Variation 2

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VARIATION Practice Exercise - 2 ___________________________________________________________________________________

Q-1.The area of a circle varies as the square of its radius. The area of a circle of radius 7 cm is 154 sq cm. Find the area of the circle of radius 14 cm. Q-2.The volume of a cube is in direct variation to the cube of its length. If the length is 1 cm, the volume is 1 cc. Find the volume, when the length is 2 cm and find the length if the volume is 64 cc. Q-3.If 10 persons complete a job work in 8 days, then how many days will 16 persons need to complete it? Q-4.At a fixed temperature, the volume of a gas varies inversely to its pressure. When the volume is 5 units, the pressure is 16 units. What will be the pressure, if the volume is 8 units? Q-5.The quantity of the grains is sufficient to last for 5 days for 10 persons. Suppose there are 25 persons, then how many days will the quantity last? If the quantity of grains should last for 12 days, find the maximum possible number of persons. Q-6.The thermal energy produced in a resistance is in direct variation to the square of the current passing through it and also to the time period for which the current passes through it. If the current of 3 ampere passes for 9 seconds, the energy produced is 486 units. For how much time the current of 1.5 ampere should be passed so that 108 units of energy is produced? Q-7.The volume of a cylinder is in direct variation to the square of the radius of its base and to its weight. When the radius is 7 cm and height is 12 cm, then the volume is 1848 cube cm. Find the volume when the radius is 3.5 cm and weight is 10 cm. Q-8.The speed of a vehicle is partly constant and partly varies according the square of the petrol consumed. When the speed is 40 units, the petrol consumed is 4 units and when the speed is 58 units, the petrol consumed is 5 units. Then find the speed if the petrol consumed is 7 units. Q-9.The life of an electric bulb is partly constant and partly varies inversely to its average hours of use. If the average use of the bulb is 10 hours, its life is 810 hours and if the average use is 20 hours, the life is 805 hours. Suppose we wish to have the life of the bulb to be 1000 hours, what should be the average use? Suppose we wish to have the life of the bulb to be 200 hours, what should be the average use.

Q-10.The period of oscillation of a pendulum varies as the square root of its length. The period of oscillation of a pendulum of length 36 cm is 1.2 seconds. Find the period of oscillation of a pendulum of length 100 cm and find the length of the pendulum if the period of oscillation is 1 second. Q-11.In an objective question paper, the marks obtained by a student are in direct variation to the number of correct answer given by him. If one gets 15 marks for 5 correct answers, how many marks would 7 correct answers fetch? If a student gets 36 marks, how many of his answers are correct? Can a student get 35 marks? Q-12.A rod of length l1 is at a temperature T1. On being heated to temperature T2, the length increases to l2. The extension l2 - l1 in the length is in compound variation as the initial length l1 and the increase in temperature T2 - T1 in the temperature. The constant of variation for the increase in length of the metal sheet is 12 x 10 -6. If the temperature rises from 100 C in winter to 400 C in summer, find the increase in the length of a 2000 km long rail track. Q-13.The monthly salary of an employee partially varies directly as the number of years of service put in by him and is partially constant. After 5 years of service, his salary is Rs. 4325 and after 8 years of services, the salary is Rs. 4700. Find the number of years of services put in by him, when his salary is Rs. 5700. Q-14.At a given temperature, the volume of a given quantity of a gas and the pressure on it are in inverse variation. The volume of a certain quantity of a gas is 1000 cc under 2 units atmospheric pressure. Find the volume of the gas when there is 5 units atmospheric pressure on it. Q-15.The cost of printing a book is partially constant and partially varies directly as the number of copies printed. If the printing of 100 copies costs Rs. 1000 and that of 200 copies costs Rs. 1800, find the cost of printing 400 copies. Q-16.The weight of a sphere varies jointly as the cube of its radius and its density. The ratio of the radii of two spheres is 5:3 and the ratio of their respective densities is 2:5. If the weight of the second sphere is 108 gms, find the weight of the first sphere. Q-17.A railway engine can run at a speed of 96 km / hr without carriage. When carriages are joined the speed reduces. The reduction in the speed varies directly as the square root of the number of carriages joined. When 16 carriages are joined, the speed reduces to half. What will be the maximum number of carriages that can be pulled by the engine? Q-18.The resistance obstructing the speed of a train is partly constant and partly varies as the square of its speed. The resistance is 27 kg when the speed is 30 km / hr and the resistance is 41 kg when the speed is 40 km / hr. Find the resistance when the speed is 50 km / hr. Q-19.The area of a triangle varies directly as its base when the altitude is constant and varies directly as its altitude when the base is constant. For a triangle, the base is

6 cm, the altitude is 5 cm and the area is 15 sq. cm. Find the area of a triangle if its base is 18 cm and its altitude is 16 cm. Q-20.The value of a diamond varies directly as the square of its weight. If a diamond of value Rs 10,000 is divided into two pieces whose ratio of weights is 3 : 7, find the decrease in its value. ********** *****************