# Class – X Mathematics-Basic (241) Sample Question Paper .

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Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineClass – XMathematics-Basic (241)Sample Question Paper 2019-20Max. Marks: 80Duration: 3 hrs.General Instructions:a) All questions are compulsoryb) The question paper consists of 40 questions divided into four sections A, B, C & D.c) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6questions of 2 marks each. Section C comprises of 8 questions of 3 marks each.Section D comprises 6 questions of 4 marks each.d) There is no overall choice. However internal choices have been provided in twoquestions of 1 mark each, two questions of 2 marks each, three questions of 3 markseach and three questions of 4 marks each. You have to attempt only one of thealternatives in all such questions.e) Use of calculators is not permitted.SECTION – AQ 1- 10 are multiple choice questions. Select the most appropriate answer from thegiven options.1.HCF of 168 and 126 is(a) 212.(b) 421(c) 14(d) 18Empirical relationship between the three measures of central tendency is11No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDF(a) 2 Mean 3 Median – Mode(b) 2 Mode 3Median – Mean(c) Mode 2 Mean – 3 Median(d) 3 Median 2Mode Mean3.In the given figure, if TP and TQ are tangents to a circle with centre O, so 1that POQ 110 , then PTQ is(a) 110 (c)4.(b) 90 80 (d) 70 325 can be expressed as a product of its primes as(a) 52 7(d) 2 32 52One card is drawn from a well shuffled deck of 52 cards. The probabilitythat it is black queen is(a)6.(b)(c)(d)(b) 341(c) - 4Which of the following is the decimal expansion of an irrational number(a) 4.561(b) 0.121(d)The sum of the zeroes of the polynomial 2x2-8x 6 is(a) - 37.1(b) 52 13(c) 5 1325.www.cbse.online(c) 5.010010001 1(d) 6.032No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 20208.Answer Key/Marking Scheme Attached with this PDFThe following figure shows the graph of y p(x), where p(x) is a 1polynomial in variable x. The number of zeroes of the polynomial p(x) is(a) 19.(b) 2(c)3(d) 4The distance of the point P (3, - 4) from the origin is(a) 7 units(d) 3 units10.www.cbse.online(b) 5 units1(c)4 unitsThe mid point of the line segment joining the points (- 5, 7) and (- 1, 3) is(a) (-3, 7)(d) (5, -3)(b) (-3, 5)1(c) (-1, 5)(11 – 15) Fill in the blanks:11.The point which divides the line segment joining the points A (0, 5) and 112.The pair of lines represented by the equations 2x y 3 0 and 4x ky 6 B (5, 0) internally in the ratio 2:3 is0 will be parallel if value of k is .1ORIf the quadratic equation x2 – 2x k 0 has equal roots, then value of k3No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineis .13.The value of sin 60 cos 30 sin 30 cos 60 is .114.Value of cos 0 . Cos 30 .cos 45 . cos 60 . cos 90 is .115.The sides of two similar triangles are in the ratio 2:3, then the areas ofthese triangles are in the ratio(16 – 20) Answer the following :16. PQR is right angled isosceles triangle, right angled at R. Find value ofsin P.1ORIf 15 cot A 8, then find value of cosec A.17.If area of quadrant of a circle is 38.5 cm2 then find its diameter(use π 1)18.A dice is thrown once. Find the probability of getting a prime number.119.In the given fig. If DE ‖ BC Find EC.14No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 202020.Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineFind the common difference of the A.P whose first term is 12 and fifthterm is 0.1SECTION – B21.If two coins are tossed simultaneously. Find the probability of getting 2222.A lot of 25 bulbs contain 5 defective ones. One bulb is drawn at random2heads.from the lot. What is the probability that the bulb is good.ORTwo dice are thrown simultaneously at random. Find the probability ofgetting a sum of eight.23.Prove that the tangents drawn at the ends of a diameter of a circle are224.Show that tan 48 tan 23 tan 42 tan 67 1.2parallel.OREvaluate cos 48 cos 42 sin 48 sin 4225.Find the area of circle whose circumference is 22cm.226Read the following passage and answer the questions that follows:2A teacher told 10 students to write a polynomial on the black board.Students wrote1. x2 26. x – 32. 2x 37. x4 x2 14. x3 2x2 19. 2x3 – x23. x3 x2 18. x2 2x 15No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 20205. x2Answer Key/Marking Scheme Attached with this PDF– 2x 1www.cbse.online10. x 4 – 1(i) How many students wrote cubic polynomial(ii) Divide the polynomial (x2 2x 1) by ( x 1).SECTION C27.Find the zeroes of the quadratic polynomial x 3x 10 and verify the328.Draw a circle of radius 4 cm.From the point 7 cm away from its centre,3relationship between the zeroes and coefficient.construct the pair of tangents to the circle.ORDraw a line segment of length 8 cm and divide it in the ratio 2:329.Following figure depicts a park where two opposite sides are parallel andleft and right ends are semi-circular in shape. It has a 7m wide track for3walkingTwo friends Seema and Meena went to the park. Meena said that area ofthe track is 4066m2. Is she right? Explain.30.Prove that3 ORProve that: 6No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 202031.Answer Key/Marking Scheme Attached with this PDFProve that 5 - 3 is irrational, given that 3 is irrational.www.cbse.online3ORAn army contingent of 616 members is to march behind an army band of32 members in a parade. The two groups are to march in the samenumber of columns. What is the maximum number of columns in whichthey can march ?32.Prove that the lengths of tangents drawn from an external point to a circle333.Read the following passage and answer the questions that follows:3are equal.In a class room, four students Sita, Gita, Rita and Anita are sitting atA(3,4), B(6,7), C(9,4), D(6,1) respectively. Then a new student Anjali joinsthe class(i)(ii)Teacher tells Anjali to sit in the middle of the four students. Find the1Calculate the distance between Sita and Anita.1coordinates of the position where she can sit.(iii) Which two students are equidistant from Gita.17No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 202034.Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineSolve 2x 3y 11 and x 2y 12 algebraically and hence find the value 3of ‘m’ for which y mx 3.SECTION D35.36.Find two consecutive positive integers sum of whose squares is 365.If the sum of first 14 terms of an A.P. is 1050 and its first term is 10,find the 20thterm.44ORThe first term of an A.P. is 5, the last term is 45 and sum is 400. Findthe number of terms and the common difference.37.As observed from the top of a 75m high light house above the sea level, 4the angles of depression of two ships are 30O and 45O respectively If oneship is exactly behind the other on the same side of the light house andin the same straight line, find the distance between the two ships. (use 3 1.732)38.If a line is drawn parallel to one side of a triangle to intersect the other 4two sides in distinct points, then prove that the other two sides are dividedin the same ratio.ORState and prove the Pythagoras theorem.39.A copper rod of diameter 1 cm and length 8 cm is drawn in to a wire oflength 18 m of uniform thickness. Find the thickness of wire.4Or8No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineA metallic sphere of radius 4.2 cm is melted and recast into the shape ofa cylinder of radius 6 cm. Find the height of the cylinder.40.4The following distribution gives the daily income of 50 workers of afactoryDaily income400-420-440440-460460-480480-500Number of12148610workers420Convert this distribution to less than type of cumulative frequencydistribution and draw its ogive.9No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineClass – XMathematics-Basic (241)Marking Scheme-SQP 2019-20Max. Marks: 80Duration: 3 hrs.1.(b) 42(1)2.(a)2 Mean 3 Median – Mode(1)3.(d)70 (1)4.(b) 52 13(1)5.(a)(1)6.(d) 4(1)7.(c) 5.010010001 (1)8.(c) 3(1)9.(b) 5 units(1)10.(b) (- 3, 5)(1)11.(2, 3)(1)12.2 OR 1(1)13.1(1)14.0(1)15.4:9(1)16.Sin P 1/ 2(1)1No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineORcosec A 17/1517.Area of quadrant r2 38.5 (use π )( ) r 7cm18.19. diameter 14 cm( )121 ( )(By B.P.T.)1.51 3 20.1( )2 2A5 a1 4d 0( )12 4d 01( )2d - 3SECTION – B21.22.(1)P (Two Head) (1)Good bulbs 25 – 5 20P (good bulb) (1)(1) OROf all those outcomes, the ones for which a b 8 are:2 6, 3 5, 4 4, 5 3, 6 2 or 5 outcomes.P 5/36(1)(1)2No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDF23.ALwww.cbse.onlineB(1)CMD 90 90 Which are alternate angles, hence AB CD(1)24.LHS tan 48 tan 23 tan 42 tan 67 (1) Cot (90 -48 ) cot (90 -23 ) tan 42 tan 67 Cot 42 cot 67 tan 42 tan 67 (1) 1OR Cos 48 cos 42 – Sin 48 Sin 42 Sin (90 – 48 ) sin (90 -42 ) – Sin 48 Sin 42 Sin 42 Sin 48 – Sin 48 Sin 42 025. Area of Circle 26.72(1)(1)(1)2cm(1)(i) 3 Students(1)(ii)(1) () 1SECTION – C3No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 202027.Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlinex2-3x-10 0(3)x2-5x 2x-10 0x(x-5) 2(x-5) 0(x-5) (x 2) 0X 5, -2 Sum of the roots which is same as 5 - 2 3product of the roots -10which is same as 5x(-2) -10Hence verified28.Correct construction of given circle(1)Correct construction of two tangents(2)OR(1)Line of given lengthCorrect position of point which divides the line segment in the given(2)ratio29.(35)2 – [120 56 Area of track 120 70 (1)[(35)2 - (28)2] 120 14 1680 (28)2] 7 63 1680 13861 3066m21( )2Yes, Meena is wrong.30.L.H.S. 12(1) ()() ( R.H.S))(1)4No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFORL.H.S.www.cbse.online(1) ( ) – [][] R.H.S( )(1)(1)31.Let us assume that 5 - 3 is a rational( )We can find co prime a & b ( b 0 )such that5 - 3 Therefore 5 - 3So we get 3(1)Since a & b are integers, we getis rational, and so 3 is( )rational. But 3 is an irrational numberWhich contradicts our statement(1) 5 - 3 is irrationalOR616 32 x 19 8 r 8 032 8 x 4 0 r 0(2)The HCF of 32 and 616 is 8.(1)32.(1)5No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online(1)(1)In ( ( (ℎ 90 ))) Hence PA PB (CPCT)33.((i) (6,4)(ii)(1)(1)(6 3) (1 4) 3 2units(1)(iii) Sita and Rita34.2x 3y 11----(1)x-2y -12(2) x 2y -12(1)----(2)----(3)Substitute value of x from (3) in (1), we get2(2y -12) 3y 11 4y – 24 3 y 11 7y 35 y 5Substituting value of y 5 in equation (3), we get(1)x 2(5) - 12 10 - 12 -2Hence x -2, y 5 is the required solutionNow 5 -2m 3 2m 3-5 2m -2m -1(1)SECTION – D35.Let two consecutive positive integers beand 1( )6No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDF www.cbse.online(1 ) ( 1) 365(1) 182 0( 14)( 13) 0 13Hence two consecutive positive integers are 13 and 1436.(1)Let common difference be 14[2(10) ( 1) ] 10502 10 19 10 19 (10) 200(2)(2)ORa 5 S 400 (5 45) 40050 800 16(2)also a 455 15d 4515d 40d 8/3(2)7No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online37.(1)(1)For correct fig(1)In ADC , tan 45 1 CD 75In ADB , tan 30 1 BD 75 3 3 75(1) Distance between two ships BC 75 ( 3 1)m 54.9 m38.For correct, Given, To prove, construction and Figure(4 For correct proof 2)(2)ORFor correct statement, Given, To prove, Construction and Figure121(5 21 2 )28No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online(1 )For correct proof39.(2)A.T. Q. 1800 8 (1 ) r Thickness of wire ( )OR4 ℎ34(4.2) (6) ℎ3 ℎ (2)(1 ) ℎ 2 744( )40.DailyNumber of 1426440-4608349No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online460-480640480-5001050(2)Correct TableDrawing an ogive with co-ordinates(2)(420,12), (440,26), (460, 34), (480,40), (500, 50)10No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineClass XMathematics –Standard (041)Sample Question Paper 2019-20Max. Marks: 80Duration : 3 hrsGeneral Instructions:(i)(ii)(iii)(iv)(v)All the questions are compulsory.The question paper consists of 40 questions divided into 4 sections A, B, C, and D.Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of6 questions of 4 marks each.There is no overall choice. However, an internal choice has been provided in twoquestions of 1 mark each, two questions of 2 marks each, three questions of 3 markseach, and three questions of 4 marks each. You have to attempt only one of thealternatives in all such questions.Use of calculators is not permitted.SECTION AQ 1- Q 10 are multiple choice questions. Select the most appropriate answer from thegiven options.1The decimal representation of will1a) terminate after 1 decimal placeb) terminate after 2 decimal placesc) terminate after 3 decimal placesd) not terminate1No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 20202Answer Key/Marking Scheme Attached with this PDFwww.cbse.onlineConsider the following frequency distribution of the heights of 60 students of a classHeight (in 150-155cm)No 08951The upper limit of the median class in the given data isa)b)c)d)1651551601703The LCM of smallest two digit composite number and smallest composite number isa) 12b) 4c) 20d) 4414For which value(s) of , will the lines represented by the following pair of linearequations be parallel3 5 06 2 0a) all real values except 10b) 10c) 5/2d) 1/212No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 20205Answer Key/Marking Scheme Attached with this PDFIf triangle ABC is right angled at C, then the value of sec (A B) isa) 0b) 1c)www.cbse.online1 d) not defined6 Ifa)b)c)d)7, ( 90 ) then the value ofis1 2 1 2 1 2 2Given thata)b)c)d) 2 and 0, then the value of is10 90 60 30 8The point which divides the line segment joining the points (8, – 9) and (2, 3) inratio 1 : 2 internally lies in thea) I quadrantb) II quadrantc) III quadrantd) IV quadrant19The distance of the point P ( 3, 4) from the x-axis (in units) isa) 3b) 3c) 4d) 513No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online10 If A( , 5)is the mid-point of the line segment joining the points Q (– 6, 7) andR (– 2, 3), then the value ofa) 12b) 4c) 12d) 61is(Q 11- Q 15) Fill in the blanks11 The total surface area of the given solid figure is112 If one root of the equation ( 1)1value of 10 3 0 is the reciprocal of the other, then theisORThe graph of ( ), where ( ) is a polynomial in variable x, is as follows:YXThe number of zeroes of ( ) is13 The perimeters of two similar triangles ABC and PQR are 35cm and 45cm 1respectively, then the ratio of the areas of the two triangles is4No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online14 Fill the two blanks in the sequence 2, , 26, so that the sequence forms an 1A.P15 A number is chosen at random from the numbers -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then 1the probability that square of this number is less than or equal to 1 is(Q 16- Q 20) Answer the following16 Write one rational and one irrational number lying between 0.25 and 0.32117 In the figure, if ACB CDA, AC 6 cm and AD 3 cm, then find the length of AB1CABD18 If the angle between two tangents drawn from an external point ‘P’ to a circle of radius ‘r’ 1and centre O is 600, then find the length of OP.ORIf the radii of two concentric circles are 4 cm and 5 cm, then find the length of eachchord of one circle which is tangent to the other circle.19 If the first three terms of an A.P are b, c and 2b, then find the ratio of b and c120 Find the value(s) of for which the quadratic equation1 2 2 18 0 has equalrootsSection – B21 Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 2both.22 Prove that the rectangle circumscribing a circle is a square.25No NEED to Purcahse Sample Paper from MarketDownload 20 Sample Paper Sets Free PDF from www.cbse.online

Original CBSE Sample Paper Exam 2020Answer Key/Marking Scheme Attached with this PDFwww.cbse.online23 In the given figure, DEFG is a square and BAC 900. Show that FG2 BG x FC2ORIn an equilateral triangle, prove that three times the square of one side is equal to fourtimes the square of one of its altitudes.24 ‘Skysails’ is that genre of engineering science that uses extensive utilization of wind 2energy to move a vessel in the sea water. The ‘Skysails’ technology allows the towingkite to gain a height of anything between 100 metres – 300 metres.The sailing kite is made in such a way that it can be raised to its proper elevation andthen brought back with the help of a ‘telescopic mast’ that enables the kite to be raisedproperly and effectively.Based on the following figure related to sky sailing, answer the questions:(i)(ii)In the given figure, if sin cos (3 30 ), where and 3 30 are acuteangles, then find the value of .What should be the length of the rope of the kite sail in order to pull the s

Original CBSE Sample Paper Exam 2020 www.cbse.online No NEED to Purcahse Sample Paper from Market Download 20 Sample Paper Sets Free PDF from www.cbse.online Answer Key/Marking Scheme Attached with this PDF. 2 (a) 2 Mean 3 Median – Mode (b) 2 Mode 3 . Sample Question Paper 2019-20 Max. Marks: 80 Duration : 3 hrs .

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