, 2, 3 3 2 , x 1, 2, 3 3 U , U 5 24 , U U U , 10 , U U U ? ( p5 22 7 ) A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use p5 22 ) 7 18. 12 , U U , U U , U 5 U U 9 A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the S U 3 water level in the cylindrical vessel rises by 3 cylindrical vessel. 19. 5 cm. Find the diameter of the 9 U , S U 10 . , U 608 308 U A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 608 and the angle of depression of the base of hill as 308. Find the distance of the hill from the ship and the height of the hill. 30/1 9 P.T.O. 20. U (i) 2 (ii) (iii) U Three different coins are tossed together. Find the probability of getting (i) exactly two heads (ii) at least two heads (iii) at least two tails. U - SECTION - D 21 31 4 Question numbers 21 to 31 carry 4 marks each. 21. U U U U U 50 l U U U U 1500 U S S l U U U U , U 2.8 . 3.5 . U U U U U 2.8 . 2.1 . U U ` 120 . , l m U m U ? ( p5 22 7 ) Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs ` 120 per sq.m, find the amount shared by each school to set up the tents. What value is generated by the above problem ? (Use p5 30/1 22 ) 7 10 22. h s U S U Prove that the lengths of the tangents drawn from an external point to a circle are equal. 23. 4 U S U 608 Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 608 to each other. 24. 7 , O O' US U X U S U OO' U O' A U U A O U AC S U O'D ^ AC DO' CO 7 In Fig. 7, two equal circles, with centres O and O', touch each other at X.OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular to AC. Find the value of DO' . CO figure 7 30/1 11 P.T.O. 25. x Solve for x : 26. 1 2 4 1 5 , x 21,22,24 x 11 x1 2 x1 4 1 2 4 1 5 , x 21,22,24 x 11 x1 2 x1 4 X U U PQ U Q 608 Y, X 40 . U M , Q 458 U PQ U PX ( 3 51.73 ). The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 608. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 458. Find the height of the tower PQ and the distance PX. ( Use 27. 3 51.73 ) U S U U 1 49 ( U) X X U U , X U U The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X. 30/1 12 28. 8 ABC A(4, 6), B(1, 5) C(7, 2) U U DE AB AC D E U U U AD AE 1 5 5 AB AC 3 DADE DABC 8 In fig. 8, the vertices of DABC are A(4, 6), B(1, 5) and C(7, 2). A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that AD AE 1 5 5 . Calculate the area of DADE and compare it with area of AB AC 3 DABC. Figure 8 30/1 13 P.T.O. 29. 1, 2, 3 4 x U 1, 4, 9 16 y U x y 16 A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16. 30. 9 , O U OAP U U u AB OA U OP U B U U h U U r tanu 1 secu 1 pu 21 180 9 In Fig. 9, is shown a sector OAP of a circle with centre O, containing u. AB is perpendicular to the radius OA and meets OP produced at B. Prove that pu 21 the perimeter of shaded region is r tanu 1 secu 1 180 Figure 9 30/1 14 31. U U, S U 24 / U , U 32 , U U 1 U U A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream. 30/1 15 P.T.O.

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