7. Find the value of If (a+1) and (a-1) are the factors of p(a)= a 3 x+2a 2 +2a - y, find x and y

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1 AJANTA PUBLIC SCHOOL ASSIGNMENT (MATHS) SESSION CLASS - IX 1. Are the following Statements are True or False, also give reasons? (i) zero is a rational number (ii) Zero is natural number (iii) Every integer is a rational number 2. Write in simplest form Locate: - 2, 5 & 3 on Number line. 4. Write the 3 numbers whose decimal expansion is non-terminating and non-repeating. 5. Express the following in p/q form: (i) 0.06 (ii) (iii) Find the value of If (a+1) and (a-1) are the factors of p(a)= a 3 x+2a 2 +2a - y, find x and y Page 1 of 13

2 What must be subtracted from g(x)= x 3-6x 2 +x-2, so that result is exactly divisible by x Find the value of k, if x 1 is a factor of 4x 3 + 3x 2 4x + k. 15. Factorise x 3 23x x Simplify- (i) (X 3 Y 3 ) 3 + (Y 3 Z 3 ) 3 + (Z 3 X 3 ) 3 (ii) (a b) 3 + (b c) 3 + (c a) In which quadrants do the following points lie? a) (x> 4, y < 0) b) (x=0, y< 8) c) (x> 7, y < 0) d) (x< 0, y = 5) e) (x = 0, y=0) 20. Plot the points (5,5), (5,-3) and (-5,-3). Join them to find the figure. 21. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. 22. Give the equations of two lines passing through (2, 14). How many more such lines are there, and why? 23. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a. 24. See the figure and fill the following: Page 2 of 13

3 If the point (3, -- 4) lies on the graph of equation -y=ax+9. Find the value of a The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph. Page 3 of 13

4 31. Draw the graph of the linear equation 2x-3y=6. Shade the region enclosed in between the line of 2x 3y = 6, x-axis & y- axis, also find the area of figure so obtained Show that BC = DE. From the given figure: 34. Show that from given below figure: Page 4 of 13

5 BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles. 39. The sum of two sides of triangle is greater than third side, prove it. With the help of above theorem also show that : AB +BC +CA <2(OA + OB + OC) Page 5 of 13

6 40. D is a point on side BC of ABC such that AD=AC. Show that AC<AB. 41. Parallelograms on the same base and between the same parallels are equal in area PROVE IT P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC). 44. In the given figure ABCDE is a pentagon. A line through B Parallel to AC meets DC produced at F. Show that- a) area ( ACB = area( ACF) b) ar (AEDF)=ar (ABCDE) 45. Page 6 of 13

7 46. Show that a median of a triangle divides it into two triangles of equal areas. 47. XY is a line parallel to side BC of a triangle ABC. If BE AC and CF AB meet XY at E and F respectively, show that ar (ABE) = ar (ACF) 48. Equal chords of a circle subtend equal angles at the Centre. 49. If the angles subtended by the chords of a circle at the center are equal, then the chords are equal. 50. If a line intersects two concentric circles with centre O at A, B, C and D, prove that AB = CD 51. AND ALSO SHOW THAT PQR OPR = If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. 53. If the non-parallel sides of a trapezium are equal, prove that it is cyclic. Page 7 of 13

8 Prove that a cyclic parallelogram is a rectangle Chapter 11 Construction Page 8 of 13

9 58. A traffic signal board, indicating SCHOOL AHEAD, is an equilateral triangle with side a. Find the area of the signal board, using Heron s formula. If its perimeter is 180 cm, what will be the area of the signal board? 59. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm. 60. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area. 61. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle. 62. P and Q are two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar ( APB) = ar( BQC). 63. Prove that the angle subtended by an arc at the center is double the angles subtend by it at any point on the remaining circle. 64. Find x in the given figure 65. A triangle and a parallelogram have a same base and same area. If the sides of the triangle are 26cm, 28cm and 30cm and the parallelogram stands on the base 28cm, find the height of the parallelogram 66. Find the percentage increase in perimeter of an equilateral triangle, if its each side is tripled. 67. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field. 68. If the volume of cube is 243a 3, then find its total surface area. 69. The height of a cylinder is 15cm, if its curved surface area is 660cm 2, find its volume. 70. Find surface area of sphere of radius 5.6cm. Page 9 of 13

10 71. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per m2 is Rs 15000, find the height of the hall. 73. The paint in a certain container is sufficient to paint an area equal to m2. How many bricks of dimensions 22.5 cm 10 cm 7.5 cm can be painted out of this container? 74. The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find (i) its inner curved surface area, (ii)the cost of plastering this curved surface at the rate of Rs 40 per m Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.(iii) Volume of cone 76. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7cm. If the bowl is filled with soup to a height of 4cm. How much soup the hospital must prepare daily to serve 250 patients. If the cost of soup is not added in the bills of patients, then which value you depict about the hospital management? 77. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14). 78. A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl. 79. The capacity of a cuboidal tank is litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m. 80. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m 15 m 6 m. For how many days will the water of this tank last? 81. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it? 82. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite. 83. The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3? 84. Page 10 of 13

11 85. Draw the frequency polygon of above data. 86. An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table: Page 11 of 13

12 87. Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds which had germinated in each collection were counted and recorded as follows: 88. Eleven bags of wheat flour marked 5kg, contained the following weights of flour (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00 Find the probability that any of these bags chosen at random contains exact 5kg of flour. 89. Two coins are tossed simultaneously 200 times, with the following frequencies of different outcomes- OUTCOME 2 heads 1 head NO head FREQUENCY If the two coins are simultaneously tossed again, compute the probability of getting less than two tails. Exercise 14.4 Page 12 of 13

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