The distance (in km) of 40 engineers from their residence to their place of work were found as follows :

Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation ?

A company manufactures car batteries of particular type. The life (in years) of 40 batteries was recorded as follows: Construct a grouped frequency distribution table with exclusive classes for this data, using class intervals of size 0.5 starting from the interval 2-2.5.

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

A company manufactures car batteries of a particular type. The lives in years) of 40 such batteries were recorded as follows: Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 - 2.5.

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: (i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10. (ii) How many children watched television for 15 or more hours a week ?

The heights of 50 students, measured to the nearest centimetres, have been found to be as follows: (i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165,165-170, etc. (ii) What can you conclude about their heights from the table ?

Let us now consider the following frequency distribution table which gives the weights of 38 students of a class : Convert the classes of above frequency distribution to continuous classes to include two new students weighing 35.5 kg and 40.5 kg.

Two blocks of mass m_(1)=10kg and m_(2)=5kg connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of the turntable. The coefficient of friction between the table and m_(1) is 0.5 while there is no friction between m_(2) and the table. the table is rotating with an angular velocity of 10rad//s . about a vertical axis passing through its center O . the masses are placed along the diameter of the table on either side of the center O such that the mass m_(1) is at a distance of 0.124m from O . the masses are observed to be at a rest with respect to an observed on the tuntable (g=9.8m//s^(2)) . (a) Calculate the friction on m_(1) (b) What should be the minimum angular speed of the turntable so that the masses will slip from this position? (c ) How should the masses be placed with the string remaining taut so that there is no friction on m_(1) .

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in figure. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms^(2) . At what distance from the starting point does the box fall off the truck ? (Ignore the size of the box)