IX M SAII WORK ENERGY SURFACE AREA

            

1.     [1]A cycle together with its rider weighs 100 kg. How much work is needed to set it moving at 3 m/s?

2.       [1]What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

3.       [1]A man performs 270 J of work in 9 s. Calculate the power.

4.       [1]Calculate the speed of a body of mass 20 g having a kinetic energy of 10 J.

5.       [1]Convert 1kWh into joules.

6.       [1]How much work is done at the rate of 40 W in 40 s?

7.       [2]A 1000-W heater is used for 2 hour every day for 30 days. Find the cost of electricity if the rate is Rs 8.00/unit.

8.       [2]A body of mass 25 g has a momentum of 0.40 kg m/s. Find its kinetic energy.

9.       [2]Find the expression for the gravitational potential energy of a body of mass m at a height h.

10.   [2]Find the expression for kinetic energy of a body of mass m moving at a speed v.

11.   [2]A boy of mass 50 kg runs up a staircase of 25 steps in 10 s. If the height of each step is 15 cm, find his power. Take g = 10 m s^–2.

12.   [2]Calculate the work required to be done to stop a car of 1200 kg moving at a velocity of 60 km/h?

13.   [2]What is the work to be done to increase the velocity of a car from 2m/s to 5 m/s if the mass of the car is 2000 kg?

14.   [3]Harish has built a cubical water tank wit lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is Rs 600 per dozen.

15.   [3]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.

16.   [3]A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i) What is the area of the glass?

(ii) How much of tape is needed for all the 12 edges?

17.   [3]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?

18.   [3]A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

IX M SAII BASIC TEST (VOLUME & SURFACE AREAS)

                                           TEST-IX (VOLUME & SURFACE AREAS)                                          

Q1.      A joker¢s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps?

Q2.      A sphere is tightly enclosed in a cylinder. Find ratio of curved surface area of cylinder to sphere?

Q3.      A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the   volume of the solid so obtained?                                           

SECTION-B (3 MARKS QUESTIONS)

Q4.      Monica has a piece of canvas whose area is 551 m². She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approx. 1 m², find the volume of the tent that can be made with it.

Q5.      Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S¢. Find the:        (i) radius r¢ of the new sphere,                   (ii) ratio of S and S¢.

Q6.   The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m² ?

Q7.      Three solid spheres of iron whose diameters are 2 cm, 12 cm and 16 cm, respectively, are melted into a single solid sphere. Find the radius of the solid sphere.

SECTION-C (4 MARKS QUESTIONS)

Q8.      A small indoor greenhouse is made entirely of glass panes held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.      (i) What is the area of the glass?

(ii) How much of tape is needed for all the 12 edges?

Q9.      The dimensions of a rectangular box are in the ratio 2 : 3: 4 and the difference between the cost of covering it with sheet of paper at the rate of Rs. 4 and Rs. 4.50 per square metre is Rs. 416. Find the dimensions of the box.

Q10.  The difference between outside and inside surfaces of a cylindrical metallic pipe 14 cm long is 44 cm². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe ?                                              

IX M SAII STATISTICS TEST

Q 1.     (2)The class marks of a distribution are 105, 115, 125, 135, 145. Find class size and class limits.                                                                                                                                                       

Q 2.    (2) The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.                 

         29, 32, 48, 50, x, x + 2, 72, 78, 84, 95                                                                                           

Q 3.   Find  mean & mode of the following data:                                                                                                

Marks	10	20	30	40	50	60	70
Number of students	7	9	10	18	22	16	8

Q 4.     (3)If mean of observations  is 9, find mean of last 3 observations.                  

Q 5.    (3)The mean of a data is 64. Find the new mean if  each of the observation of a data is

  (a) increased by 2   (b) decreased by 3         (c) multiplied by 0.25                                                   

Q 6.    (4)  Draw a histogram for marks of students given below:                                                                             

Marks                        0 – 10           10 – 30               30 – 45              45 – 50        50 – 60

No of students            8                      32                     18                        10              6                            

Q 7.    (4)Construct a frequency polygon for following data without using histogram:                                 

Income (in Rs)                            No. of workers

  60 – 90                                          12

 90 – 120                                         14

120 – 150                                        18

150 – 180                                        10

180 – 210                                        9

210 – 240                                       4                                                                                    

Q 8. (4)If mean of the following data is 20.6 and and total observation is 50 , find missing frequencies:                       

                      x               10        15        20        25        35

                     f                 3          f₁        25         f₂          5                                                                                               

Q 9.     (4) The marks obtained by 40 students of class IX are

18, 8, 12, 6, 8, 16, 12, 5, 23, 2, 10, 20, 12, 9, 7, 6, 5, 3, 5, 13, 21, 13, 15, 20, 24, 1, 7, 21, 16, 13, 18, 23, 7, 3, 18, 17, 16, 16, 23, 2.                                                                                                               

(i)                 Construct a frequency distribution table with one class being 15 – 20.

(ii)               Also construct a cumulative frequency distribution of more than type.                                                                                                                                                                                 )

IX SAII MATHS STATISTICS ASSIGNMENT

1.       The relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1	98.6	99.2	90.3	86.5	95.3	92.9	96.3	94.2	95.1
89.2	92.3	97.1	93.5	92.7	95.1	97.2	93.3	95.2	97.3
96.2	92.1	84.9	90.2	95.7	98.3	97.3	96.1	92.1	89

                (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc.

                (ii) Which month or season do you think this data is about?

                (iii) What is the range of this data?

2.       100 surnames were randomly picked up from a local telephone directory and a frequency             distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters	1 - 4	4 - 6	6 - 8	8 - 12	12 - 20
Number of surnames	6	30	44	16	4

                (i) Draw a histogram to depict the given information.

                (ii) Write the class interval in which the maximum number of surnames lie.

3.       The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:                      

Length (in mm)	118 - 126	127 - 135	136 - 144	145 - 153	154 - 162	163 - 171	172 - 180
Number of leaves	3	5	9	12	5	4	2

                (i) Draw a histogram to represent the given data.

                (ii)Also represent by a polygon ( Separately )

                (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

4.       Find out mean, mode  ( Calculate).

Marks	10	20	30	40	50	60	70
Number of students	7	10	10	17	23	15	8

5.       Find the value of p if mean is 7.5

Marks	3	5	7	9	11	13
Number of students	6	8	15	p	8	4

6.       Find the value of  ‘m’ and ‘n’  if mean is 50 and total observations are 90.

Class Marks	10	30	50	70	90
Number of students	17	m	32	n	19

7.       Find median of 

20,26,8,18,24,18,46,23,62,55,70,44

8.       The class mark for a certain continuous frequency distribution are . find class intervals and draw hisrogram.

Class Marks	6	12	18	24	30
Number of students	12	15	20	9	16

9.       The mean of a data is 46. Find the new mean if  each of the observation of a data is

(a) increased by 3   (b) decreased by 2         (c) multiplied by 0.5

10.   Find less than and more than cumulative frequency.

Number of letters	0 - 4	4 - 8	8 - 12	12 - 16	16 - 20
Number of surnames	6	17	23	13	11