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Practice Paper X Class I Subject: Mathematics (041) Time:3 Hours Maximum Marks: 80 l. All 2. Please write down the Serial Number of the question before attempting it. 3' the questions are compulsory. The question paper consists of 40 questions and it is divided into four sections A, B, Section A comprises of 20 questions c and D. carrying I mark each. 5. Section B comprises of 6 questions carrying 2 marks each. 6. Section C comprises of g questions carrying 3 marks each. 7. Section D comprises of 6 questions carrying 4 marks each. 8' There is no overall choice' However, an internal choice has been provided in two questions of I mark' two questions of 2 marks, three questions of 3 marks and three questions of 4 marks each. you have to attempt onry one ofthe alternatives in a, such questions. 9. Use of calculator is not permitted. 4 ) Section 1. If HCF of (26, 1691:13, then LCM (26,169) (A)26 (B) -A is s2 (c) 33s If cos A + cos2A: l, then the value of sin2A * riroa i, (A)-l 3. (B)0 (c)l . 13 @)2 L45a7 The decimal expansion of the rational nunlber (A)One decimalplace (B) Two decimal places (D) will terminate after l;;- (C) Three decimal places (D)Four decimalplaces 4. The distance between the points (A) 6 5. units (B) The pair ofequation 5x 8 units - l5y (A)One solution (B) Two solutions A (0, 6) and B (0, _ 2) is (C) 4 = g and 3x _ 9y : f units (D) 2 units nu, (C) Infinite solutions (D)No solutions 6. The area of a triangle with vertices (3, 0), (7, 0) and (g, 4) is (A) 14 sq' units (B) 2g sq. units (c) 8 sq. units (D) 6 sq. units 7 ' A tower stands vertically on the ground. From a poini o, the ground which is 25 m awayfrom the foot of the tower, the angle of elevation of the top of the tower is found to be 450. Then the height (in meters) of the tower is 8' (^) 2slT (g) 25y'3 G)2s rtP(:,4) is the mid-point of the line segmentjoining the points value of a is (A)-8 (B)3 (c)_4 (D) l2.s A (- 6, 5) and B (-2,3), then the @)4 g. lf 4 tanfl = 3, then the value of (fl"-ros -- (A)i 10. For the re) ; (c) following distribution: Class i rinffiilrf \+ rol is egual to i 0-8 8-16 l2 26 Frequency a\ upperlimitsofthemffi (A)24 (B) 40 (c) 32 (D) 16 Ihe sum o 16-24 l0 24 -32 9 32-40 l5 1l . Complete the missing entries in the following factor tree: 12. rf 4 1, 13' lf x= 14' a,2 are three consecutive terms of an A.p., then find the varue of a. 1 --is a solution ofthe quadratic equation t* 3:0, find the value ofk. In figure, S and T are points on the sides PQ and PR, respectively of ApeR, such that TR:4 cm and ST is parallel to eR. Find the ratio of the arlas of ApST and apeR. a 15. Two concentric circles +zt<x- pr : 2 cm, R of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle. In figure, PQ is a chord of a OR circle with centre o and pT is a tangent. If zepT:600, find zpRe. 16. A ----- is a polynomial of degre e zero. OR A quadratic polynomial, whose zeroes are _3 and 4, is -_ " i:ltjl:H|.ffi,! |j"J;rrz "u.o* ,," .,.,ir *-*r, .*o is not an ace of hearts. rhe number 18'The nth term of an A.p. whose *, -*; and common difference, d is 19' The total surface area of a sorid hemisphere having radius r is 20'The perimeters of two.similar triangLs Anc anJxyz ur."zo ., *a 39 cm respectivery, then the ratio of the corresponding medians Jf ,*o triangles is a..rrr, '' l|,[Lil"thefirsttermis 22'rf sec 44 r- 2,thelasttermis2gandsumof thetermsis l55.Findthecommon : cosec (A - 200), where 44 is an acute angle, find the value of A. 23' Apair of dice is thrown once' Find the probabiliry "igorirg OR 24 the same number on each dice. Find the probability of 53 Fridays in a leap year. is a side AD ptoj'".d ora parallelogram ABCD and BE intersects cD at oE F. show that Po'l:"#t OR In figure' aABD is a right angle triangle, right angled at A and ACJ- BD. prove that AB2: BC.BD. A 25' Prove that the tangents drawn at the ends of a diameter of a circre are parailer. 26' A solid sphere of radius l0'5 cm is melted and recast into smailer sorid cones, vs of radius 3.5 cm ----v' each and height 3 cm. Find the number of cones so formed. (Use n =f,1 Section 27.1n a A.p., terms. if the l2th term is _ 13 and the sum 28. Find all the zeros of the polynomial xo + 29. Solve for x and y: *' - -C of its four terms is 24, find the sum of its first ten 34x2- 4x + r20, iftwo of its zeroes are 2 and_ 2. ax by b -; =a+b ax-by :zab The sum of numerator and denominator fi'";}, is 3 ress than twice the denominator. If each of "f " the numerator and denominator is decreased by 1, the fraction b..o,,.r rj. ;;r;;';*,,*. 30'IfPdividestherinesegmentjoiningthepoints COOrdinates Of 31. Prove that 2 p. Ac2,-2)andB(2,_4)such 3_ _, s,,v D \L) _.r,, sucn t,-.Ap rnat G: ;, find the - 3r,E is an irrational number. Ylli'l ['t?'.'#:irt#ffi:" 32. show that the sq?]re orany positive integer is either orthe rorm 3m Prove that sl.no-coso stn g+cos +@_cosa _ z e ' aEil- : ;mi "i, OR Findtheuulr.ol@n24so 33.In figure, ABC ,, , orrll"",i,uiil:'#3oo,,; diameter. Find the area of the shaded region. (Use n 34. t"nt t',o*,n* *.ouency Yuto'"T Class 0- l0 t0-20 J*g!g.y x ) 14 cm and a semi circle is drawn with BC as =|l distribution is32.5,then find the values ofx and y 20-30 30-40 9 t2 40-50 50-60 v 60-70 Total J 2 40 Section - D 35. Solve the following for x: 1 _1 1 t za+b+2x zi' i-i OR -:__l_lJ In a flight of 2800 km' an aircraft was slowed down due to bad weather. Its average by 100 km/tr and time increasto speed is reduced uy io minutes. Find the o.igirur duration of the flight. 36' Prove that if a line is drawn parallel to one side of a triangre to intersect the other distinct points, the other two sides in two sides are divided in the same ratio. 37'The angle of elevation oru' ut'optun. fro, a point a on ttre ground is 600. After a seconds' the angle of elevation flight of 30 to 300. is flying "hung". at a constant height of 360018 m, find the speed of the u.roplun. in km/hour. ";; ";;orane 38. Find the mean and mode for the following data: Classes Frequency t0 -20 4 39. An open metalllc bucket ir ir :1ff":::T,::."iyi:11:1.10 20 30-40 l0 -30 8 ?,r "y1,d t 40-50 50-60 t2 l0 verticar 22 22, ;)7' n.d;of the bucket 60 -70 4 70-80 2 me rwo cfcular. is24 cm,nnd the area ;;;ffiil";:,1?,(#,:T: OR A field is in the form of rectangle of length 20 m and width 14 m. A l0 m deep well of diam eter 7 m is dug in one corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the lever of the fierd. (Use o I 40' Draw a right triangle in which the sides containing the right angle are 5 cm and 4 cm. construct a similar triangle whose sides are ti.", the sides of the above triangle. I :f, Draw a pair of tangents to a circle of radius , .,n,or}r,.n are inclined to each other at an angle of 600.
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