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Solve the following pair of linear equations by the elimination method and the substitution method: (i) x + y = 5 and 2x – 3y = 4 (ii) 3x + 4y = 10 and 2x – 2y = 2 (iii) 3x – 5y – 4 = 0 and 9x = 2y + 7 (iv) x/2 + 2y/3 = -1 and x-y/3 = 3

(i) x + y = 5 and 2x – 3y = 4 Solving by elimination method x + y = 5 ……………………………….. (i) 2x – 3y = 4 ……………………………..(ii) When the equation (i)... View Article

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: 1 6 2 3 5 12 5 8 4 8 10 3 4 12 2 8 15 1 17 6 3 2 8 5 9 6 8 7 14 12 (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?

Solution Grouped frequency distribution table with class width 5. The data is represented in the grouped frequency distribution is tabulated... View Article

(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North – South direction and another in the East – West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North – South direction and 5th in the East – West direction meet at some crossing, then we will call this cross-street (2, 5) . Using this convention, find: (i) how many cross – streets can be referred to as (4, 3) . (ii) how many cross – streets can be referred to as (3, 4) .

Draw two perpendicular lines that will be considered as the two main roads, mark them as N-S and E-W. Considering the scale as 1 cm = 200 m as... View Article

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminum sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Given Height of cylinder = 12–4 = 8 cm Radius = 1.5 cm Height of cone = 2 cm Find out We have to find out the volume of air contained in... View Article