SAMPLE PAPER CLASS X MATHS Time: 3hrs. Marks : 80 SECTION-A
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1 SAMPLE PAPER CLASS X MATHS Time: 3hrs. Marks : 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided into four sections A, B, C and D. (iii) Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each. (iv) There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. (v) (v) Use of calculators is not permitted. SECTION-A Without performing the actual long division find if will have terminating or non 1050 terminating (repeating decimal expansion). लम ब व भ जन व वध क प रय ग ककए वबन बत आए कक 395 क दशमल प रस र स त ह य ऄस त 1050 अ त 2 If x = 2 is a solution of P x x 4 = 0, then find the value of P. यकद x = 2, सम करण P x x 4 = 0 क एक म ल ह त P क म न ज ञ त 3 If n th term of an A.P. is 7 4n. Find its common difference d. यकद एक सम तर श र ण क n पद 7 4n ह त आसक स व ऄन तर d ज ञ त 4 Find the distance between the lines 3x + 6 = 0 and x 7 = 0. र ख ओ 3x + 6 = 0 तथ x 7 = 0 क ब च क द र बत आए 5 In given figure, ST RQ, PS=3cm and SR=4cm. Find the ratio of the area of PST to the area of PRQ. कदए गए वचत र म ST RQ, PS=3cm तथ SR=4cm PST क क ष त रफल क ऄन प त PRQ क क ष त रफल क स थ ज ञ त 6 If cosa= 2 5, then find the value of 4+4tan2 A. यकद cosa= 2 5 त 4+4tan2 A क म न ज ञ त SECTION-B 7 If n is a positive odd integer then show that n 2-1 is divisible by 8. यकद n एक धन त मक व षम प ण क ह त दश व आए क n 2-1, 8 स व भ ज य ह 8 If the sum of first n terms of an A.P. is S n = 5n 2 +3n then find out the 10 th term of the A.P. यकद ककस सम तर श र ढ़ क प रथम n पद क य ग S n = 5n 2 +3n ह त आसक दस पद ज ञ त
2 9 Find out the value(s) of k for which the pair of linear equations kx + y = k and x + ky = 1 have infinitely many solutions. k क ककस म न क वलए र वखक सम करण य ग म kx + y = k तथ x + ky = 1क ऄन क हल ह ग 10 Find out the value of p for which the points (2,1), (p,-1) and (-1,3) are collinear. p क ककस म न क वलए वबन द (2,1), (p,-1) तथ (-1,3) स र ख ह? 11 Two dice are rolled simultaneously. Find the probability that the sum of the two numbers appearing on the two dice is a perfect square. द प स क एक स थ ईछ ल ज त ह द न प स पर अन ल ऄ क क य ग क प णव गव ह न क प र वयकत ज ञ त 12 In a non leap year, what is the probability of 53 Mondays? एक वबन ल प षव म 53 स म र ह न क प र वयकत क य ह ग? 13 Prove that 5 is an irrational number. SECTION C वसद ध क वजए कक 5 एक ऄपररम य स ख य ह 14 If α and β are the zeros of the polynomial 6y 2-7y+2, find a quadratic polynomial whose zeroes are 1 α and 1 β. यकद αतथ β बह पद 6y 2-7y+2 क म ल ह त ह बह पद ज ञ त क वजए वजसक म ल 1 α तथ 1 β ह 15 Solve the following pair of equations forx and y. 5 x y 2 = = 1 ; x 1, y 2 x 1 y 2 x तथ y क वलए वनम न सम करण य ग म क हल क वजए 5 x y 2 = = 1 ; x 1, y 2 x 1 y 2 16 Find the ratio in which the point P(x,2) divides the line segment joining the points A(12,5) and B(4,-3). Also find the value of x. ह ऄन प त ज ञ त क वजए वजसम वबन द P(x,2) वबन द ओ A(12,5) तथ B(4,-3) क वमल न ल र ख खण ड क व भ वजत करत ह x क म न भ ज ञ त If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a parallelogram taken in order then find its area. यकद A(-5,7), B(-4,-5), C(-1,-6) तथ D(4,5) एक सम तर चत भ वज क क रम न स र वनद श क ह त ईसक क ष त रफल ज ञ त 17 In given figure if 1= 2 and NSQ MTR, then prove that PTS PRQ. कदए गए वचत र म यकद 1= 2 तथ NSQ MTR, त वसद ध क वजए क PTS PRQ.
3 E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ABE CFB. सम तर चत भ वज ABCD क बढ़ इ गय भ ज AD पर वथथत E एक वबन द ह तथ BE भ ज CD क F पर प रवतच छ द करत ह दश व आए कक ABE CFB. 18 A quadrilateral ABCD is drawn to circumscribe a circle prove that AB+CD = AD+BC एक त क पररगत एक चत भ वज ABCD ख च गय ह त वसद ध AB+CD = AD+BC 19 If tanθ + sinθ = m and tanθ - sinθ=n. Show that m 2 -n 2 =4 mn यकदtanθ + sinθ = m तथ tanθ - sinθ=nत दश व आए कक m 2 -n 2 =4 mn Evaluate (म न ज ञ त क वजए) cos30 +sin60 1+cos30 +sin30 20 The median of the following distribution is Find out the values of x and y if the total frequency is 20. Class Interval Total Frequency 4 x 5 y 1 20 वनम न ब टन क म ध यक 14.4 ह त x तथ y क म न ज ञ त क वजए जबकक ब र ब रत क य ग 20 ह गव ऄन तर ल Total ब र ब रत 4 x 5 y In the given figure. ABCD is a square of side 14cm with centres A,B,C and D, four circles are drawn such that each circle touch externally two of the remaining three circles find the area of the shaded portion.
4 द ग इ अक वत म ABCD भ ज 14cm ल एक गव ह A, B, C, और D क क द र म नकर च र त आस प रक र ख च गए ह कक प रत य क त त न श ष त म स द त क ब ह य र प स थपशव करत ह छ य ककत भ ग क क ष त रफल ज ञ त 22 How many silver coins, 1.75cm in diameter and of thickness 2mm, must be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm. व म ओ 5.5cm x 10cm x 3.5cm ल एक घन भ बन न क वलए 1.75cm व य स और 2mm म ट इ ल ककतन च द क वसक क क वपघल न पड़ ग? A bucket of height 30cm is in the form of frustum of a cone with radii of its lower and upper ends as 10cm and 20cm respectively. Find the capacity of the bucket. Also find the cost of milk which can completely fill the container at the rate of Rs. 25 per liter. (take π = 3.14) एक श क क वछनक क र प क ब ल ट क उ च इ 30 cm ह आसक उपर तथ वनचल वसर कक वत रज य ए क रमश 10cm तथ 20cm ह ब ल ट क ध ररत ज ञ त क वजए और 25 र पय प रवत ल टर क दर स ब ल ट म अ सकन ल द ध क म ल य ज ञ त (π = 3.14 ल वजय ) SECTION-D 23 An aeroplane starts late by 30 minutes to reach the destination which is 1500 km away. The pilot increases the speed by 250km/hour just to reah on time. Find the original speed of the aeroplane. एक ह इ जह ज ऄपन वनयवमत समय स 30 वमनट द र स चलत ह ऄपन ग तव य थथ न ज कक 1500 km द र ह पर समय स पह चन क वलए ईस ऄपन गवत 250 ककम /घ ट बढ़ न पड़त ह ह इ जह ज क थतव क गवत ज ञ त If the equation (1+m 2 )x 2 + 2mcx + c 2 -a 2 =0 has equal roots, then prove that c 2 = a 2 (1+m 2 ) यकद व घ त सम करण (1+m 2 )x 2 + 2mcx + c 2 -a 2 =0 क म ल बर बर ह त वसद ध क वजए c 2 = a 2 (1+m 2 ). 24 The sum of first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161 find the 28 th term of this A.P. एक सम तर श र ण क प रथम 7 पद क य ग 63 ह और ऄगल 7 पद क य ग 161 ह आस श र ण क 28 पद ज ञ त 25 Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. वसद ध क वजए कक द समर प वत रभ ज क क ष त रफल क ऄन प त आन वत रभ ज क ककन ह द स गत भ ज ओ क ग क ऄन प त क बर बर ह त ह Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, the other two sides are divided in the same ratio. वसद ध क वजए यकद ककस वत रभ ज क एक भ ज क सम तर ख च ग इ र ख ऄन य द भ ज ओ क वजन द वबन द ओ पर प रवतच छ द करत ह त वबन द भ ज ओ क सम न ऄन प त म व भ वजत करत ह 26 Draw a triangle ABC with side BC=6cm, B =30 o and A =120 o. Then construct a triangle whose sides are 5 times the corresponding sides of ABC. 4 एक वत रभ ज ABC क रचन क वजए वजसम BC=6cm, B =30 o तथ A =120 o ऄब एक वत रभ ज क रचन क वजए वजसक भ ज ए ABCक स गत भ ज ओ क 5 ग न ह 4
5 27 Prove that (वसद ध क वजए) secθ + tanθ 1 tanθ secθ + 1 = cosθ 1 sinθ 28 An aeroplane at an altitude of 200m has angles of depression at opposite points on the two banks of the river as 45 o and 60 o. Find the width of river. एक य य न 200 म टर क उ च इ पर ह आसस नद क द ककन र पर व पर त कदश ओ म वथथत वबन द ओ क ऄ नमन क ण 45 o और 60 o ह नद क च ड़ इ ज ञ त 29 A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at other and their diameter is 4.2cm. The height of cylindrical and conical portions are 24cm and 14cm respectively. Find the volume of the toy. एक ठ स वखल न ब लन क र ह वजसक एक वसर ऄधवग ल य तथ द सर वसर पर एक श क ह आन सभ क व य स 4.2cm ह तथ ब लन क र और श क क र भ ग क उ च इ क रमश: 24cm तथ 14cm ह वखल न क अयतन ज ञ त 30 The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency k. वनम नवलवखत व तरण एक म हल ल क बच च क द वनक ज ब खचव दश वत ह यकद औसत द वनक खचव Rs. 18 ह त ब रम ब रत k क म न ज ञ त Daily Pocket Allownace द वनक ज ब खचव Number of children बच च क स ख य K Following table shows the rainfall in a city in 60days. Draw a more than type Ogive for given data and find the median with the help of curve. एक शहर म 60 कदन म दजव क ग इ ष व वनम नवलवखत स रण म द ग इ ह आन अ कड़ र स ऄवधक प रक र क त रण ख वचए तथ आसस म ध यक ज ञ त Rainfall (cm) ष व (cm) Number of Days कदन क स ख य
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