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CBSE Class 9 Pre Board 2020 : Mathematics - Paper 1 (Delhi Public School (DPS), Jammu)

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DELHI PUBLIC SCHOOL, JAMMU ASSIGNMENT ANNUAL EXAMINATION (2019-20) Class: IX Sub: Maths TOPICS:- Chapter 1- Number System. Chapter 8. Quadrilateral. Chapter 2- Polynomials. Chapter 9. Area of parallelogram and triangle Chapter 3- Coordinate Geometry. Chapter 10. Construction. Chapter 4- Lines and Angles. Chapter 11. Surface area and volume. Chapter 5- Triangles. Chapter 12. Statistics. Chapter 6- Heron s Formula Chapter 13. Probability Chapter 7.Linear Equation Chapter 14. Circles. Section 1 ( MCQ type) Q1. Which of following numbers can be represented as non-terminating, repeating decimals? (a) 39 24 (b) 3 16 (c) 3 11 137 25 (d) Q2. The number 0.3 in the form , where p and q are integers and q 0, is (a) 33 100 3 (b) 10 (c) 1 3 3 (d) 100 Q3. Which of the following is irrational? (a) 0.15 (b) 0.01516 (c) 0.1516 (d) 0.501500150005.. Q4. An irrational number between 2 and 2.5 is (a) 11 (b) 5 (c ) 22.5 (d) 12.5 Q5. If ABC PQR and ABC is not congruent to RPQ then which of following is not true (a) BC=PQ (b)AC=PR (c)AB=PQ Q6. If 8 +1 =64, what is the value of 32 +1 ? (d)QR=BC (a) 1 (b)3 (c)9 (d)27 2 Q7. If (23) = 4 ,then 3 = (a) 3 (b) 6 1 (c)9 (d) 27 1 Q8. If x + =5, then 2 + 2 = (a) 25 (b) 10 (c)23 (d) 27 Q9. If a+b+c =9 and ab+bc+ca = 23, then 2 + 2 + 2 = (a) 35 (b) 58 (c) 127 (d) none of these Q10. ( + )3 - ( )3 can be factorized as (a)2y(3 2 + 2 ) (b)2x(3 2 + 2 ) (c)2y(3 2 + 2 ) (d)2x( 2 + 3 2 ) Q11. If x+2 is a factor of 2 + mx + 14,then m = (a) 7 (b) 2 (c) 9 (d) 14 Q12. If x+1 is a factor of the polynomial 2 2 +kx, then k = (a) -2 (b) -3 (c) 4 (d) 2 Q13. The ordinate of any point on x-axis is (a) 0 (b) 1 (c) -1 (d) any number Q14.The perpendicular distance of the point P (4,3) from y-axis is (a) 4 (b) 3 (c) 5 (d) none of these Q15.Side BC of a triangle ABC h has been produced to a point such that ACD = 1200 1 If = 2 , then = (a) 800 (b) 75 (c) 60 (d) 90 Q16. An exterior angle of a triangle is 108 and its interior opposite angles are in ratio 4:5. The Angles of the triangles are (a) 48 , 60 ,72 (b) 50 ,60 ,70 (c) 52 ,56 , 72 (d)42 , 60 , 76 Q17. In a ABC, If AB=AC and BC produced to D such that ACD = 1000 then A = (a) 20 (b) 40 (c) 60 (d) 80 Q18. The sides of triangles are 7cm, 9cm, 14cm. Its area is (a) 12 5 cm2 (b) 12 3 cm2 (c) 24 5 cm2 (d) 63 cm2 Q19. The sides of triangles are 50cm, 78cm, 112cm. Its smallest altitude is (a) 20 cm (b) 30 cm (c) 40 cm (d) 50 cm Q 20. If every side of a triangle is doubled, then increase in area of triangle, is (a) 100 5 % (b) 200 % (c) 300 % (d ) 400 % Q 21. Diagonals of rhombus are Q22. Perpendicular bisector of chord always passes through ..of circle Q23. Volume of cube of side a is . Q24. Mode of 5,6,7,6,3,2,0,7,6,5 is. . Q25. Probability of atleast 2 head in tossing of two coins is .. Q26. Calculate mean of natural numbers from 1 to 10. Q27. Probability of even prime number in tossing of one die is? Q28. Ratio of surface area to the volume of a sphere is? Q29. Find Median of 1st ten even numbers. Q30. Find relation between slant height and radius of cone . Section B (Very Short Type) Q31. Prove that sum of angles of triangle is 1800 Q32. . Prove that when two lines intersect then vertically opposite angles are equal or .Prove that equal chords of circle are equidistant from centre of circle. Q33. Prove that in a triangle angle opposite to equal sides are equal. Q34. AD is an altitude of Isosceles triangle ABC in which AB=AC. Show that AD bisects BC And AD bisects A. Q35. Find area of triangle two sides of which are 18cm and 10cm and perimeter 42cm. Q36. The sides of triangle are in ratio 13:14:15 and its perimeter is 84cm. Find area of Triangle. Q 37. Two supplementary angles are in ratio 2 : 7, find angles Q 38. Angles of quad in ratio 2:3:4:5 find them. Q 39. Radius and height of cone are 3cm and 4cm respectively. Find surface area. Q40. Give examples of primary data and secondary data. Section C ( Short Type) 1 Q41. If of x2 + 2 = 79. Find the value (i) 1 1 3 + 3 ii) 3 3 Or 1 1 1 If ab + bc + ca = 0, find the value of 2 + 2 + 2 Q42. If a + b = 10 & a b = 16, find a2 a b + b2 and a2 + a b + b2 . Q43. Plot A(0,2), B(-2.5,0) and C(3.5,0) in graph and find area of triangle ABC. Q44. PQ ST, =1100 and = 1300, find S. P S T Q R Q45. . = 620 and = 540 . IF YO and ZO are the bisectors of and respectively of triangle XYZ, Find and . Q46. Prove that in triangle ABC, AB+BC > AC. A Q47. . In isosceles triangle ABC with AB=AC. D and E are points on BC such that BE=CD. Prove that AD= AE. B D E C Q48. A field is in shape of a trapezium whose parallel sides are 25m and 10m. The Non parallel sides are 14m and 13m. find area of field. ( Or The perimeter of Rhombus is 20 cm. One of its diagonal is 8 cm. Find area of Rhombus And length of the other diagonal. Q49. Two coins are tossed 500 times and the following data obtained. Number of heads Number of times 2 105 1 275 0 120 Find probability of getting (i) 2 heads (ii) 1 head (iii) no head. Or From a well shuffled deck of playing cards black king and red ace are removed. Find probability of (i) A king (ii) A black card (iii) A queen (iv) An ace of spade (v) A face card. Q 50. Show that the line segment joining the mid-points of opposite side of quadrilateral bisect each other. Or If non parallel sides of trapezium are equal, then prove that it is cyclic. . Q51. Construct angles of 75 ,135 , 15 and 105 Q52. Diameter of a roller is 84cm and its height is 120cm. It takes 500 complete revolutions to move once over to level a playground, Find the area of playground in m2. Q53. .Diameter of moon is approximately one-fourth of the diameter of earth. Find ratio of their surface areas. Also find ratio of their volumes. Or The radius of a spherical balloon increases from 7cm to 14 cm as air is being pumped into it. Find the ratio of the surface areas of the balloon in the two cases. . Q54. Prove th. at a median of a triangle divides it into two triangles of equal area. Or Prove that parallelogram on same base and between same parallel are equal in area. Section D ( Long Type) Q55. Represent 6.5 9.3 on number line and give justification. Q56. Expand (i) 2 + 2 2 .2 - 2 2 + 2 .2 ii) + + .2 Q57. Side QR of PQR is produced to S. If bisector of and meet at 1 T, then prove that = 2 . Q58. Two sides AB and AC of ABC are produced to P and Q respectively. The 1 Bisectors of PBC and QCB intersect at O, prove that BOC =900 - 2 Or 1 In a ABC, bisectors of ABC and ACB intersect at O, prove that BOC =900 + 2 Q59. Prove that two triangles are congruent if two angles and included side of One triangle are equal to two angles and included side of other triangle. Q60. In given figure AC=AE, AB=AD BAD = EAC , show that BC=DE E A B D C Q61. Given below are the seats won by different political parties in a poll. Draw bar graph. Political party Seats won A B C D E F 75 55 37 29 10 35 11-15 40 16-20 16 Q62 For given data construct frequency polygon. Number of letters 1-5 6-10 Number of surnames 6 30 21-25 4 Q63. Show that diagonals of square are equal and bisect each other at right angles Q64.The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Q65.Construct a triangle PQR in which PR-PQ= 2cm, QR =6cm and Q = 60 . Or Construct a PQR, such that QR = 8cm, Q = 30 and PQ PR= 3.5cm Q66.Twenty seven solid iron spheres, each of the radius r and surface area S are melted to form a sphere with surface area S . Find the: (I) Radius r of the new spheres (II) Ratio of S and S Q67.A dome of building is in the form of hemisphere. From inside it is whitewashed at the rate of Rs4 per square metre. If total cost of whitewashing is Rs 800. Find inner surface area and volume of air in dome. Q68.For given data construct histogram. Number of letters Number of surnames 1-4 6 4-6 30 6-8 44 8-12 16 12-20 4 Q69. Show that the line segment joining the mid-points of sides rectangle forms a rhombus . Q 70. Represent 5 3 on number line and give justification

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