SAMPLE QUESTION PAPER CLASS-X ( ) MATHEMATICS

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1 SAMPLE QUESTION PAPER CLASS-X (07 8) MATHEMATICS Time allowed: Hours Max. Marks:80 General Instructions: (i) All questions are comulsory. (ii) The question aer consists of 0 questions divided into four sections A, B, C and D. (iii)section A contains 6 questions of mark each. Section B contains 6 questions of marks each. Section C contains 0 questions of marks each. Section D contains 8 questions of 4 marks each. (iv) There is no overall choice. However, an internal choice has been rovided in four questions of marks each and three questions of 4 marks each. You have to attemt only one of the alternatives in all such questions. (v) Use of calculators is not ermitted. SECTION- A Question numbers to 6 carry mark each..if a= x,b=xx5,c= n x5 and LCM(a,b,c)= x x5,then find n.. For what value of k are k, k+0 and k + in AP.. If in the given figure DE II BC,then find the value of AD. 4. If α =/, β =/, find degree measure of α + β. 5. Find the values of k if x + kx + = 0 has two equal real roots. 6. If (,) is the mid oint of line segment joining the oints A(6,5) and B(-,),find value of. SECTION - B Question numbers 7 to carry marks each. 7. If the H.C.F (90,44) = 8, find the L.C.M (90,44). 8. The 7th term of an AP exceeds its 0th term by 7. Find the common difference. 9. For what value of k will the following system of linear equations have infinite number of solutions. 0x + 5y (k-5)=0 and 0x + 0y k=0 0. Prove that the oints (a,b+c) (b,c+a) and (c,a+b) are collinear.. A box contains cards numbered from to 7. A card is drawn at random from the box. Find the robability that the number of the card is (i) a rime number (ii) a multile of..one card is drawn from a well shuffled 5 laying cards. Find the robability of getting (i) a non-face card (ii) a black king or (ii) red queen SECTION- C Question numbers to carry marks each. Prove that 5 is an irrational number 4. If two zeroes of the olynomial x 4 + x 0x 6x + 6 are and -, find the other zeroes of the olynomial. Find the zeroes of the quadratic olynomial 5x 4 8x and verify the relationshi between the zeroe and the coefficients of the olynomial. 5. Reresent the following system of linear equations grahically. 4x -5y +6 = 0 and x + y -6 =0 Shade the triangular region enclosed by the lines with X axis. htts://jsuniltutorial.weebly.com/

2 6. ABC is a right angle triangle, right angled at C. Let BC = a, CA = b, AB = c and let be the length of erendicular from C on AB. Prove that: c = ab (ii) a b, In ABC, if AD is the median, then show that AB + AC = ( AD + BD ) 5 cot5 4 ec47 7.Evaluate 65 tan 75 tan0 tan 40 tan 50 tan 80 8.Show that the quadrilateral PQRS formed by P (,5), Q(7,0), R(,) and S(,4) is not a arallelogram., Find the oint on x-axis which is equidistant from (, -5) and (-, 9) 9. If the Mode of following distribution table is 54, find the value of. class Frequency Find the area of the shaded region in the given figure, where ABCD is square of side 4cm. ( π=/7). A quadrilateral ABCD is drawn to circumscribe a circle as given in figure. Prove that AB + CD = AD + BC D R C Q S. A container, oened A P from the B to and made u of metal sheet, is in the shae of a frustum of a cone of height 6 cm with radii of its lower and uer ends as 8 cm and 0 cm resectively. Find the t of the container if the t of metal sheet used is Rs 8 er 00 cm.( π =.4), A toy is in the form of a cone mounted on hemishere of diameter 7 cm. The total height of the toy is 4.5 m. Find the volume of the toy. ( π=/7) SECTION- D Question numbers to 0 carry 4 marks each.. Solve for x., a + b 0 a b x a b x 4. Which term of the sequence 0, 9 4, 8, 7, is the first negative term? Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60. Then construct a triangle whose sides are of the corresonding sides of the triangle ABC Prove that, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresonding sides. htts://jsuniltutorial.weebly.com/

3 , Prove that in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle oosite the first side is a right angle. tan cot 7. Prove that sec.ec where is an acute angle. cot tan If sec tan rove that where is an acute angle. 8. From the to of a building 60m high the angles of deression of the to and the bottom of a tower are observed to be 0 0 and Find the height of the tower. 9.Three sides of a triangular field are 5m,6m and 7m with the three corners of the field a cow,a buffalo and a horse are tied searately with roes of length 7m each to graze the field.find the area of the field which can not be grazed by the three animals. ( π=/7) 0.To highlight the child labour roblem,some students organized a javelin throw cometition.50 students articiated in this cometition.the distance (in metres) thrown are recorded below. Distance (in metres) Number of students Draw less than tye Ogive for the given data. Which value is deicted by the students? Students of a locality decided to create an awareness about Save Electricity Camaign.They recorded the monthly consumtion of electricity of 68 consumers of that locality.the following frequency distribution table gives the monthly consumtion of electricity of these consumers of that locality. Monthly consumtion(in units) Number of consumers Find the median of the above data by ug the formula. Which value is deicted by the students? htts://jsuniltutorial.weebly.com/

4 MARKING SCHEME(SAMPLE PAPER) SECTION -A n= Given numbers are in AP (k+0) - k = k + (k +0) Or k = 6. As DE II BC,by BPT AD /DB = AE /EC Or AD =.4 cm 4. 0 =/ and 60 =/ α + β =90 k = = SECTION -B 7. HCF X LCM = 90x44 8 X LCM=90x44 LCM = Let the first term=a and the common difference =d a+6d=a+9d+7 d= 9. For Infinite solutions = = 0.. k -5 k k area 0 [ a(c + a - a - b) ac - ab + ab - bc + bc - ac + b(a + b - b - c)+ c(b + c - c - a)] 0 The given oints are collinear. (i)p( a rime number)= 7 7 (ii)p( a multile of )= htts://jsuniltutorial.weebly.com/ 4

5 . P(a non face card)=0/ P(a black king or red queen)=/ + SECTION C Let 5+ is a rational number.so 5+ = where a & b are co-rime integers and b 0 After simlification = Which contradicts the fact that is an irrational number and hence 5+ is an irrational number. 4. Let f(x)=x 4 + x 0x 6x + 6 Since and - are zeroes of f(x) (x- )(x + ) = x is a factor of f(x) Division algorithm, we have x 4 + x 0x 6x + 6 = (x )(x + x 6) =(x )(x+6)(x-) The other zeroes are -6 and 5x 4 8x = 5x 8x 4 = 5x 0x + x 4 =(5x+)(x-) Zeroes are -/5, Sum of zeroes + = = Product of zeres = = = 5. Finding correct set of solutions for the air of equations. Correct lotting of oints on grah and joining of oints. Shading of the triangular region enclosed with X axis. + htts://jsuniltutorial.weebly.com/ 5

6 6 Given, To rove,figure and construction Proving ACB CDB (by AA similarity) AB AC BC CD c b a c ab (ii)ab =BC + AC c =a +b c a b c c a b a b a b a b a b b a a b Given, To rove, figure and construction In ADE, AD =AE +ED (Pythagoras theorem) AE =AD -DE In ABE, AB =AE +BE (B=90 0, Pythagoras theorem) AB =AD -DE +(BD-DE) Ug (I) AB =AD +BD -BD.DE..(II) In ACE, AC =AE +EC AC = AD - DE +(CD+DE) AC = AD +CD +CD.DE AC = AD +BD +BD.DE (As BD=CD). (III) Adding (II) and (III) AB +AC =(AD +BD ) 7. 5 cot5 4ec tan 75 tan0 tan 40 tan 50 tan 80 htts://jsuniltutorial.weebly.com/ 6

7 ( 90 65) cot(90 75) 4ec(90 4) = 65 tan 75 tan(90 80) tan(90 50) tan 50 tan tan 75 4sec4 65 tan 75 cot80cot50 tan 50 tan PQ=5 0 QR= 6 RS=5 0 SP=9 Here QR SP. So quadrilateral PQRS is not a arallelogram. 4x Let P(x,0) is equidistant from oint A(, -5) and B(-, 9) AP = BP = x= -7 The oint on the x-axis equidistant from the given oints is (-7, 0) 9. Modal class is l=45,f =6,f 0 =,f =,h= Or = Area of square ABCD = 4 X 4 = 96 cm Diameter = 7cm, r= 7/ cm Area of 4 circles = 4 X = 54 cm Area of shaded region = Area of square ABCD- Area of 4 circles = = 4 cm. We know that the tangents to a circle from an external oint are equal in length. AP = AS..( i ) BP = BQ.. ( ii ) D R C CR = CQ..(iii) DR = DS..( iv ) Q S Adding (i), (ii), (iii) & (iv), we get B ( AP + BP ) + ( CR + DR ) = ( AS + DS ) + ( BQ + CQ ) A P or, AB + CD = AD + BC 4x htts://jsuniltutorial.weebly.com/ 7

8 . Calculating l=0cm Area of metal sheet= (r + r ) l + r =959.6 cm Cost of metal sheet= Rs Rs Radius of hemishere = 7 =.5 cm Height of cone = (4.5.5) = cm Now, volume of toy = Volume of hemishere + Volume of cone = r r h r r h 7 7 cm SECTION D. a b x x a b a b x x a b ab a b x a b x ab 7 ( ) cm or, x ( a + b + x ) + ab = 0 x + ax + bx + ab = 0 x ( x + a ) + b ( x + a ) = 0 or, ( x + a ) ( x + b ) = 0 x = a or x = b + 4 Let the n th term of the given AP be the first negative term. Then a n < 0 or, a + ( n ) d < 0 or, 0 + ( n ) ( 4 ) < 0 or, 8 n < 0 or, n > 8 or, n > 8 n 8 or, n > 7 Thus, 8 th term of the given sequence is the first negative term. htts://jsuniltutorial.weebly.com/ 8

9 htts://jsuniltutorial.weebly.com/ 9 5 Construction of ΔABC Construction of similar triangle 6 Given, To rove,figure and construction Correct roof 7 tan cot cot tan. sec ) ( ) ( ) ( ec ) ( tan sec 8

10 For correct figure Let AB = Building, CD = Tower,AC=DE=x In, DEB tan0 0 = or, BE DE 60 h or x = ( 60 h ) x In, CAB, tan60 0 = or x 60 ( ii ) AB CA or 60 From (i) & (ii) 60 h 60 x.. ( i ) or h = 40m Thus, the height of the tower is 40m. 9 Area of three sectors r r r m ( ) 7 m m 567 s m 4m Area of the triangle= s( s a)( s b)( s c) 4 m Area of the field which can not be grazed by the three animals = ( 4 77) m htts://jsuniltutorial.weebly.com/ 0

11 0. Distance (in metres) Cumulative frequency Less than 0 6 Less than 40 7 Less than 60 4 Less than Less than Drawing Ogive Value-Social service (or any other value) Monthly consumtion Number of consumers Cumulative frequency Total 68 Median class=5-45 L=5,n=68,f=0,cf=,h=0 n ( cf ) Median l h f (4 ) Value-Social service (or any other value) Note- Proortionate marks are to be awarded for any alternate correct answers. htts://jsuniltutorial.weebly.com/

CBSE Board Class X Mathematics

CBSE Board Class X Mathematics Time: 3 hrs Total Marks: 80 General Instructions: 1. All questions are compulsory.. The question paper consists of 30 questions divided into four sections A, B, C, and D.