Test No. 5 Variation

S.S.C 30HRS ALGEBRA

OMTEX – CLASSES “THE HOME OF TEXT”

TIME – 2.

TEST – 75 MARKS

NAME OF THE STUDENT CHAPTER NAME

VARIATION

ROLL NUMBER

TEST NO. 5

Q1. Solve the following questions

(10 marks)

Q2. Solve the following questions

(15 marks)

Q3. Solve the following questions

(16 marks)

Q4. Solve the following questions

(9 marks)

1. Transform the following into mathematical statements. i. If the cookies in a tin are equally distributed among children, then the number (y) of cookies each child gets varies inversely as the number (x) of children. ii. Temperature remaining constant, the volume (v) of a compressed gas and its pressure (p) are inversely proportional to each other. iii. The potential difference remaining constant, the electric current (I) in a circuit is inversely proportional to resistance (R). 2. Transform the following into mathematical form. i. Cost of note books (c) and the number of notebooks (n), have direct variation between them. ii. The mass (m) of an iron block has direct variation with its volume (v). iii. The pressure (p) of a liquid is directly proportional to the depth (d) of the liquid. 3. The electric current (I) flowing through a circuit is directly proportional to the potential difference (V) in it. When the potential difference is 40 volts, the electric current is 1.2 amperes. Find the potential difference when the electric current is 1.5 amperes.

Q5. Solve the following questions

(25 marks)

1. The volume of a sphere and the cube of its diameter are in direct variation. Two solid spheres of diameters 4cm and 5cm were melted together and cast into a hollow sphere of diameter 6cm. Find the thickness of the outer cover of the sphere. 2. A tractor without any sugar bag in its trailer can run at the maximum speed of 20 km/hr. The speed is diminished by a quantity which varies directly as the square root of number of sugar bags kept in it. When 9 bags are kept in it, its maximum speed is 8 km/hr. Find the maximum number of sugar bags the tractor can carry. 3. A railway engine without a wagon can run with a maximum speed of 30 km / hr. Its diminished speed varies as the cube root of number of wagons attached. With 8 wagons, the engine runs at a maximum speed of 15 km/hr. Findthe maximum number of wagons that can be attached to the engine so that it can just run. 4. The volume of a sphere varies directly as the cube of its radius. Three solid spheres of radii 4.5cm, 6cm and 7.5cm were melted and cast into a big solid sphere. Find the radius of that sphere. 5. The distance through which a heavy body falls down from rest varies directly as the square of time for which it is falling. In 5 seconds an object covers a distance of 78.4 metres more than the distance covered by it in 3 seconds. Find the distance through which it will fall in 10 seconds.